How much work?
The concept of work in thermodynamics is well known and can be well defined in a process in which a property of the system (the position of a piston, the strength of a field) changes from an initial to a final value. In quantum mechanics it has been recently realized that work cannot be associated with the expectation value of an observable but rather with the transition probabilities between energy eigenstates [1]. As a consequence, only the work probability distribution can be properly defined for a given process. In this seminar I will first revise the recent developments concerning the definition of work in quantum mechanics. Then I will discuss a proposal, based on Ramsey interferometry, for measuring the work probability distribution in an experiment. Although the proposal can be adapted to most quantum technologies, I will explicitly discuss one example based on an optomechanical setup [2]. Finally, I will discuss an experimental realization of this protocol in an NMR setup thus demonstrating, for the first time, the measurement of the work characteristic function in a fully quantum setup [3]. [1] M. Campisi, P. Haenggi and P. Talkner, Rev. Mod. Phys. 83, 771 (2011). [2] L. Mazzola, G. De Chiara and M. Paternostro, Phys. Rev. Lett. 110, 230602 (2013). [3] T. Batalhao, et al., in preparation.

Many-body Anderson localization in cold atomic gases
A quantum particle placed in a disordered potential may be localized thanks to quantum interferences between the various multiply scattered paths. This phenomenon - known as strong or Anderson localization - is a pure one-body effect. How particle-particle interaction affects Anderson localization is a difficult problem, far from being solved, with lots of open issues and contradictory predictions. Ultra-cold atomic gases can be prepared experimentally in well controlled disordered configurations and/or with tunable atom-atom interaction, opening the way to experimental answers. I will discuss, using quasi-exact numerical simulations, how typical few/many-body one-dimensional excitations, bright and dark solitons, behave in the presence of disorder.

Toward quantum nanophotonics
I will review several new ideas how to exploit nano-photonic and nano-plasmonic structures for applications in quantum many body physics and quantum optics. First, I will describe how is it possible to combine nano-plasmonic forces and Casimir-Polder forces near a metal surface to create a nano-size trap for atoms. Such traps can be used to achieve confinement induced resonances in atomic scattering, and may serve to induce strong p-wave interactions. Second, i will discussed how an atom (NV center, quantum dot) fixed in a solid may serve as an detector of micro-motion of suspended graphene. Optical response of such detector allows to measure position of the moving graphene sheet in a real time, and to squeeze its fluctuations.

Optical lattice shaking: Simulating magnetism in triangular optical lattices
The creation of artificial gauge fields is a key ingredient to the emulation of strong field physics with ultracold atoms in optical lattices. The talk focusses on techniques to experimentally realize tunable gauge fields by periodically diving an optical lattice [Phys. Rev. Lett. 108, 225304 (2012)]. After introducing the general idea, the talk discusses the study of frustrated classical magnetism in a triangular geometry and the observation of all possible magnetic spin states. In addition, symmetry breaking for strong spin frustration is shown [Science 333, 996-999 (2011)]. In the case of maximal frustration, the doubly degenerate superfluid ground state breaks both a discrete Z2 (Ising) symmetry and a continuous U(1) symmetry. By measuring an Ising order parameter, we observe a thermally driven phase transition from an ordered antiferromagnetic to an unordered paramagnetic state and textbook-like magnetization curves [arxiv: 1304.5520].

Quantum Simulation with Cold Atoms and Ions
Recently, the condensed matter and atomic physics communities have mutually benefited from synergies emerging from the quantum simulation of strongly correlated systems using atomic setups. In the first part of the talk we give an overview of analog and digital quantum simulation with cold atoms in optical lattices and trapped ions. In the second part we discuss possible future directions: while there is presently significant interest in artificial gauge fields mimicking magnetic fields in (neutral) atom setups to observe phenomena like fractional quantum Hall physics, we will discuss prospects of realizing simple models of dynamical gauge fields (lattice gauge theories) as a next generation of possible cold atom experiments, where the (very long term) vision is to perform quantum simulation of lattice gauge theories of QED and QCD with cold atoms and ions.

