Interfacing cold atoms with nanophotonic systems
Significant efforts have been made to interface cold atoms with micro- and nano-photonic systems in recent years. Originally, it was envisioned that the migration to these systems from free-space atomic ensemble or macroscopic cavity QED experiments could dramatically improve figures of merit and facilitate scalability. However, a more interesting question is whether nanophotonic systems can yield intrinsically new capabilities to manipulate quantum light-matter interactions, such as by exploiting the ability to engineer the dimensionality and optical dispersion relations. Here, we discuss two examples of fundamentally new possibilities. The first involves the engineering of quantum vacuum ("Casimir") forces in the vicinity of dielectric structures. We show that these forces can be used to create stable atomic traps within 10 nm distances of dielectric surfaces, with parameters (such as depth) beyond what is achievable with conventional trapping techniques. The second example exploits the tailoring of dispersion relations to enable the formation of exotic atom-photon "bound states," in which atoms become dressed with photonic clouds of a controllable size. We show that this effect allows one to realize and control long-range atomic interactions mediated by the photonic clouds, providing a powerful new tool for quantum simulation with cold atoms.

Tensor Networks and efficient description of many-body quantum systems
Many body quantum systems are very hard to describe due to the exponential increase of parameters with the number of constituents. Tensor network states and, in particular, projected entangled-pair states (PEPS), provide an alternative method to describe such systems. I think this talk I will show how all thermal states of local Hamiltonians at any finite temperature can be efficently described in terms of PEPS. I will also explain some of the consequences of this result.

Bands with a twist and quantum sized steps
We use fermionic quantum gases to study the topological Haldane model in an optical lattice and the quantized conductance in an optically engineered quantum point contact for atoms. The Haldane model on the honeycomb lattice features topologically distinct phases of matter and describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band-structure, rather than being caused by an external magnetic field. In our experiment we have realized the Haldane model in a periodically modulated honeycomb lattice and characterized its topological band-structure. Our approach allows for dynamically tuning topological properties and is even suitable for interacting fermions. In transport experiments the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps, with a size determined solely by Planck's constant h. I will report on our observation of quantized conductance in the transport of neutral atoms. In our isolated atom device we enter a new regime for this fundamental phenomenon, which has so far not been observed with neutral matter.

Antiferromagnetism and Fragmentation in Spin 1 Bose-Einstein Condensates
In this talk, I discuss the magnetic properties of ultracold bosons with antiferromagnetic interactions. Antiferromagnetic interactions results in this system in an unusual kind of magnetic ordering called spin-nematic ordering, where the order parameter has the symmetry of an ellipsoid as in nematic liquid crystals. I will show how this order can be detected directly by driving coherent Rabi oscillations and looking at the magnetization statistics, and how it affects the magnetic phase diagram at very low temperatures. I will finally discuss in details the behavior of the system for small magnetic fields and magnetizations, where anomalously large fluctuations are observed. We show they can be explained by collective spin fluctuations (fluctuations in the direction of the spin-nematic order parameter), that would vanish in the thermodynamic limit but are important due to the small size (atom number~few thousands) of the samples we study. This illustrates on a particular example how collective fluctuations in small systems are effective to restore a broken symmetry (here spin rotational symmetry).

Asymptotic behavior of subradiant states in homonuclear diatomic molecules
Weakly bound molecules have physical properties that do not have atomic analogues, even as the bond length approaches the dissociation limit. The internal symmetries of homonuclear diatomic molecules result in the formation of two-body superradiant and subradiant excited states. While superradiance has been theoretically predicted and experimentally observed in many molecular systems, subradiance is challenging to explore due to the inherently weak matter-light interaction. Optical transition moments that are strictly forbidden for atoms become allowed just below the dissociation asymptote due to the new molecular selection rules associated with the subradiant states. In my talk I will report a joint theoretical/experimental study of the subradiant states in ultracold diatomic strontium molecules and characterize their properties near the intercombination atomic line by theoretical and experimental spectroscopy of doubly-forbidden transitions. This spectroscopy reveals very long molecular lifetimes and thus is a direct probe of subradiance. Two competing mechanisms contributing to the finite lifetimes of the subradiant molecules with different asymptotic behaviors are demonstrated. The first is the radiative decay that proceeds through the magnetic-dipole and electric-quadrupole interactions. Its rate increases quadratically with the bond length, a trend that is predicted by theory and observed in a high-precision experiment for the first time. The second is the nonradiative decay through the gyroscopic predissociation facilitated by the nonadiabatic coupling between the molecular states, with a rate that falls as the fourth power of the bond length. This work bridges the gap between atomic and molecular metrology based on lattice-clock techniques, yielding some of the most accurate understanding of the long-range interatomic interactions.

Flux lattices for periodically driven ultra-cold atoms
(Tomas Andrijauskas, Gediminas Juzeliunas)
We theoretically describe optical flux lattices produced for ultra-cold atoms by a periodic in time perturbation. First we give a general theoretical description of creating a geometric vector potential with gauge-dependent Aharonov-Bohm singularities in the flux lattices. We explain how these singularities lead to the non-staggered magnetic flux in each elementary cell. Subsequently we provide an example illustrating how a periodic driving of ultra-cold atoms with two internal states could create the square flux lattice.  In this example the energies of two internal states have opposite gradients in one spatial direction, while the driving consists of periodic in time pulses that couple the internal states and propagate in a perpendicular direction.  Such a time-depending perturbation effectively creates the square flux lattice with two gauge-dependent singularities over the elementary cell that do not compensate each other, leading to a non-staggered magnetic flux.

Control of cold atoms in optical lattices with magnetic pulses - the magnetic shaking
(Egidijus Anisimovas, Brandon Anderson, Gediminas Juzeliunas, and Andre Eckardt)
Cold atomic gases trapped in optical lattices offer an unprecedented level of control over quantum matter. One of the key ingredients in this control is the ability to create synthetic gauge fields that affect neutral atoms. Recently, lattice shaking was proposed as a universal and very successful method to generate tunable gauge potentials. In the present contribution, we will discuss a natural extension to include the spin degree of freedom. Our method, which can be referred to as the magnetic shaking, gives access to creation of non-Abelian Peierls phases. We demonstrate how specific model Hamiltonians featuring spin-orbit coupling on a lattice can be produced. In particular, a simple protocol leading to realization of Chern insulator with a large band gap and the Chern index equal to two on a triangular lattice will be presented.

Breathing modes of one-dimensional trapped BEC
(G. E. Astrakharchik, Andrii Gudyma, Mikhail Zvonarev )
One-dimensional ultracold atomic gas of bosons is studied. Frequencies of low-lying excitations are calculated for the parameters of the model relevant for the recent experiment from Innsbruck group [Science 325, 1224 (2009)]. Perturbative methods are combined with the exact Bethe Ansatz solution for the model. Analysis of results are made for both the weak coupling and the Tonks-Girerdeau regimes. Analytical calculations are complement with the results from the quantum Monte Carlo simulations. On the example of the two-particle system compared different methods of calculation of the breathing mode. Theoretical results confronted with data from experiment.

Faraday Waves in Collisionally Inhomogeneous Bose-Einstein Condensates
(Antun Balaz, Remus Paun, Alexandru I. Nicolin, Sudharsan Balasubramanian, and Radha Ramaswamy)
We will study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement [1]. Considering a Gaussian-shaped radially inhomogeneous scattering length, we will show through numerical simulations and variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scattering lengths, the radial profile of the condensate is akin to that of a hollow cylinder, while in the weakly inhomogeneous case the condensate is cigar-shaped and has a Thomas-Fermi radial density profile. Finally, we will show that when the frequency of the modulation is close to the radial frequency of the trap, the condensate exhibits resonant waves which are accompanied by a clear excitation of collective modes, while for frequencies close to twice that of the radial frequency of the trap, the observed Faraday waves set in forcefully and quickly destabilize condensates with weakly inhomogeneous two-body interactions. [1] A. Balaz, R. Paun, A. I. Nicolin, S. Balasubramanian, and R. Ramaswamy, Phys. Rev. A 89, 023609 (2014).

Ground-state entanglement of spin-1 bosons undergoing superexchange interactions in optical superlattices
(A. Barasinski, W. Leonski, T. Sowinski)
We discuss a model with ultra-cold atoms confined in optical superlattices. In particular, we study the ground-state properties of our system. Applying model involving spin-1 bosons trapped in a double-well potential, we quantify the bipartite entanglement between particles. Depending on the external magnetic field and biquadratic interactions different phases of magnetic order are realized and hence, various phases of the system's entanglement. We show that changing the values of the parameters determining superlattices, we can switch the system between differently entangled states. What is important, our model seems to be a good candidate for practical realization of the device which can be a switchable tool for generation on demand of various maximally entangled states. [1] A. Barasinski, W. Leonski, T. Sowinski, J. Opt. Soc. Am. B 31, 1845 (2014).