Stability of persistent currents in two-component condensates
(Marta Abad, Alberto Sartori, Stefano Finazzi and Alessio Recati)
The very recent experimental observation of persistent currents in two-component condensates [1] and the lack of a theory that fully describes their stability condition [2,3,4,5], makes this a very challenging subject. To address this subject we consider the mean-field Gross-Pitaevskii theory for a two-component Bose-Einstein condensate confined in a toroidal trap, both in the presence and absence of a Rabi coupling term. We obtain a stability criterion for the miscible phase of the mixture which is closely related to the instabilities shown by Bogoliubov excitations, in particular of the spin-density mode. We find a first critical threshold given by the spin-density speed of sound [4], which is confirmed by numerical simulations. In addition we find a second threshold below which only the minority component decays, while the majority component keeps the persistent current stable. The presence of the Rabi coupling allows the system to carry higher quantized currents, and only one stability threshold exists. In the phase separated regime the condition of stability of the persistent current is related to the geometry of the system, showing a spin polarization threshold above which currents are maintained. The presence of the Rabi coupling again favors the stability of the currents, which can be understood from the shift in the phase transition brought about by the Rabi term [6]. [1] S. Beattie, S. Moulder, R. J. Fletcher, and Z. Hadzibabic, Phys. Rev. Lett. 110, 025301 (2013). [2] J. Smyrnakis, S. Bargi, G. M. Kavoulakis, M. Magiropoulos, K. Karkkainen, and S. M. Reimann, Phys. Rev. Lett. 103, 100404 (2009). [3] S. Bargi, F. Malet, G. M. Kavoulakis, and S. M. Reimann, Phys. Rev. A 82, 043631 (2010). [4] K. Anoshkin, Z. Wu, and E. Zaremba, ArXiv:1207.3449 (2012). [5] T. Shimodaira, T. Kishimoto, and H. Saito, Phys. Rev. A 82, 013647 (2010). [6] M. Abad and A. Recati, ArXiv:1301.6864 (2013); accepted in EPJD.

Topological properties of band structure of complex optical lattices
(Tomas Andrijauskas, Egidijus Anisimovas, Nathan Goldman, Gediminas Juzeliunas)
Since the discovery of the quantum Hall effect, topological properties of band structure of periodic quantum systems has been a very interesting topic in condensed matter physics. In particular, the quantised Hall conductance of each magnetic band is directly related to the topological Chern number. The quantised Hall conductance of each energy band is proportional to the Chern number, associated with the band. The Chern number is insensitive to various perturbations of the system and is related only to the bulk system properties. This allows to use it by characterising various topological system phases. In our work we analyse the topological properties of band structure of the two complex optical lattices: coupled hexagonal and triangle and coupled three triangle lattices. The couplings are induced by the laser-assisted hopping between sub-lattices. Both lattices have hexagonal geometry and can be described by three-level tight-binding models in the k-space. The laser-assisted coupling introduces non-trivial magnetic flux and the ultra-cold atoms in these lattices may have Chern insulator or non-trivial conducting phases. In the presentation we describe phase diagrams of various topological phases of both optical lattices. We show that such three-level quantum systems may exhibit various Chern number values from minus three up to three.

Detecting nonlocality with two-body correlators
(J. Tura, A. B. Sainz, R. Augusiak, A. Acin, M. Lewenstein)
A natural tool to detect nonlocality in composite quantum systems are Bell inequalities. Among the known inequalities the majority involves the correlation functions of all parties, and, intuitively, these are the most optimal ones. On the other hand, they are hard to implement experimentally for systems consisting of many constituents. Here we demonstrate that higher-order correlators are not necessary to certify nonlocality in multipartite quantum states. In fact, we show that Bell inequalities constructed only from one and two-body correlators do serve the purpose. Interestingly, these are also violated by some of the Dicke states that arise naturally in many-body physics as the ground states of two-body Lipkin-Meshkov-Glick Hamiltonian. Clearly, our results are promising from the experimental point of view.

Bound states of slow light polaritons
(Przemysław Bienias, Jonathan Simon, Hans Peter Buechler)
We develope the many-body theory of slow light polaritons in Rydberg gas under the condition of electromagnetically induced transparency. The van der Waals interaction between Rydberg atoms induces strong interaction between polaritons. We apply field theoretical methods to derive microscopically the effective interaction between slow light polaritons. As a first application we study existence and properties of bound states of polaritons.

In situ probing of interacting fermions in an optical lattice
(E. Cocchi, J. Bohn, J. H. Drewes, L. Miller, M. Koschorreck, D. Pertot, M. Koehl)
We experimentally investigate the Fermi Hubbard model by locally probing its phases. We prepare a degenerate Fermi gas of potassium-40 atoms and load it into a three-dimensional optical lattice. Our high resolution imaging system combined with a selective RF transfer lets us independently image the in situ density profiles of the atoms in doubly or singly occupied lattice sites. Varying the onsite interaction by means of a Feshbach resonance we can explore the phases of the Fermi Hubbard model. I will report on our steps towards the local characterization of the transition to a Mott insulator state.

New Approach to Entanglement and Spin Squeezing for Systems of Identical Bosons
( B J Dalton)
Entangled quantum states are considered for systems of identical particles, where in order to represent physical states, the system density operator must satisfy the symmetrisation principle (SP) and conform to super- selection rules (SSR) that prohibit states which have coherences between differing total particle numbers [1]. Both the system and sub-systems are modes (or sets of modes), particles being associated with different mode occupancies [2]. In defining the non-entangled or separable states, the subsystem density operators are also required to satisfy the SP and conform to SSR which forbid states with coherences between differing subsystem particle numbers [3], [4] - in contrast to other approaches [5]. The work mainly focuses on two mode entanglement both for massive bosons (e.g. bosonic atoms) and for photons. It is shown here [4] that the presence of spin squeezing in at least one of the spin components Sx=(b(+)a+a(+)b)/2, Sy =(b(+)a-a(+)b)/2i, Sz=(b(+)b-a(+)a)/2, (<(DelSx)^2> < (1/2)|| and <(DelSy)^2> > (1/2)|| for squeezing in Sx compared to Sy etc) is a sufficiency test for entanglement of the modes a,b. Whilst previous tests for entanglement in two mode systems, such as <(DelSx)^2>+<(DelSy)^2> < (1/N) related to spin squeezing [6] and strong correlation tests [7] |<(a)^m.(b+)^n>|^2 > <(a+)^m.(a)^m.(b+)^n.(b)^n> still apply for the present concept of entanglement, new tests have been obtained - such as the spin squeezing test and a simple correlation test |<(a)^m.(b+)n>|^2 > 0. For the case of relative phase eigenstates, the new spin squeezing test is satisfied (for principle spin operators) whilst the test [6] above is not. In [8] the spin entanglement test (<(DelSz)^2> > (1/N) (^2+^2) was based on a concept of entanglement inconsistent with the SP, but a revised treatment [4] leads to spin squeezing as an entanglement test. The sub-systems are now pairs of internal state modes, not particles - each pair only occupied by one boson. [1] S Bartlett, T Rudolph and R Spekkens, Rev. Mod. Phys. 79 (2007) 555. [2] C Simon, Phys. Rev. A 66 (2002) 052323. [3] S Bartlett, A Doherty, R Spekkens and H Wiseman, Phys. Rev. A 73(2006) 022311. [4] B Dalton, ArXiv Quant-ph 1305.0788 (2013). [5] F Verstraete and J Cirac, Phys. Rev. Letts. 91 (2003) 010404. [6] M Hillery and M Zubairy, Phys. Rev. Letts. 96 (2003) 050503. [7] M Hillery, H Dung and J Nisbet, Phys. Rev. A 80 (2009) 052335. [8] A Sorensen, L-M Duan, J Cirac and P Zoller, Nature 409 (2001) 63.

Fidelity susceptibility of the quantum Ising model in a transverse field
(Bogdan Damski)
It has been recently proposed that quantum phase transitions can be studied by looking at the overlap between two ground states calculated for two different external fields inducing a quantum phase transition. Such an approach is known as the fidelity approach to quantum phase transitions. Dramatic change of the system's properties across the critical point results in a drop of fidelity enabling both the location of the critical point and determination of the universal critical exponent characterizing divergence of the correlation length. In this talk I will discuss an exact closed-form expression for the so-called fidelity susceptibility of the quantum Ising model in the transverse field (i.e., the paradigmatic model of a quantum phase transition). I will also show an exact one-to-one correspondence between fidelity susceptibility in the ferromagnetic and paramagnetic phases of this model. The talk is based on B. Damski, Phys. Rev. E 87, 052131 (2013).

Spontaneous time-reversal symmetry breaking for spinless fermions on a triangular lattice
(Olivier Tieleman, Omjyoti Dutta, Maciej Lewenstein, André Eckardt)
As a minimal fermionic model with kinetic frustration, we study a system of spinless fermions in the lowest band of a triangular lattice with long-range repulsion. We find that the combination of interactions and kinetic frustration leads to spontaneous symmetry breaking in various ways. Time-reversal symmetry can be broken by two types of loop current patterns, a chiral one and one that breaks the translational lattice symmetry. Moreover, the translational symmetry can also be broken by a density wave forming a kagome pattern or by a Peierls-type trimerization characterized by enhanced correlations among the sites of certain triangular plaquettes (giving a plaquette-centered density wave). We map out the phase diagram as it results from leading order Ginzburg-Landau mean-field theory. Several experimental realizations of the type of system under study are possible with ultracold atoms in optical lattices.

Inhomogeneous quantum Kibble-Zurek mechanism
(Jacek Dziarmaga, Marek M. Rams)
We argue that in a second order quantum phase transition driven by an inhomogeneous quench density of quasiparticle excitations is suppressed when velocity at which a critical point propagates across a system falls below a threshold velocity equal to the Kibble-Zurek correlation length times the energy gap at freeze-out divided by $hbar$. This general prediction is supported by an analytic solution in the quantum Ising chain. Our results suggest, in particular, that adiabatic quantum computers can be made more adiabatic when operated in an "inhomogeneous" way.