Manipulation of ultracold atoms in novel optical superlattices
(M. G. Bason, R. Muller, N. B. Jørgensen, R. Heck, A. Thorsen, W. Zhang, J. Arlt and J. F. Sherson)
The purity and controllability of ultracold atoms in optical lattices has greatly benefited many-body physics [1]. The long coherence times of atoms in such systems also makes them suitable candidates for performing quantum computation. To this end, steps towards implementing a collision-based two-qubit gate in optical lattices have previously been realized by the parallel merging of all pairs of atoms in a periodicity two superlattice [2]. I will present an architecture which allows for the merger of a selected qubit pair in a long-periodicity superlattice structure consisting of two optical lattices with close-lying periodicity [3]. This superlattice architecture also induces a differential hyperfine shift, allowing for single-qubit gates. With the goal of informing the construction of our experimental apparatus, the fastest possible single- and two-qubit gate times, given a maximal tolerable rotation error on the remaining atoms at various values of the lattice wavelengths, are identified. We find that robust single- and two-qubit gates with gate times of a few hundred microseconds and with error probabilities of around 0.001 are possible. Having established a range of experimental parameters, I will discuss how one may further use superlattice structures for atomtronics [4], and for the investigation and manipulation of quantum phase diagrams using non-destructive measurements. I will conclude by reporting on our progress towards these goals. [1] I. Bloch, J. Dalibard, and S. Nascimbene, Nature Physics 8, 267 (2012). [2] M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, W. D. Phillips, and J. V. Porto, Nature 448, 452 (2007). [3] Nils B. Jørgensen, Mark G. Bason, and Jacob F. Sherson PRA. 89, 032306 (2014). [4] Malte C. Tichy, Mads K. Pedersen, Klaus Mølmer, and Jacob F. Sherson, PRA 87, 063422 (2013).

An ultra stable laser for orbital magnetism simulations with ultra-cold Ytterbium atoms
(Quentin Beaufils, Alexandre Dareau, Matthias Scholl, Jérôme Beugnon, Fabrice Gerbier)
Orbital magnetism is at the origin of quantum Hall effect, which appears in two dimension electron gases under a strong magnetic field. We plan to simulate such a system with ultra cold quantum gases of neutral ytterbium atoms in an optical lattice. Laser assisted tuneling in the lattice will allow us to impose a phase to the atomic wave function that is similar to the Aharonov-Bohm phase associated to the magnetic vector potential for charged particles. I will present the latest progress of the experiment. In particular we developed an ultra stable laser source resonant with the clock frequency of ytterbium for driving coherent laser assisted tuneling.

Interferometry with interacting Bose-Einstein condensates
(T. Berrada, S. van Frank, R. Bücker, T. Schumm, J.-F. Schaff and J. Schmiedmayer)
We have implemented a full Mach-Zehnder interferometric sequence with trapped atomic Bose-Einstein condensates (BEC) confined on an atom chip [1]. Particle interactions in our BEC matter waves lead to an intrinsic non-linearity, absent in photon optics. We exploit these interactions to generate a non-classical state with reduced number fluctuations as an input to the interferometer. Making use of spatially separated wave packets in a double-well potential, a controlled phase shift is applied. To read out this phase shift, we have developed a new recombiner for BECs that relies on a non-adiabatic transformation of the confining potential in order to transform the accumulated phase into an atom number difference between the two output ports. We demonstrate how the use of a number-squeezed state reduces the phase diffusion due to atomic interactions, and observe coherence times a factor of three beyond what is expected for a classical coherent state, highlighting the potential of non-classical states as a resource for metrology. [1] T. Berrada, S. van Frank, R. Bücker, T. Schumm, J.-F. Schaff and J. Schmiedmayer, Nature Communications, 4:2077 (2013)

Life cycle of supefluid vortices in the unitary Fermi gas
(A. Bulgac, M.M. Forbes, K.J. Roche, and G. Wlazlowski)
The unitary Fermi gas is the only other system (apart from dilute Bose gas described by Gross-Pitaevskii equation) for which a well founded microscopic theory of the dynamics exist. In this talk I will tell the tale of a superfluid soliton. Starting its life as a phase imprinted domain wall in cold cloud of 6Li at MIT [1], it behaved mysteriously, moving an order of magnitude more slowly than expected. Using some of the largest computer simulations, we demonstrated [2] that the wall is rapidly promoted to a vortex ring that explains almost all aspects of the experiment, including some subtle effects due to the imaging process. Improved observations [3] reveal that the soliton is a vortex - the early retirement of the vortex ring induced by asymmetries present in the trap - and suggests that these experiments may provide an excellent forum for studying the microscopic nature of vortex crossing and recombination processes that are at the heart of quantum turbulence. The agreement between experiment and simulation [3, 4] validates the superfluid density functional theory (DFT), paving the road to understanding complex superfluid dynamics in cold atoms, nuclear matter, and neutron stars. [1] Yefsah et al., Nature 499, 426 (2013) [arXiv:1302.4736]. [2] Bulgac, Forbes, et al, PRL 112, 025301 (2014) [arXiv:1306.4266]. [3] Ku et al. (2014) [arXiv:1402.7052]. [4] Wlazlowski, Bulgac, Forbes, Roche, arXiv:1404.1038

Synthetic gauge fields in synthetic dimensions & further developments
(A.Celi, P.Massignan, N.Goldman, J.Ruseckas, G.Juzeliunas,I.B. Spielman, M.Lewenstein)
After introducing the concept of extradimension, i.e. the encoding some of the spatial degrees of freedom as internal states of cold atoms, I will show how it offers the possibility of simulating: i) 4d Hubbard models; ii) artificial gauge fields in synthetic 2d lattices; iii) lattices on surfaces with non-trivial topology. I will discuss which are interesting observable characterizing the three families of quantum simulators and describe recent experimental progresses to their realization.

Optimal persistent currents for bosons on a ring with a gauge field
(Marco Cominotti, Davide Rossini, Matteo Rizzi, Frank Hekking, Anna Minguzzi)
Quantum gases are realized by advanced techniques of atom trapping and cooling, and constitute a versatile, tunable system for the exploration of extreme states of matter, in the regime where quantum mechanics plays a fundamental role. After many astonishing advances in this field, nowadays quantum gases are also regarded in a new light, as a playground to realize quantum devices for quantum computation and atomtronics. In this direction, a lot of experimental effort has been recently devoted to the realization of a novel generation of traps with ring topology. This geometry is particularly suitable for the study of superfluidity and current states. In the limit of a very tight (quasi)-1D trap, we have studied persistent currents for interacting bosons, subjected to a rotating barrier potential, which induces an artificial U(1) gauge field. Applying several methods, suitable for different regimes of interparticle interaction strengths, we are able to unveil a subtle interplay of effects due to the barrier, the interactions and quantum fluctuations. In particular, we show that at intermediate interactions the persistent current response is maximal. These results are relevant for ongoing experiments aiming at the realization of macroscopic superpositions of current-carrying states.

Spectroscopy of environmental noise via measurement of decoherence of qubits
(Lukasz Cywinski)
When a qubit is driven by a sequence of N dynamical decoupling pulses, the measurement of its coherence at different times and different values of N can be used to reconstruct the spectral density of environmental noise that is affecting the qubit. In the case of linear coupling to Gaussian noise the relation between the coherence and the noise spectrum is very simple, and it has been succesfully used to perform noise spectroscopy in many recent experiments [1]. On the other hand, the case of quadratic coupling to Gaussian noise, which is relevant for a qubit at an optimal working point, is much more nontrivial theoretically. A solution [2] allowing for reconstruction of noise spectrum in this case will be given. Furthermore, the possibility of using entangled states of spatially separated qubits for spectroscopy of noise correlation spectrum will be discussed. [1] J. Bylander et al., Nat. Phys. 7, 565 (2011); J. Medford et al., Phys. Rev. Lett. 108, 086802 (2012); J. T. Muhonen et al., arXiv:1402.7140 (2014); Y. Romach et al., arXiv:1404.3879 (2014). [2] L. Cywinski, arXiv:1308.3102 (2013).