Isolated Quantum Heat Engine
(Oleksandr Fialko and David Hallwood)
In this talk I will present our recent work, Phys. Rev. Lett. 108, 085303 (2012), where a theoretical and numerical analysis of a quantum system that is capable of functioning as a heat engine is studied. This system could be realized experimentally using cold bosonic atoms confined to a double well potential that is created by splitting a harmonic trap with a focused laser. The system shows thermalization, and can model a reversible heat engine cycle. This is the first demonstration of the operation of a heat engine with a finite quantum heat bath. I will also show that the same system can serve as a finite heat bath for a different particle coupled to it. This is used to study decoherence of the single particle fully quantum-mechanically.

Resonant Bose-Fermi Mixtures
(Elisa Fratini and Pierbiagio Pieri)
We consider a resonant Bose-Fermi mixture, namely an ultracold gas of bosons and fermions, with a strongly-attractive interaction between these two components. For sufficiently strong attraction, and a density of bosons smaller than the density of fermions, the boson condensation is completely suppressed even at zero temperature in favor of a phase with dominant molecular correlations. For very strong Bose-Fermi attraction the gas becomes a Fermi-Fermi mixture of fermionic molecules and unpaired fermions. Aim of the present work is to characterize such a "molecular" phase, by a thorough study of the spectral functions and associated quasi-particle dispersions and widths at zero temperature. We use a T-matrix diagrammatic approach and vary the boson-fermion attraction from the critical value where the condensate first disappears to the strongly attractive (molecular) regime. We study the effect of both mass- and density-imbalance on the spectral weights and dispersions. Our theoretical results could be verified experimentally with momentum resolved radio-frequency spectroscopy. We believe indeed that in the near future the powerful technique of radio-frequency spectroscopy, which lately has been applied to probe strongly interacting Fermi gases, may be applied to investigate successfully also Bose-Fermi mixtures.

Single Rydberg impurities in a Bose-Einstein-Condensate
( A.Gaj, J.B.Balewski, A.T.Krupp, D.Peter, H.P.Buechler, R.Loew, S.Hofferberth & T.Pfau)
Rydberg atoms are atoms with one or more electrons excited to a state with high principle quantum number. The Rydberg electron is only weakly bound to the core, making the Rydberg electron very susceptible to interaction with its environment. Nevertheless these highly excited states can survive in a dense environment, where one Rydberg atom can contain several thousands of ground state atoms [1]. We use the strong van der Waals interaction between two Rydberg atoms to isolate one single Rydberg atom at a state with high principle quantum number (n=100-200) in a Bose-Einstein condensate. The Rydberg electron can be treated as an impurity trapped by the positively charged Rydberg core and interacting with the condensate as a whole. We find that it can excite phonons and eventually set the condensate into a collective oscillation. We observe surprisingly long lifetimes and finite size effects due to the Rydberg orbit exploring the wings of the BEC at very high principal quantum numbers reaching n=200. We anticipate future experiments on electron wavefunction imaging, investigation of phonon mediated coupling of electrons and applications in quantum optics, as the Rydberg orbit contains an optically dense medium, which can couple strongly to light fields. [1] E. Amaldi and E. Segre, Nature 133, 141 (1934)

From composite fermionization to phase separation in small mixtures of ultracold bosons
(M.A. Garcia-March, B. Julia-Diaz, G. E. Astrakharchik, J. Boronat, Th. Busch, and A. Polls)
A mixture of a few weakly interacting ultracold atoms in a one dimensional trap is in the composite fermionization limit if the interactions among both components is large enough to promote the appearance of strong correlations in the ground state of the system. These strong correlations prevent the interaction between atoms in the two components. In this limit none of the species is completely condensed. We show that increasing the interaction in one of the species, we reach a second limit, the phase separated one, in which the weakly interacting species stays condensed at the centre of the trap, while in its edges stays the other strongly interacting species. The crossover between these two limits is sharp, as observed in the degree of condensation of the weakly condensed species. We also discuss other intermediate regimes, in which the interactions in one of the species is kept small, while the interactions in the other species and between species is tuned from small to large.

Quantum Hall States of Two-Component Bosons
(Tobias Grass, Bruno Julia-Diaz, Nuria Barberan, Maciej Lewenstein)
A huge variety of topological states can be realized by bringing bosons into the quantum Hall regime. This reaches from the well-known Laughlin state to more exotic fractional quantum Hall states with non-Abelian excitations. In the case of two-component bosons, the so-called non-Abelian spin singlet (NASS) states compete with composite fermion states and interacting integer quantum Hall states. Theoretical results are obtained by numerical diagonalization, restricted to small system sizes. This motivates to perform quantum simulations which can readily be realized by using cold atoms in artificial gauge fields. [1] T. Grass, B. Julia-Diaz, N. Barberan, M. Lewenstein, Phys. Rev. A 86, 021603(R) (2012) [2] B. Julia-Diaz, T. Grass, N. Barberan, M. Lewenstein, New J. Phys. 14, 055003 (2012)

Phase diagram of the two dimensional Fermi Hubbard model with synthetic spin orbit interaction
(Benoit Gremaud and Jiri Minar)
We study the 2D Fermi-Hubbard model in the presence of a synthetic gauge coupling of the spin orbit Rashba type, at half-filling. Using a real space meanfield theory, we numerically determine the ground state for different values of the gauge field parameters. For a fixed value of the gauge field, we observe that when the strength of the repulsive interaction is increased, the system first enters into an antiferromagnetic phase, then undergoes a first order phase transition to an itinerant magnetic phase. Depending on the gauge field parameter, this phase further evolves to the one predicted from the effective Heisenberg model obtained in the limit of large interaction strength (spiral phase, skyrmion...). Finally, we discuss the properties of these phases in a cold atoms experiment (harmonic trap, Raman laser imperfections...).

Simple quantum gate powered by Feshbach resonance
(Krzysztof Jachymski, Zbigniew Idziaszek and Tommaso Calarco)
We study the properties of a pair of identical fermions in a double well trap in the presence of a Feshbach resonance controlled by magnetic field. Due to the presence of the trap the center of mass and relative motion are coupled. We propose a scheme for realizing a quantum gate in this system using controlled Raman transitions. Utilizing the Feshbach resonance and Pauli exclusion principle, one can realize a simple effective Hamiltonian, which allows for suppressing losses. The fidelity of the gate can be enhanced by optimal control of the driving fields.

A correspondence between spontaneous solitons and Lieb-Liniger or Yang-Yang excitations
(Tomasz Karpiuk, Miroslaw Brewczyk, Mariusz Gajda and Kazimierz Rzazewski)
In the previous work [1] it has been shown that solitons occur generically in the thermal equilibrium state of a weakly-interacting elongated Bose gas, without the need for external forcing or perturbations. The present work focuses on establishing a link between these solitons and the Type II excitations in the Lieb-Liniger (L-L) model for low temperatures and the excitations in the Yang-Yang (Y-Y) model for higher temperatures. Namely we show that the number of solitons corresponds to the number of the Type II L-L excitations or the Y-Y excitations in low or high temperatures respectively. To do so we develop a new method of counting the number of solitons using the spectral density. [1] Phys. Rev. Lett. 109, 205302 (2012)

Condensate Phase Microscopy
(Arkadiusz Kosior, Krzysztof Sacha)
In time-of-flight images, obtained in a free expansion of initially trapped atoms in optical lattices, the information on the phase of a condensate wave-function is concealed because the images are related to initial distributions of atomic momenta. However, the initial atomic cloud is bounded and this information in addition to the time-of-flight images is sufficient in order to employ phase retrieval algorithms. We analyze the phase retrieval methods for model wave-functions, including a degenerate ground state.

Towards experimental realisation of dipolar quantum magnets
(Anna Kowalczyk, Mark Brannan and Kai Bongs)
Ultracold atoms allow us to control and manipulate the internal and external states of atoms and offer a unique tool to model quantum systems. Specifically, Bose-Einstein condensates (BEC) with additional spin degrees of freedom (so-called spinor condensates) can be used to explore quantum magnetism phenomena. We aim to produce spinor BECs in an optical lattice at ultralow magnetic field. In this regime, magnetic dipole interactions dominate the system and will allow us to study quantum many body phenomena and create dipolar quantum magnets. At ultralow magnetic field, ferromagnetic contact interactions coupled with a cigar-shaped trap geometry cause multiple spins to couple to each other and align, creating a single large spin for the whole atomic ensemble. The goal of this research is to investigate dipolar interactions using these large spin ensembles in order to understand dipolar quantum phases and dynamics, as well as affording the potential to build very sensitive magnetometers and gravimeters

The influence of the micromotion on the sympathetic cooling
(Michal Krych, Zbigniew Idziaszek)
In our research we try to understand the influence of the micromotion in the Paul traps on the interaction of the single ion with the ultracold gas and Bose-Einstein Condensate. The motivation for our investigation are the experiments made in Cambridge and Ulm. In order to trap an ultracold ion time-dependent trap is needed. Apart from the main effective harmonic frequency (secular motion) also the so called "micromotion" appears. Its influence on the interaction with the ultracold gas has not been calculated nor understood properly yet. It is observed in experiments that the ion can be sympathetically cooled or heated by the gas - depending on the atom-ion mas ratio and interaction strength. In case of increasing average energy of the ion - quantas of energy are transferred from the micromotion degree of freedom.

Distributing and concentrating entanglement on networks
(John Lapeyre)
Quantum information tasks require entangling widely separated systems. I examine this task on networks with a given initial distribution of entanglement over short ranges. In general, both operations that distribute, and that concentrate entanglement are required do produce long-range entanglement. Assumptions on the network topology and initial states dictate the figures of merit and optimal protocols. I will present progress on the minimum initial entanglement for regular lattices, as well as optimal protocols for complex networks. In the latter case, I give an exact calculation of entanglement resulting from combining distribution with one level of concentration from neighboring paths at the critical point on the Erdos-Renyi graph.