Grassmann Phase Space Theory for Fermions
(B J Dalton, J Jeffers, S M Barnett)
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables [1] to represent these operators. However, in spite of the seminal work by Cahill and Glauber [2] and a few applications [3, 4], the use of Grassmann phase space methods in quantum - atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. The theory of Grassmann phase space methods for fermions is developed, showing how the distribution function is defined and used to determine quantum correlation functions, Fock state populations and coherences via Grassmann phase space integrals, how the Fokker-Planck equations are obtained and then converted into equivalent Ito equations for stochastic Grassmann variables. The number of c-number Wiener increments involved is 2n^2, if there are n modes. The situation is somewhat different to the bosonic c-number case where only 2n Wiener increments are involved, the sign for the drift term in the Ito equation is reversed and the diffusion matrix in the Fokker-Planck equation is anti-symmetric rather than symmetric. The un-normalised B distribution [3, 5] is of particular importance for determining Fock state populations and coherences, and as pointed out in [3], the drift vector in its Fokker-Planck equation only depends linearly on the Grassmann variables. Using this key feature we show how the Ito stochastic equations can be solved numerically for finite times in terms of c-number stochastic quantities. Averages of products of Grassmann stochastic variables at the initial time are also involved, but these are determined from the initial conditions for the quantum state. The problem of carrying out numerical calculations for Grassmann phase space theories of fermion systems is now solved. As a simple test case we apply the B distribution theory and solve the Ito stochastic equations to demonstrate Cooper pairing in a four mode fermionic system involving spin conserving interactions between the spin 1/2 fermions, where modes with momenta −k, +k - each associated with spin up, spin down states, are involved. The theory has been extended to the situation where fermion field operators are involved. Here Grassmann fields, distribution functionals, functional Fokker-Planck equations and Ito stochastic field equations are involved [5]. [1] F. A. Berezin, The Method of Second Quantization (Academic Press, New York, 1966). [2] K. E. Cahill and R. J. Glauber, Phys. Rev. A 59, 1538, 1999. [3] L. Plimak, M. J. Collett & M. K. Olsen, Phys. Rev. A 64, 063409, 2001. [4] B. J. Dalton, B.M. Garraway, J. Jeffers & S. M. Barnett, Ann. Phys. 334, 100, 2013. [5] B. J. Dalton, J. Jeffers & S. M. Barnett, Phase Space Methods for Degenerate Quantum Gases, (Oxford University Press, Oxford, - Expected Publication 2015).

Exact preparation of many-body ground states in an Ising chain
(Bogdan Damski, Adolfo del Campo)
We will discuss in this talk an exact driving protocol allowing for a dynamical preparation of a ground state of an Ising chain in an arbitrary external transverse field. This is possible through a proper modification of the Ising Hamiltonian. Such a modification was recently proposed [del Campo et al., Phys. Rev. Lett. 109, 115703 (2012)]. We will show how one can analytically obtain exact closed-form expressions for several coefficients of such a modified Hamiltonian.

Quantum work distribution in many-body systems
(G. De Chiara)
I will talk about the latest development in quantum thermodynamics regarding the full distribution of work done on a quantum many-body system embodied by chains of harmonic oscillators or spins. I first consider a chain of harmonic oscillators initially uncoupled and in thermal equilibrium. The work done on the system to raise the coupling to a non-zero value is computed. I will discuss the relation between the irreversible work produced and quantum correlations, e.g. entanglement and discord [1]. For a system close to a quantum phase transition, showcased by the 1D transverse Ising model, I will show signatures of criticality in the statistical moments of work and in its characteristic function [2]. [1] A. Carlisle, L. Mazzola, M. Campisi, J. Goold, F. L. Semião, A. Ferraro, F. Plastina, V. Vedral, G. De Chiara, M. Paternostro, arXiv:1403.0629 [2] L. Fusco, S. Pigeon, T. Apollaro, A. Xuereb, L. Mazzola, M. Campisi, A. Ferraro, M. Paternostro, and G. De Chiara (in preparation).

The detection and simulation of spontaneous many-body objects such as solitons in ultracold gases
(Piotr Deuar)
Inherently many-body excitations such as superfluid solitons and vortices are an intriguing class of collective excitations, particularly when they form spontaneously. They are then invisible or unrecognisable to standard experimental techniques such as ensemble averaged images, spectral measurements, or two-particle and other low-order correlation functions. As such, they pose a serious and tantalising challenge for both experimental detection and theoretical simulation. Their observation and analysis demand consideration of the behaviour of single realisations. I will describe how solitons can be detected in single realisations by phase-contrast imaging, and how their behaviour can be simulated with c-field methods. I will also give some details regarding how a meaningful comparison between experiment and theory can then be made.

Dynamics of the Mott-superfluid transition in the Bose-Hubbard model
(J. Dziarmaga)
I will briefly review recent theoretical and experimental progress on the dynamics of the quantum phase transition from Mott insulator to superfluid in a system of ultracold atoms described by the Bose-Hubbard model. This phenomenon is expected to be described by the quantum version of the Kibble-Zurek mechanism, but experimental limitations and/or thevery nature of the Kosterlitz-Thouless transition in the 1D case make the interpretation of experimental results less than straightforward.

A waveguide frequency converter connecting rubidium-based quantum memories to the telecom C-band
(Boris Albrecht, Pau Farrera, Xavier Fernandez-Gonzalvo, Matteo Cristiani and Hugues de Riedmatten)
Coherently converting the frequency and temporal waveform of single and entangled photons will be crucial to interconnect the various elements of future quantum information networks. Of particular importance is the quantum frequency conversion of photons emitted by material systems able to store quantum information, so-called quantum memories. There have been significant efforts to implement quantum frequency conversion using nonlinear crystals, with non-classical light from broadband photon-pair sources and solid-state emitters. However, solid state quantum frequency conversion has not yet been achieved with long-lived optical quantum memories. Here we demonstrate an ultra-low-noise solid state photonic quantum interface suitable for connecting quantum memories based on atomic ensembles to the telecommunication fibre network. The interface is based on an integrated-waveguide nonlinear device. We convert heralded single photons at 780 nm from a rubidium-based quantum memory to the telecommunication wavelength of 1,552 nm, showing significant non-classical correlations between the converted photon and the heralding signal.

Quantum Interferometry with trapped BEC with tunable interaction
(A. Trenkwalder, M. Landini, G. Spagnolli, G. Colzi, G. Semeghini, G. Modugno, M. Inguscio, M. Fattori)
We report on the operation of an atom interferometer with trapped Bose Einstein condensates of K39 where interactions can be tuned using broad magnetic Feshbach resonances. An ultra-stable double well trapping potential allows to split and recombine the atomic matter wave in two distinct spatial modes. Canceling the homo-nuclear scattering length it is possible to achieve long coherence times and demonstrate the operation of a sensor with high sensitivity and high spatial resolution in the measurement of forces. In addition we show preliminary tests on the production of quantum entangled states using repulsive and attractive interactions. Our system is the ideal test bench to study the usefulness of non-classical states for quantum enhanced metrology.

A Mixture of Bose and Fermi Superfluids
(I. Ferrier-Barbut, M. Delehaye, S. Laurent, A. T. Grier, M. Pierce, B. S. Rem, F. Chevy, C. Salomon)
We present the experimental realization of a mixture of a Bose and a Fermi superfluids. The mixture was obtained in a ultracold gas of Lithium 7 and Lithium 6. It consists of a weakly-interacting Bose-Einstein condensate at equilibrium with a strongly-interacting Fermi superfluid in the BEC-BCS crossover. By a study of the dipole modes of the system we probe the interaction between the two superfluids. Our observations are in close agreement with a perturbative treatment and prove to be sensitive to equilibrium properties. We pursue the investigation of the dipole modes at high amplitudes and demonstrate the existence of a critical velocity for relative motion of the two superfluids, in agreement with general properties of superfluid flows. We will discuss different mechanisms for dissipation in this case.

Tuning Interactions in Two and Three Dimensions
(R J Fletcher, N Navon, M Robert-de-Saint-Vincent, A L Gaunt, R P Smith, Z Hadzibabic )
We present recent work on a Bose gas with tuneable interactions in two very different geometries. In three dimensions, we study the stability of a thermal 39K Bose gas across a broad Feshbach resonance, focusing on the unitary regime. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. As a consequence of species-specifc Efimov physics, we find 39K to be particularly promising for studies of many-body physics in a unitary Bose gas. We also present more recent work on a two-dimensional trapping configuration. Such a setup permits investigation of the subtle interplay between interactions and condensation in this regime, in particular the crossover between BEC and BKT physics.

Josephson physics of spin-orbit coupled elongated Bose-Einstein condensates
(M.A. Garcia-March, A. Polls, G. Mazzarella, L. Dell'Anna, L. Salasnich, and B. Julia-Diaz)
We consider an ultracold bosonic binary mixture confined in a one-dimensional double-well trap. We assume that these two components are spin-orbit coupled between each other. Within a bimodal approximation and at the meanfield level we derive a system of equations governing the evolution of the inter-well population imbalance of each component and that between the two bosonic species. In such a system we find three different types of tunnelling-like phenomena. The first one is the conventional tunnelling between both wells, namely the external Josephson effect. The second one is analogous to an internal Josephson effect, as it is associated to the process that transforms atoms of one species to the other species within the same well. The third one, associated to the spin-orbit coupling term, is an hybrid between internal and external Josephson effects, as it transforms atoms of one species in one well to atoms of the other species in the other well. We study the interplay of the atom-atom interactions with these three processes. Different new regimes for macroscopic tunnelling and self-trapping depending on the relationship between all of them are found. The study of the equilibrium points reveals an enriched dynamical scenario when compared to that of conventional two-mode bosonic Josephson junctions. We discuss the experimental feasibility for the observation of these new phenomena.

Probing critical phenomena with a quench
(Markus Karl, Markus K. Oberthaler, and Thomas Gasenzer)
Quantum critical phenomena such as zero-temperature, second-order phase transitions are of central interest for future quantum technologies. Here, we report the experimental observation of universal properties probed during the short-time evolution after a fast quench close to a quantum critical point in a 1D two-component Bose gas. While the system is well described by a non-linear Heisenberg model, our measurements of critical exponents are in good agreement with exact results for the transverse Ising model in equilibrium. This demonstrates the universality defined by the spontaneous Z_2 symmetry breaking in the sine-Gordon model which the bosonic degrees of freedom can be described by. Our results show that an ultracold Bose gas can be used to quantum simulate dynamical quantum critical phenomena which require exact diagonalisation methods in the original spin formulation. We will discuss our findings in the context of Non-thermal Fixed Points which have been proposed as new critical phenomena far from thermal equilibrium and can be related to pattern formation and ensembles of quasi-topological defects [1-4]. [1] M. Karl et al., Scientific Reports 3, 2394 (2013) [2] M. Karl, et al., Physical Review A 88, 063615 (2013) [3] B. Nowak, et al., arXiv:1302.1448 [4] B. Nowak, et al., Physical Review B 84, 020506(R), (2011)

Ground State Properties of a Homogeneous Bose-Einstein Condensate
(Alexander Gaunt, Igor Gotlibovych, Tobias Schmidutz, Nir Navon, Zoran Hadzibabic)
We will present measurements of the coherence, energy and free expansion of a quasi-homogeneous atomic Bose-Einstein condensate (BEC) in an optical box potential. We have measured the ground state wave function of a trapped quasi-pure BEC in momentum space using Bragg spectroscopy and compare this with the real-space wave function. We find excellent quantitative agreement with the Heisenberg uncertainty principle and also confirm the expected scaling of the momentum uncertainty with the box length. In addition, by varying the condensate atom number, we have studied the effect of interactions on the momentum distribution and mean-field energy of the condensate. Finally, we will present our recent efforts to address the coherence properties of a Bose gas following a rapid temperature quench.

Density correlation function of expanding Bose gas
(K. Gawryluk, M. Gajda, A. Perrin and M. Brewczyk)
We study, within a framework of the classical field approximation, the density correlation function of expanding Bose gas for the whole range of temperatures across the Bose-Einstein condensation threshold. We are particularly interested in the case of elongated system where there is a huge discrepancy between the existing theory and experimental results (A. Perrin et al., Nature Phys. 8, 195 (2012)). We find, in agreement with the experiment, that the density correlation function is not reduced for temperatures below the critical one as it is predicted by the ideal Bose gas theory. This behavior is attributed not just to the presence of interactions in the system. It is strictly related to the existence of dark solitons in the elongated gas at thermal equilibrium.

Rabi interferometry in a double well potential
(K. Gietka)
We calculate the estimation sensitivity of the external force, which drives the oscillations of the Bose gas in a double-well potential. We discuss three possible estimation schemes, allowing for the measurements to be performed at different stages of the evolution. First, we consider the case, when the force is determined in-situ, from the measured population-imbalance. Next, we discuss the estimation protocol based on the near-field oscillations of the center-of-mass of the gas released from the trap. We compare these results with the far-field estimation from the density of the interference pattern.

Engineering long-range spin interactions between atoms trapped near photonic crystals
(Hessam Habibian, James Douglas, Darrick Chang)
One of the most spectacular developments in the field of atomic physics has been the use of ultracold atoms to simulate other many-body systems and increase our understanding of strongly correlated quantum many-body phenomena. An outstanding challenge in this field, however, has been to simulate phenomena that arise from long-range interactions, as cold atoms are essentially neutral point particles. Separately, in recent years researchers have been successful in interfacing cold atoms with nanophotonic systems, with the goal of achieving control over strong interactions between individual atoms and light quanta. Here, we propose and will investigate a novel concept merging these two fields, wherein specially engineered nanophotonic interfaces enable one to achieve and tailor long-range interactions between atoms. Specially, our approach makes use of photonic crystal structures, where the dispersion of light and density of states can be tailored at will. We find that when an atom has a transition frequency in a “band-gap” region (a spectral window where the density of states vanishes), an atom-photon polaron can form, where the atom is dressed by a photonic cloud whose size and mixing angle can be controlled via the system properties. This enables two atoms to interact once one atom enters the polariton cloud of the other. This general mechanism offers a wealth of opportunities. Here, we describe how this system can be used to simulate long-range quantum spin Hamiltonians. As a specific example, we consider the long-range transverse Ising model, and analyze in detail the size of the spin system that can be simulated versus realistic system imperfections.

Spin dynamics in a two dimensional quantum gas
(Andrew J. Hilliard, Poul L. Pedersen, Miroslav Gajdacz, Frank Deuretzbacher, Luis Santos, Carsten Klempt, Jacob F. Sherson, and Jan J. Arlt)
In this talk, I will report on experimental work into spin dynamics in a 2D quantum gas [1]. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate held in an optical lattice. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimposed angular density modulations. The measured density distributions depend on the applied magnetic field and are well explained by a simple Bogoliubov model. I will demonstrate that the two clouds are anti-correlated in momentum space. The observed momentum correlations pave the way towards the creation of an atom source with non-local Einstein-Podolsky-Rosen entanglement. [1] Poul L. Pedersen, Miroslav Gajdacz, Frank Deuretzbacher, Luis Santos, Carsten Klempt, Jacob F. Sherson, Andrew J. Hilliard, and Jan J. Arlt, Under review.

Inelastic collisions of triplet Rb molecules under strong anisotropic confinement
(Bjorn Drews, Markus Deiss, Krzysztof Jachymski and Johannes Hecker Denschlag)
Using magnetoassociation and STIRAP process, we create triplet rubidium molecules in rovibrational ground state. We trap them in anisotropic optical lattice, realizing a quasi-one dimensional system. The molecules can undergo a transition to singlet state, which introduces losses. We investigate the dependence of inelastic collision rates on the transverse confinement and rotational quantum state, which is well-controlled. The experimental results can be understood by using a simple theoretical model.

Quantum Hall phases of two-component bosons
(T. Grass, D. Raventos, M. Lewenstein, B. Julia-Diaz)
The recent production of synthetic magnetic fields acting on electroneutral particles, like atoms or photons, has boosted the interest in the quantum Hall physics of bosons. The scenario gets further broadened by a adding a pseudospin-1/2 to the bosons. Then, the system is allowed to form an interacting integer quantum Hall (IQH)[1] phase with no fermionic counterpart. Here we show that, for a small two-component Bose gas on a disk, the complete strongly correlated regime, extending from the integer phase at filling factor ν=2 to the Halperin phase at filling factor ν=2/3, is well described by composite fermionization of the bosons. Moreover we study the edge excitations of the IQH state, which, in agreement with expectations from topological field theory, are found to consist of forward-moving charge excitations and backward-moving spin excitations [2]. Finally, we demonstrate how pair-correlation functions allow one to experimentally distinguish the IQH state from competing states, like non-Abelian spin singlet (NASS) states. [1] Senthil, Levin, Phys. Rev. Lett. 110, 046801 (2013). [2] Grass, Raventos, Lewenstein, Julia Diaz, Phys. Rev. B 89, 045114 (2014).