Dynamical coupling to higher Bloch bands - a study of few relevant examples
(Mateusz Łącki, Jakub Zakrzewski)
Often it is assumed that physics of ultracold atoms in the optical lattice potential is restricted to a single, lowest Bloch band (with obvious exception of the so-called orbital physics). Excitations to higher Bloch bands may be taken into account by exact iagonalization of the single-site problem, which yields also an effective single "dressed" band description, appropriate for quasistatic processes. Still time-dependent processes often require description involving many Bloch bands. We analyze exact description of the dynamics within multiband Bose Hubbard hamiltonian. We find that ordinary Bose-Hubbard time-dependent hamiltonian does not describe the dynamics reliably for fast dynamics. We propose terms that make this description quasi-exact. We compare results of evolution in the proposed equation of motion with ordinary time-dependent Schrodinger equation and find serious discrepancies. [1] Mateusz Lacki, Jakub Zakrzewski, Phys. Rev. Lett. 110, 065301 (2013)

On the superfluid response of a disordered Bose gas
(C. A. Müller)
According to a classical argument by Landau, superfluidity is characterized by the ability of condensed bosons to flow around obstacles without disspation. On the other hand, we know that spatial inhomogeneity reduces the superfluid fraction. Here, I revisit this tricky subject by calculating the superfluid fraction of disordered condensed bosons from the microscopic current-current response. We employ an inhomogeneous Bogoliubov theory (Gaul and Müller, PRA 2011) valid at large density and moderate interaction strength in any dimension, and derive analytical results for weak disorder.

Effect of correlated tunneling on the extended Bose-Hubbard model.
(Michal Maik, Philipp Hauke, Omjyoti Dutta, Jakub Zakrzewski, Maciek Lewenstein)
We study the influence of density dependent tunneling on the ground state phase diagrams of a two dimensional extended Bose Hubbard model. Using Quantum Monte Carlo simulations we see how the these diagrams are affected when the additional hopping term has the same or opposite sign as the regular hopping. By studying the interplay of the on-site repulsion, U, the nearest neighbor repulsion, V and the density dependent hopping, T, we show that the ground state phase diagrams differ significantly from the ones that are expected from the regular extended Bose-Hubbard model. Specifically we discuss the changes of the superfluid, supersolid and phase separated regions of the system.

Universality in condensation of exciton-polaritons
(Michal Matuszewski, Emilia Witkowska)
Phase transitions of second order taking place on a finite timescale exhibit a transition from adiabaticity to nonadiabaticity. Such phase transitions can lead to random formation of topological defects if symmetry is broken at the same time, as shown in numerous models ranging from the dynamics of the early Universe to liquid crystals. This process is described by the so-called Kibble-Zurek mechanism which provides power-law scalings due to the underlying universality. We consider the condensation of exciton-polaritons, which is an example of an uncommon phase transtion, in which the transition connects an intrinsically nonequlilbrium state to a quasi-equilibrium state. We show that this process can lead to the formation of domains of polaritons and uncondensed excitons, and demonstrate scaling laws that give an estimate for the number of created defects.

Impurity problem of a bilayer dipolar Fermi system.
(N. Matveeva and S. Giorgini)
We consider two-dimensional dipolar fermions in a bilayer configuration at zero temperature, where the dipole moments are polarized perpendicular to the planes. The top layer contains only one particle and the bottom layer has many particles. This system represents an interesting impurity problem with long-range anisotropic interactions. The partially attractive interaction between the impurity and fermions of the bottom layer leads to an effective mass of the impurity larger than its bare mass. Using the fixed node diffusion Monte Carlo method we calculate the chemical potential of the impurity, as well as its effective mass, as a function of the intra- and inter- layer interaction strength. The jump of the effective mass at the point of the liquid to crystal quantum phase transition is observed. In the strongly interaction regime the impurity is coupled with the eigenmodes of the triangular crystal which allows one to study the condensed matter models of electron-phonon interaction, such as the Frohlich polaron concept.

Quantum Optics of Strongly Correlated Systems
(Igor B. Mekhov)
Introducing quantum light and quantum optical methods into many-body systems of ultracold particles will lead to novel phenomena and methods of quantum control and simulations, which are unachievable using traditional approaches of quantum gases, trapped in prescribed potentials (e.g. optical lattices). While the latter treats light as an essentially classical tool, this work focuses on the phenomena, where the quantizations of light and ultracold atoms are both crucial. The results for bosonic atoms [1] can be generalized for ultracold molecules [2] and fermionic atoms. First, light serves as a quantum nondemolition (QND) probe of atomic or molecular states: the particle high-order correlation functions (beyond the density-density ones) and full counting statistics can be measured. We show that the angular diffraction pattern is richer than a classical one: e.g. light scattering from atoms in a 3D lattice shows non-trivial peaks, even if classical Bragg scattering is forbidden. We derive generalized Bragg conditions for intensity and quadrature measurements as well as for the multiple-beam configurations. Second, due to the light-matter entanglement, the measurement-based preparation of many-body states is possible (number squeezed, Schroedinger cat states, etc.). Light scattering constitutes the quantum measurement with controllable form of measurement back-action, allowing the dissipation tailoring in a strongly correlated system. Third, in cavity QED with quantum gases, the self-consistent solution for light and atoms is required, enriching quantum phases of atoms trapped in fully quantum potentials. For a review of this field cf. [1]. [1] I. B. Mekhov and H. Ritsch, Journ. Phys. B. 45, 102001 (2012) (Review). [2] I. B. Mekhov, Laser Phys. 23, 015501 (2013).