Detecting and imaging single Rydberg electrons in a Bose-Einstein condensate
(Tomasz Karpiuk, Miroslaw Brewczyk, Kazimierz Rzazewski)
The quantum mechanical states of electrons in atoms and molecules are discrete spatial orbitals, which are fundamental for our understanding of atoms, molecules, and solids. They determine a wide range of basic atomic properties, ranging from the coupling to external fields to the whole field of chemistry. Nevertheless, the manifestation of electron orbitals in experiments so far has been rather indirect. In a detailed theoretical model, we analyze the impact of a single Rydberg electron onto a Bose-Einstein condensate and compare the results to experimental data. Based on this validated model we propose a method to optically image the shape of single electron orbitals using electron-phonon coupling in a Bose-Einstein condensate. This scheme requires only established and readily available experimental techniques and allows to directly capture textbook-like spatial images of single electronic orbitals in a single shot experiment.

Simulation of non-Abelian lattice gauge theories with a single component atomic gas
(Arkadiusz Kosior, Krzysztof Sacha)
We show that non-Abelian lattice gauge theories can be simulated with a single component ultra-cold atomic gas in an optical lattice potential. An optical lattice can be viewed as a Bravais lattice with a $N$-point basis. An atom located at different points of the basis can be considered as a {it particle} in different internal states. The appropriate engineering of tunneling amplitudes of atoms in an optical lattice allows one to realize U$(N)$ gauge potentials and control a mass of {it particles} that experience such non-Abelian gauge fields. We provide and analyze a concrete example of an optical lattice configuration that allows for simulation of a U(2) gauge model with an adjustable mass of {it particles}. In particular, we observe that the non-zero mass creates large conductive gaps in the energy spectrum, which could be important in the experimental detection of the transverse Hall conductivity.

Propagation of quantum correlations after a quench in the Mott-insulator regime of the Bose-Hubbard model
(K.V.Krutitsky, P.Navez , F.Queisser, R.Sch"utzhold)
We have developed a new method which allows to study dynamics of nquantum correlations in higher dimensional lattices of large size and gives reliable results for long times. The formalism is based on the equations of motion for the reduced density matrices. An infinite set of equations is truncated such that only two-point correlations are taken into account. This approximation is justified by exact diagonalization for small lattices in one and two dimensions. Approximate analytical solutions of the resulting equations are obtained within the framework of a perturbative expansion in powers of the inverse coordination number. Exact solutions are obtained by numerical integration of the equations of motion and show qualitative agreement with the analytical approximations. On the other hand, numerical calculations allow to achieve higher accuracy which is confirmed by comparison with the exact diagonalization. As an application we study the dynamics of interacting bosons in a lattice after quench within the Mott-insulator regime. It is shown that the time evolution of the local particle-number distribution is directly related to the propagation of correlations. In particular, we find the revival of oscillations of the local quantities after the propagation of correlations through the whole system. In two dimensions, the propagation of correlations is anisotropic with the minimal velocity along the lattices axes and maximal along the diagonals. Our method can be easily applied to inhomogeneous lattices which allows to include into consideration the harmonic traps as well as disorder potentials.

An eccentrically perturbed Tonks–Girardeau gas
(M. Krych, J. Goold, Z. Idziaszek, T. Fogarty and Th. Busch)
We investigate the static and dynamic properties of a Tonks–Girardeau gas in a harmonic trap with an eccentric perturbation of variable strength. For this, we first find the analytic eigensolution of the single particle problem and then use this solution to calculate the spatial density and energy profiles of the many-particle gas as a function of the strength and position of the perturbation. We find that the crystal nature of the Tonks state is reflected in both the lowest occupation number and the momentum distribution of the gas. As a novel application of our model, we study the time evolution of the spatial density after the sudden removal of the perturbation. The dynamics exhibits collapses and revivals of the original density distribution, which occur in units of the trap frequency. This is reminiscent of the Talbot effect from classical optics.

Towards non-linear optics with cold atoms inside a hollow-core fibre
(Maria Langbecker, Mohammad Noaman and Patrick Windpassinger)
In this talk I will present an experiment for studying strong light-matter interactions using atoms confined inside a hollow-core fibre and its prospects for non-linear quantum optics. Photons in vacuum are essentially non-interacting particles. However, in the presence of a non-linear medium (such as a cloud of cold atoms) effective photon-photon interactions can be achieved. In our setup, we guide cold Rubidium atoms inside a hollow-core photonic crystal fibre, thus confining both light field and atoms to an area of ~ λ^2. This strong confinement leads to a very good overlap between atoms and light mode, enhancing their interaction probability and therefore increasing the optical depth. In such an optically dense medium, many effects from non-linear optics, such as e.g. all-optical switching at low light levels, can be studied. In particular, the creation of slow light is possible via the process of Electromagnetically Induced Transparency (EIT). Here, photons can be temporarily stored as excitations in the non-linear medium. Due to the tunability of the interactions between those excitations, exotic phases like the crystallization of photons should be observable in our setup.

The role of local and global geometry in quantum entanglement percolation
(Gerald John Lapeyre Jr.)
We prove that enhanced entanglement percolation via lattice transformation is possible even if the new lattice is more poorly connected in that: i) the coordination number (a local property) decreases, or ii) the classical percolation threshold (a global property) increases. In fact, all examples that we are aware of violate both conditions i and ii. One might therefore conjecture that all good transformations must violate them. Here we provide a counter-example that satisfies both conditions by introducing a new method, partial entanglement swapping. This result shows that a transformation may not be rejected on the basis of satisfying conditions i or ii. Both the result and the new method constitute steps toward answering basic questions, such as whether there is a minimum amount of local entanglement required to achieve long-range entanglement.

Zero-temperature solid to superfluid transition in bosonic systems
(Yaroslav Lutsyshyn, Grigori Astrakharchik, Jordi Boronat)
Competition between bosonic solid and superfluid phases is not only driven by zero-point motion, but also directly influenced by the Bose exchange symmetry. We will present our work on treating the quantum melting by a variational anzatz. In the past, we have successfully treated the transition between solid helium-4 and its superfluid. Such a treatment became possible because of the improvements in the explicit description of the ground state of a quantum solid. In this talk, we will present our results for the corresponding transition in optical lattices.

Real-time evolution of finite temperature Bose-Hubbard model
(Jakub Zakrzewski, Dominique Delande, Mateusz Lacki)
A ultracold atom gas in the optical lattice potential is described by means of the Bose-Hubbard model. We will present how a realistic size system may be described in finite temperature by the ensemble of Matrix Product States. This representation allows for performing the real time evolution of the ensemble and subsequent studies of the dynamical properties - for example the thermal conductance.

Transport properties of unitary Fermi gas from Quantum Monte Carlo
(Piotr Magierski)
I will present an ab initio determination of the shear viscosity for the unitary Fermi gas based on finite temperature quantum Monte Carlo (QMC) calculations and the Kubo linear-response formalism. The results are confronted with bounds for the shear viscosity originating from the Kovtun-Son-Starinets universal value and from hydrodynamic fluctuations. I will show that the latter bound is violated in the low temperature regime and the violation occurs simultaneously with the onset of the Cooper pairing in the system. The temperature dependence of the spin susceptibility and the spin conductivity will be presented. Both quantities exhibit suppression above the critical temperature of the superfluid to normal phase transition due to presence of the Cooper pairs. The spin diffusion transport coefficient does not display the existence of a minimum in the vicinity of the critical temperature and it drops to very low values D_s approx 0.8hbar/m in the superfluid phase. All these spin observables show a smooth and monotonic behavior with temperature when crossing the critical temperature T_c, until the Fermi liquid regime is attained at the temperature T*, where the pseudogap regime disappears.

Interacting bosons in time dependent lattices.
(Jan Major)
We analyze dynamics of bosons in one dimensional lattices with periodically changing parameters (tunnelings, onsite energies). Renormalized coefficients in Hamiltonian are calculated by means of Floquet theorem, onsite interactions and other two-particle processes are included, possibilities of experimental realization are sketched.

Single Atom Imaging with high NA system
(Hector Mas)
Cold Atoms, BEC and Atom Lasers are the starting point for some fascinating approaches to fundamental physics, quantum coherence or high sensitivity interferometry. However, the technical challenges are widespread and there is need of feasible pathways matching current technologies yet pushing them forward. I will present my first steps in single atom fluorescence imaging. We improved our previous system by four times in collection by using a high NA Achromat Lens at less than 1mm from the glass cell. This was a first checking which will be followed by an even more efficient system capable of resolving single atoms in free flight. This system will have also a crucial role in one of our main experiments, the TAAP Ring Atom-Guide. Some interesting results related to our Novel Ioffe-Pritchard Trap (which has the highest flux of atoms atom laser reported to date) will also be presented.

PT-symmetric lattices and symmetry breaking in exciton-polariton condensates
(Michal Matuszewski, Anton Desyatnikov, and Elena Ostrovskaya)
In quantum mechanics, all physical observables are represented by self-adjoint or Hermitian operators. The hermiticity of the Hamiltonian ensures that the eigenvalue spectrum is entirely real and the norm of the wavefunction is conserved in time. Interestingly, as shown by Bender et al. (PRL 80, 5243, 1998), non-hermitian Hamiltonians possessing parity-time symmetry can still exhibit a real eigenvalue spectrum. Recently, the possibility of practical realization of PT-symmetric Hamiltonians in optical systems has been pointed out by several groups. We suggest that exciton-polariton Bose-Einstein condensates are ideal systems for the application of these ideas. The possibility to create the relevant complex potentials through engineering of the structural potential and pumping profiles is demonstrated. We apply the concept to propose a polaritonic device generating a unidirectional flow of polaritons in a one-dimensional configuration.

Static properties of 2D dipolar bosons in the continuum
(Ferran Mazzanti)
In recent years, significant advances in the field pf ultracold Bose and Fermi gases have allowed for the experimental realization of condensates of species presenting large and permanent electric or magnetic dipole moments [1]. From a microscopic point of view, these systems are characterized by an anisotropic and long ranged interaction potential that departs from the typical Van der Waals models found in most condensed-matter systems, making them extraordinarily appealing from a theoretical point of view. Dipolar condensates have been realized in many different geometries, 3D and 2D, under the action of confining potentials or in optical latices [2]. In this context we present recent results concerning the quantum properties of dipolar bosons in 2D, under the action of an external field that fully polarizes the system. We consider the cases were the polarization angle is not large enough to produce collapse instabilities, but still large so as to reveal the anisotropic properties induced on the system. We discuss the equation of state at zero temperature and the formation of a new stripe phase that emerges at large polarization angles and densities. Finally we analyze a bilayer system of dipoles in 2D and show how by changing the density and interlayer distance, the systems changes from a atomic superfluid to a molecular regime, similarly to what happens in the optical lattice [3]. As far as we know, this is the first example physical system showing pair superfluidity in the continuum that could be explored in current experiments on cold Bose gases with predominant dipolar interactions. [1] T.Lahaye, C.Menotti, L.Santos, M.Lewenstein and T.Pfau, Rep. Prog. Phys. 72, 126401 (2009). [2] M.A.Baranov,M.Dalmonte, G.Pupillo and P.Zoller, Chem. Rev. 112, 5012 (2012). [3] A.Safavi-Naini, S.G.Soyler, G.Pupillo, H.R.Sadegh-pour and B.Capogrosso-Sansone, New J. Phys. 15, 013036 (2013).

Artificial gauge potentials induced by evanescent waves
(Malgorzata Mochol, Krzysztof Sacha)
We show that artificial gauge potentials for ultra-cold atoms can be created by means of evanescent waves. A theoretical description of the adiabatic motion of atoms in the presence of an external electromagnetic field involves artificial vector and scalar potentials that are the stronger the larger gradient of the external field amplitude. An evanescent wave possesses a large gradient of the amplitude and a gradient of the phase that are the most important features in the generation of synthetic gauge potentials. We consider an evanescent wave created by a single plane wave as well as by a realistic laser beam.

A case study of spin-1 Heisenberg model in a triangular lattice
(M. Moreno-Cardoner, H. Perrin, S. Paganelli, G. De Chiara, A. Sanpera)
The quest for realistic models that can support a topological spin liquid ground-state is at the frontier of current research, not only because they might be connected to high-Tc superconductivity, but also because such states are robust against local decoherences and could have important applications in quantum computing. The spin S=1 Heisenberg model in a triangular lattice in presence of a uniaxial magnetic field has been suggested as one of these simple models that could have a spin liquid ground state in some region of its phase diagram. This model could be in principle realized with cold atoms trapped in a very deep optical lattice potential. The available theoretical methods to describe its phases are scarce and rely mostly on variational approaches. We present here our studies by using the Cluster Mean-Field approach and compare the results with other methods as the Gutzwiller mean-field ansatz or the exact diagonalization of a small plaquette. The CMF is a combined method that divides the lattice into finite size clusters which are treated in a full quantum way by exact diagonalization and which are coupled by a mean-field approach. It represents a step forward compared to the Gutzwiller ansatz, since it includes quantum correlations at the cluster level. By using this method, we obtain the complete phase diagram and search for a signature of local disorder in the lattice, necessary for a spin liquid state. We also analyze this model from a more quantum information perspective, and find that the entanglement spectrum can reveal several phase transitions.

Dynamics of Discrete Quantum Systems
(J. Mur-Petit, R. A. Molina)
We have studies the structure and dynamics of discrete quantum systems, such as cold atoms in optical lattices, photons in photonic crystals, or electrons in semiconductor heterostructures. We have identified a distinct mechanism for the formation of Bound states In the Continuum (BICs) in systems with chiral symmetry, which has an impact on their transport properties when these are coupled to leads. Depending how the leads are coupled to the system, this may block all transmission in an energy range around the band center, may feature a narrow Fano antiresonance, or a broad transmission peak. We discuss how these predictions can be observed in a number of systems, from arrays of quantum dots to nano-photonic setups.

Harnessing vacuum forces for quantum sensing of graphene motion
(C. Muschik, S. Moulieras, A. Bachtold, F. Koppens, M. Lewenstein, and D. Chang)
Vacuum forces are one of the most spectacular predictions of quantum physics and have gained great importance in modern nanotechnology, due to their large magnitude at nanoscale distances. We present a novel method to exploit the strength of vacuum forces associated with single quantum emitters. We show that vacuum fluctuations map small displacements of a nanomechanical oscillator onto large shifts in the transition frequency of a proximal emitter. This optically detectable shift consequently provides a mechanism for ultra-precise position measurements. This new technique works for a wide class of materials, as opposed to conventional methods based on optical forces. Optical forces are typically weak and cannot be applied to important materials such as graphene. Graphene is an excellent resonator with very low mass and high quality factor, which raises intriguing technological possibilities such as mass detection at the single-atom level. Current read-out techniques require averaging over many cycles of the mechanical motion. In contrast, our Casimir-based sensing scheme enables the monitoring of graphene motion at the quantum level in real time, which is not feasible using any other method. Our work constitutes the first example where Casimir potentials are utilized as a valuable resource for practical applications, which can already be realized with current technologies. This work merges the fields of graphene and quantum optics, and will open new avenues for strong-light matter interactions.

Generation of entangled atomic states in the cavity-feedback scheme
(Krzysztof Pawlowski, Jerome Esteve, Jakob Reichel, and Alice Sinatra)
We investigate the entangled states of an atomic ensemble that can be obtained by cavity-feedback in different regimes: from weak to strong atom-light coupling, systematically including the main decoherence sources. In the strong coupling regime we show that the system is rapidly driven by cavity losses to entangled many-body states that survive for a long time before being killed by decoherence. The spin-squeezed states, that we analyze in detail, appear as a “small island” in the landscape of entangled states for weak or intermediate coupling. Surprisingly the best achievable squeezing is limited by a constant, which depends on the atomic species used in the experiment.

Universal condensate fraction in resonant Bose-Fermi mixtures
(A. Guidini, G. Bertaina, P. Pieri)
We study a resonant Bose-Fermi mixture at zero temperature from weak to strong boson-fermion interaction, focusing on the case where the boson density is smaller than the fermion density, for which a quantum phase transition occurs from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. By using both diagrammatic and Quantum Monte Carlo methods, we find that the condensate fraction of the bosonic component depends universally on the boson-fermion coupling, namely, in a way which does not depend on the concentration of the bosons relative to the fermion components and which coincides with the behavior of the polaron residue as a function of coupling recently studied in the context of strongly imbalanced Fermi-Fermi mixtures.

Matter waves analog of an optical random laser
(Marcin Płodzień, Krzysztof Sacha)
The accumulation of atoms in the lowest energy level of a trap and the subsequent out coupling of these atoms is a realization of a matter-wave analog of a conventional optical laser. Optical random lasers require materials that provide optical gain but, contrary to conventional lasers, the modes are determined by multiple scattering and not a cavity. We show that a Bose-Einstein condensate can be loaded in a spatially correlated disorder potential prepared in such a way that the Anderson localization phenomenon operates as a bandpass filter. A multiple scattering process selects atoms with certain momenta and determines laser modes which represents a matter-wave analog of an optical random laser.