Measurement and control of polar molecules using trapped atomic ions
(J. Mur-Petit and J. J. Garcia-Ripoll)
We have studied a hybrid quantum system composed of a trapped ion and a polar molecule, and determined analytically its collective mode eigenfrequencies. Based on this, we propose a quantum protocol relying on the ion-dipole interaction and state-dependent forces to realize a quantum phase gate between them. I will discuss our calculations and present numerical results that demonstrate that this procedure can be used to determine the electric dipole moments of a broad range of heteronuclear molecules --from alkaline-earth hydrides such as CaH, to bialkali dimers as KRb-- trapped together with an atomic ion as Ca+. I will discuss several experimental approaches to build such hybrid setups, and potential application to molecular cooling, entangling ions and molecules, and mapping ordered phases of dipoles.

Dipole-dipole influenced Ramsey interferometry
(Laurin Ostermann, Helmut Ritsch and Claudiu Genes)
The presence of dipole-dipole interaction and collective dissipation can substantially alter the Ramsey signal obtained from an optical lattice atomic clock system. We investigate these effects in a treatment of the full system dynamics, both analytically and numerically. Further, we suggest different mechanisms geared towards particular geometries, which leverage these effects yielding an improvement in the overall signal quality and precision.

Spin-driven spatial symmetry breaking of spinor condensates in a double well
(Marina Melé-Messeguer, Simone Paganelli, Bruno Juliá-Díaz, Anna Sanpera, Artur Polls)
The properties of an F=1 spinor Bose-Einstein condensate trapped in a double-well potential are discussed using both a mean-field two-mode approach and a simplified two-site Bose-Hubbard Hamiltonian. We focus in the region of phase space in which spin effects lead to a symmetry breaking of the system, favoring the spatial localization of the condensate in one well. To model this transition we derive, using perturbation theory, an effective Hamiltonian that describes N/2 spin singlets confined in a double-well potential.

Finite temperature correlations in the 1D Bose gas
(Milosz Panfil and Jean-Sebastien Caux )
Understanding of dynamical responses in strongly correlated systems at finite temperatures, despite its experimental relevance, is still posing theoretical difficulties. We address this problem by studying the thermal density-density correlation function in the 1D Bose gas. Employing integrability of the model, the correlation function is precisely evaluated in large systems. We show how thermal fluctuations smother the critical, zero temperature behaviour of the correlation function. The presented results are in the experimentally accessible regime and are directly connected with the Bragg spectroscopy experiments. This work paves the way towards better understanding of dynamics of strongly correlated systems at finite temperature through the exact methods.

Entanglement of ultracold atoms in an optical cavity
(K. Pawłowski, J. Esteve, J. Reichel, A. Sinatra)
We discuss theoretically schemes to create useful entanglement in an ensemble of atoms trapped inside an optical cavity and interacting with a cavity mode. We consider two schemes: the pulsed scheme analyzed in [1] and a second scheme, where the cavity is continuously pumped with a coherent field. We study fundamental limits of the schemes and determine analytically the scaling of the squeezing after optimization over the squeezing time. We discuss the results in the light of possible experiments. [1] I. D. Leroux, M. H. Schleier-Smith, H. Zhang, and V. Vuletic, Phys. Rev. A 85, 013803 (2012)

Non-equilibrium quantum magnetism in a dipolar lattice gas
(A. de Paz , A. Sharma , A. Chotia , E. Marchal , J. H. Huckans , e P. Pedri , L. Santos , O. Gorceix , L. Vernac and B. Laburthe-Tolra)
Research on quantum magnetism with ultra-cold gases in optical lattices is expected to open fascinating perspectives for the understanding of fundamental problems in condensed-matter physics. Here we report on the first realization of quantum magnetism using a degenerate dipolar gas in an optical lattice. In contrast to their non-dipolar counterparts, dipolar lattice gases allow for inter-site spin-spin interactions without relying on super-exchange energies, which constitutes a great advantage for the study of spin lattice models. In this paper we show that a chromium gas in a 3D lattice realizes a lattice model resembling the celebrated t-J model, which is characterized by a non-equilibrium spinor dynamics resulting from inter-site Heisenberg-like spin-spin interactions provided by non-local dipole-dipole interactions. Moreover, due to its large spin, chromium lattice gases constitute an excellent environment for the study of quantum magnetism of high-spin systems, as illustrated by the complex spin dynamics observed for doubly-occupied sites.