Dynamical robustness of conductivity of ultracold bosons confined in layered structures
(T. P. Polak and A. S. Sajna)
We study dynamical conductivity of strongly correlated bosons loaded in an optical lattice with restricted geometry in which gauge fields are present. We show that dynamics influenced by the uniform synthetic magnetic field combined with layered lattice structures, changes into rich insulator-metallic behavior in the strongly correlated regime. Especially, the amplitude of optical conductivity for a given frequency is a non-monotonous function of the number of layers L. In particular, conductivity for frequency corresponding to on-site interaction energy, can abruptly vanish for special number of applied layers. Moreover, such an insulating behavior is stable in the whole range of parameters in the Mott phase. This robustness arises from the Dirac-like physics reflected in the quasi-particle energy spectra. Furthermore we show that the large inter-layer tunneling anisotropy destabilizes the absence of conducting state. We also investigate the critical conductivity on the Mott insulator-superfluid phase boundary and show the correspondence between the number of Hofstadter sub-bands and the number of layers. The obtained results also reveal that the value of critical conductivity gradually goes to zero when a three-dimensional system is approached. The experimental setup for generation of layered optical lattices is also proposed.

Fast generation of spin-squeezed states in bosonic Josephson junctions
(A. Yuste, B.Julia-Diaz, E. Torrontegui, J. Martorell, J.G. Muga and A. Polls)
We describe methods for the fast production of spin-squeezed many-body states in bosonic Josephson junctions. We start from the known mapping of the two-site Bose-Hubbard (BH) Hamiltonian to that of a single effective particle evolving according to a Schrodinger-like equation in Fock space. Since, for repulsive interactions, the effective potential in Fock space is nearly parabolic, we extend recently derived protocols for shortcuts to adiabatic evolution in harmonic potentials to the many-body BH Hamiltonian. A comparison with current experiments shows that our methods allow for an important reduction in the preparation times of highly squeezed spin states in comparison with the usually employed linear rampings. References: B. Julia-Diaz, E. Torrontegui, J. Martorell, J.G. Muga, and A.Polls; Phys. Rev. A86, 063623 (2012). A. Yuste, B. Julia-Diaz, E. Torrontegui, J. Martorell, J.G. Muga, and A. Polls; Phys. Rev. A88, 043647 (2013). ~

Lattice shaking in 1D for topological phenomena
(A. Przysiężna, O. Dutta, J. Zakrzewski)
Topologically protected states of matter owe a great attention to their novel properties such as robust transport on the boundary (in 2D and 3D) and localized edge states (in 1D). The simplest one-dimensional models that exhibit topological properties are: Su, Schrieffer and Heeger (SSH) model and its variant with alternating onsite energy (Rice-Mele model). Known method to simulate these models with use of coldatoms is by trapping them in superlattice with two sites per unit cell. We propose an alternative route to create one-dimensional topologically nontrivial system. In contrast to the system with superlattice, our lattice is the simplest possible (a sine potential). Topological properties come as a result not of the potential shape, but the combined effect of attractive interaction between two species fermions and lattice shaking. The attraction causes creation of composites, modifies intraband hopping and induces tunneling between different bands. Lattice shaking modify hopping amplitudes and changes the onsite potential in a stagered maner. Combined, these two ingredients lead to density-wave structure of one species and emergence of topological phenomena. We show that our system has nontrivial Zak phase and exhibit zero-energy edge states. By tunning parameters of the system we can smoothly change topological properties from non-trivial to trivial ones.

Characterisation of Bose-Hubbard Models with Quantum Non-demolition Measurements
(B. Rogers, M. Paternostro, J. Sherson, G. De Chiara)
We propose a scheme for the detection of quantum phase transitions in the 1D Bose-Hubbard (BH) and 1D Extended Bose-Hubbard (EBH) models, using the non-demolition measurement technique of quantum polarisation spectroscopy. We use collective measurements of the effective total angular momentum to characterise the Mott insulator to superfluid phase transition in the BH model, and the Haldane insulator to density wave phase transition in the EBH model. We extend the application of collective measurements to the sub-lattice fillings formed from a super-lattice potential.

A Cold-Atom Quantum Simulator for Attosecond Science
(Simon Sala, Johann Förster, and Alejandro Saenz)
The theoretical simulation of many-electron atoms or molecules exposed to intense laser fields requires substantial approximations or is limited to very small systems like helium atoms or hydrogen molecules. Clearly, even in the foreseeable future the number of electrons that can be treated completely on a classical computer is limited to a very small number. On the other hand, also systematic experimental investigations are prohibitively difficult, since changing, e.g., the number of electrons leads to a charged ion and modifies the complete electronic structure of an atom or molecule and thus its response to an ultrashort intense laser field. Therefore, this problem is a perfect example for devising a quantum simulator. Such a quantum simulator based on ultracold atoms in an optical trap will be presented. It is demonstrated that the characteristic features of strong-field physics are well reproduced using realistic experimental parameters.

Emergence of coherence and the dynamics of quantum phase transitions
(S. Braun, M. Friesdorf, S. S. Hodgman, M. Schreiber, J. P. Ronzheimer, A. Riera, M. del Rey, I. Bloch, J. Eisert, and U. Schneider)
The dynamics of quantum phase transitions poses one of the most challenging problems in modern many-body physics. Here, we present a combined experimental and numerical study of the emergence of coherence when crossing the Mott insulator to superfluid quantum phase transition in the homogeneous Bose Hubbard Model. In one dimension, we find perfect agreement between experimental observations and numerical simulations in a regime where neither free quasiparticles nor simple scaling theories can predict the dynamics. Experimentally, we additionally explore the emergence of coherence in higher dimensions where no classical simulations are available.

Evolution of two-qubit entanglement under correlated noises
(P. Szankowski, L. Cywinski, M. Trippenbach and Y.B. Band)
We investigate the decay of entanglement arising from the influence of a noise experienced by two qubits that are initially in a maximally entangled state. We compare the whole spectrum of cases: from independent noises acting on each qubit to the fully correlated case - when both qubit are exposed to the same exact noise. We find that the rotational symmetry of a state plays a crucial role as a noises acting on each qubit becomes correlated.

Orbital-FFLO state of two-orbital high spin fermionic atoms on a one-dimensional optical lattice
(Edina Szirmai)
We study the effect of the coupling between the electronic ground state of high spin alkaline-earth fermionic atoms and their metastable optically excited state, when the system is loaded into a one-dimensional optical lattice, and show that the system provides a possible realization of a finite momentum pairing (Fulde-Ferrell-Larkin-Ovchinnikov-like) state without spin- or bare mass imbalance [1]. The finite momentum of the emerging Cooper pairs is a consequence of the tunneling amplitude difference between the two electronic state of the atom. We solve the renormalization group equations for spin-9/2 Sr-87 isotope and analyze in detail its phase diagram within hydrodynamical approach. We found that the fully gapless Luttinger liquid state does not stabilize in the two-orbital system of the Sr-87 atoms, instead, different gapped non-Gaussian fixed points are identified either with dominant density or orbital singlet superconducting fluctuations. The superconducting states are stable in a nontrivial shaped region in the parameter space as a consequence of the coupling between the two electronic states. [1] E. Szirmai, Phys. Rev. B 88, 195432 (2013)

Photonic tuning of Beliaev damping in a superfluid
(G. Szirmai, G. Konya, D. Nagy and P. Domokos)
We show that the Beliaev damping of elementary excitations in a homogeneous superfluid can undergo resonant enhancement by several orders of magnitude when the superfluid is interacting with a {far-detuned} radiation field of an optical resonator. The photonic tuning of the quasi-particle damping is related to the presence of a quantum critical point in the system and can be controlled by an external laser drive. Beyond mean-field effects prove thus to be significant in the system of Bose-Einstein condensate coupled to a cavity.

Dynamics of atom pairs in a quantum quench of quasicondensates above Bogoliubov temperatures
(Tomasz Swislocki, Piotr Deuar)
We demonstrate how to simulate dynamics of atom pairs in ultracold Bose gases at temperatures that are to high for Bogoliubov description. In particular we study one dimensional quasicondensates with the significant thermal fraction. This has been elusive in the past because existing methods for higher temperature gases such as stochastic Gross-Pitaevskii method omit quantum fields effects such as pairing and shot noise. Therefore we combine a Positive-P description with stochastic Gross-Pitaevskii initial states. We simulate a quantum quench of the interaction strenght in quasicondensates. Counterpropagating atom pairs appear in the density correalation functions in momentum space. We observe also additional loose of the coherence, and antibunching and density correlation waves. The method is also applicable in two and three dimensions.

Monogamies of correlations and amplification of randomness
(R. Augusiak, M. Demianowicz, M. Pawlowski, J. Tura, A. Acin)
Physical principles constrain the way nonlocal correlations can be distributed among parties in a Bell experiment. Here, we show that in any no-signalling theory the amount of violation of a certain class of Bell inequalities tightly bounds the knowledge that an external observer can gain about outcomes of any single measurement performed by the parties. Analogous relations are then proved for quantum correlations in the simplest scenario of three parties performing two dichotomic measurements. Later, we relate these monogamy trade-offs to the generation and amplification of randomness, in the latter case, in particular, reproducing and generalizing the results of [R. Colbeck and R. Renner, Nature Phys. 8, 450 (2012)]. Finally, we show that with the aid of the chained Bell inequalities one can amplify the Santha-Vazirani epsilon-sources for epsilon < 1/6, improving the existing results.

Solitonic Vortices in a Bose-Einstein Condensate in a trap and under expansion
(Simone Donadello, Simone Serafini, Marek Tylutki, Lev P. Pitaevskii, Franco Dalfovo, Giacomo Lamporesi, Gabriele Ferrari)
We present numerical simulations, where an initially trapped cigar-shaped Bose-Einstein condensate containing a solitonic vortex undergoes a free expansion. During the expansion the solitonic depletion in the density develops a twist around the vortex line due to the vortex phase gradient. This allows to extract the sense of rotation of the vortical flow from the observation of the density distribution. The numerical results are compared with experimental data. The experiment of the interference after the coherent Bragg splitting of the atomic cloud is also simulated. The solitonic vortices are likely created as decay product of gray solitons and exhibit a very long lifetime.

Uhlmann Measure in Topological Insulators and Superconductors at finite temperature
(O. Viyuela, A. Rivas, M.A. Martin-Delgado)
I will introduce the Uhlmann geometric phase as a tool to characterize symmetry protected topological phases in 1D fermion systems, such as topological insulators and superconductors. Since this phase is formulated for general mixed quantum states, it provides a way to extend topological properties to finite temperature situations. New effects appear such as the existence of a critical temperature, appearance of a topological kink in momentum space, breakdown of the usual bulk-edge correspondence, etc. Moreover, as the Uhlmann phase is an observable itself, we analyse potential measurement schemes that could be applicable to current experimental setups like cold atoms in optical lattices. [1] O. Viyuela, A. Rivas, M.A. Martín-Delgado, arXiv: 1309.1174 (2013) [accepted in PRL].

Cauchy-Schwarz inequality and particle entanglement
(T. Wasak, P. Szankowski, P. Zin, M. Trippenbach, J. Chwedenczuk)
The creation of the ensembles of entangled particles triggered the studies of the fundamental aspects of quantum mechanics. The existence of non-classical correlations between atoms opened the possibility for the practital applications in non-trivial ways, for example in quantum computation or ultra-precise metrology. However, before the implementation stage, we must first make sure that entanglement is present in the system, which is a difficult task. We provide a simple and experimentally accessible criterion for particle entanglement in many-body systems. This is based on a violation of the Cauchy-Schwarz inequality for the second order correlation function. It applies to any quantum system of identical bosons with either fixed or a fluctuating number of particles, provided that there is no coherence between different number states.

The role of velocity-changing collisions on anomalous inhomogeneity in H2 Q(1) line broadening perturbed by Ar
(P. Wcislo, F. Thibault, H. Cybulski, R. Ciurylo)
Usually, in high-pressure regime, the Doppler-broadened profiles collapse into a simple Lorentzian shape due to frequent changes of the molecule velocity. Far different characteristic is observed when the collisional width and shift rapidly vary with collision energy. Particularly, an inhomogeneous broadening appears as a result of thermal averaging of the speed-dependent line shift [1,2]. For the H2/D2-Ar systems, fundamental discrepancies between thermally averaged collisional broadening obtained from experimentally determined law [3,4] and from ab initio close-coupling (CC) calculations were reported [5-7]. For instance at room temperature the broadening of the Q(1) line calculated from the experimental law was almost two times larger than the theoretical one. To resolve the problem of these huge discrepancies we performed highly accurate calculations of the H2-Ar potential energy surface (PES) by employing the RCCSD(T) method in combination with the large aug-cc-pCVQZ basis and the 332211 midbond basis set (in the calculations the stretching of the H2 bond was considered). However, we found that the broadening of the H2 Q(1) line determined from the CC calculations based on the new PES is even less consistent with the value from experimental law than the previous CC calculations based on less accurate, earlier PES [8]. Next, we modified the line-shape model replacing the phenomenological model of the velocity-changing collisions by much more physical ab initio billiard-ball model, for which it was already shown that it provides appropriate description of the velocity-changing collisions for the H2-Ar system [9]. We found that this approach gives the H2 Q(1) line broadening, for the mixture of 5\% of H2 and 95\% of Ar, very close to experimental values. Our model not only properly handles the dynamics of optically active molecules (in particular a strong competition between velocity-changing and phase/state-changing collisions), but also constitutes a first step toward application of advanced ab initio line-shape models in ultra-accurate optical metrology based on molecular spectroscopy. [1] R. L. Farrow et al. Phys. Rev. Lett. 63, 746-749 (1989) [2] R. Ciuryło, D. Lisak, J. Szudy, Phys. Rev. A 66, 032701 (2002) [3] J. P. Berger et al. Phys. Rev. A 49, 3396-3406 (1994) [4] F. Chaussard et al. J. Chem. Phys. 112, 158-166 (2000) [5] L. Waldron, W.-K. Liu, J. Chin. Chem. Soc. 48, 439-448 (2001) [6] L. Waldron, W.-K. Liu, R. J. Le Roy, J. Mol. Struct. 591, 245-253 (2002) [7] H. Tran, F. Thibault, J.-M. Hartmann, J. Quant. Spectrosc. Radiat. Transfer 112, 1035-1042 (2011) [8] C. Bissonnette et al. J. Chem. Phys. 105, 2639-2653 (1996) [9] P. Wcislo et al. submitted to Phys. Chem. Chem. Phys. (2014)

Selection rules, conservation laws, and correlations in permutation-symmetric spinor quantum gases
(Vladimir A. Yurovsky)
Symmetry imposes fundamental constraints on properties of physical systems, such as selection rules and conservation laws. Invariance under permutations of indistinguishable particles, contained in each physical system, is one of the basic symmetries. The present work [1] obtains permutation-symmetry related selection rules for transitions in many-body systems of particles with arbitrary spins. It also demonstrates the physical meaning of the corresponding integrals of motion, identified by Dirac [2] with characters of the symmetric group, relating them to experimentally observable correlations of several particles. The results provide a way to control the formation of entangled states, belonging to multidimensional, non-Abelian representations of the symmetric group. The states can find applications in quantum computations and metrology. These effects can be observed in an optical lattice, containing spinor atoms in the Mott-insulator regime. 1. V. A. Yurovsky, arXiv:1402.0776 (2014) 2. P. A. M. Dirac, Proc. R. Soc. A 123, 714 (1929)

Dynamical entanglement in coupled systems
(Klaus Ziegler)
The competition of tunneling kinetics and particle-particle interaction in finite atomic systems can lead to an interesting dynamical behavior that is attributed to quantum correlation effects. Here we study the evolution of a quantum state which is created after coupling two independent systems. The eigenstates of the subsystems are known before they are coupled, and the initial state is a product of two of these eigenstates. Then we evaluate the return probability of the coupled system to the initial state and the transition probability for reaching a highly entangled state. An example is the creation of a bosonic N00N state which we obtain within a recursive projection method.

Magnetism in one-dimensional few-body systems
(A.G. Volosniev, D.V. Fedorov, A.S. Jensen, M. Valiente, E.J. Lindgren, J. Rotureau, C. Forssen, A.S. Dehkharghani , N. T. Zinner)
Strongly-interacting one-dimensional few-body systems provide a great playground for studying magnetic correlations. Using a combination of numerical and analytical methods, we discuss how ferro- and antiferromagnetic few-body systems can be created and manipulated in trapped cold atomic systems. Of particular interest is the role of quantum statistics and we consider multi-component bosonic and fermionic examples. We also consider the exotic case of anyons in one dimension and how strong interactions could be used to detect them and probe their statistics. [1] E.J. Lindgren et al. arXiv:1304.2992 (2013). [2] A.G. Volosniev et al. arXiv:1306.4610 (2013). [3] N.T. Zinner et al. arXiv:1309.7219 (2013).