Spin dynamic of two bosons in an optical lattice site
(J.Pietraszewicz, T.Sowinski, M.Brewczyk, M.Lewenstein, M.Gajda)
We study a spin dynamics of two magnetic Chromium atoms trapped in a single site of a deep optical lattice in a resonant magnetic field. Dipole-dipole interactions couple spin degrees of freedom of the two particles to their quantized orbital motion, therefore a trap geometry combined with two-body contact s-wave interactions influence a spin dynamics through the energy spectrum of the two atom system. Anharmonicity and anisotropy of the site results in a `fine' structure of two body eigenenergies. The structure can be easily resolved by a weak magnetic dipole-dipole interactions. As an example we examine the effect of anharmonicity and anisotropy of the binding potential on the Einstein-de Haas effect and, in general, demagnetization processes. We show that weak dipolar interactions provide a perfect tool for a precision spectroscopy of the energy spectrum of the interacting few particle system.

Ultracold atoms in optical lattices: beyond the Hubbard model
(S. Pilati, P. N. Ma, I. Zintchenko, X. Dai, M. Troyer)
Ultracold atomic gases trapped in optical lattices offer the possibility to study the intriguing quantum phenomena due to strong correlations in a clean and tunable experimental setup. In this work, we consider shallow optical lattices and analyze the combined effect of strong short-range interactions and weak external periodic potentials on the properties of quantum gases. In the case of bosonic atoms, we simulate the superfluid-insulator transition using a novel continuous-space QMC method and find excellent agreement with accurate experimental results obtained with a tunable Mott insulator. For fermions, we investigate the ferromagnetic transition of repulsive gases in optical lattices using both QMC methods and the computational tools (based on DFT) borrowed from materials science. As an outlook, we discuss how the development of DFT for ultracold Fermi gases can contribute to the understanding of the microscopic origins of quantum magnetism in strongly correlated materials and form a strong link between atomic physics and materials science.

XYZ quantum Heisenberg models with p-orbital bosons
(Fernanda Pinheiro, Georg M. Bruun, Jani-Petri Martikainen and Jonas Larson)
The possibility of experimentally accessing many-body quantum phenomena in the strongly correlated regime offers an excited platform for understanding quantum magnetism. As suggested long ago, it is now possible to engineer different systems in the lab that mimic the physics of theoretically challenging spin models, thereby performing 'quantum simulations'. Along these lines different setups which employ systems of trapped ions and cold atoms in optical lattices have been proposed. In this work we demonstrate that cold atoms in excited bands of a two-dimensional optical lattice provide an alternative route for quantum simulation with systems of cold atoms. In particular, we demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p-band of an optical lattice in the Mott regime. The sign and relative strength of the couplings characterizing the model are demonstrated to be experimentally tuneable. We discuss the phase diagram in the one dimensional case, and show that finite size effects relevant for trapped systems lead to devil's staircase structure. Finally, we discuss experimental issues related to preparation, manipulation and detection. [1] Fernanda Pinheiro, Georg M. Bruun, Jani-Petri Martikainen and Jonas Larson, arXiv:1304.3178 (2013).

Matter-Wave Interference versus Spontaneous Pattern Formation in Spinor Bose-Einstein Condensate
(Marcin Płodzień)
We report on the observation of matter-wave interference of spinor states in anti-ferromagnetic 87Rb Bose-Einstein condensate. The components of the F = 2 manifold are populated by forced Majorana transitions and then fall freely due to gravity in an applied magnetic field. Weak inhomogeneities of the magnetic field, present in the experiment, impose relative velocities to different mF components, which show up as interference patterns upon measurement of atomic density distributions with a Stern-Gerlach (SG) imaging method. The resulting matter-wave interference patterns can mimic spontaneous pattern formation in the antiferromagnetic quantum gas. We show that interference effects may appear in experiments even if gradients of the magnetic field components are eliminated but higher order inhomogeneity is present and the duration of the interaction is long enough.

Time-of-flight patterns of ultracold bosons in optical lattices in various Abelian artificial magnetic field gauges
(T. P. Polak, T. A. Zaleski)
I will show how to calculate the time-of-flight patterns of strongly interacting bosons confined in two-dimensional square lattice in the presence of an artificial magnetic field. I will discuss the cases with the artificial magnetic field being uniform, staggered or forming a checkerboard configuration. Effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The presented time-of-flight patterns may serve as a verification of chosen gauge in experiments, but also provide important hints on unconventional, non-zero momentum condensates, or possibility of observing graphene-like physics resulting from occurrence of Dirac cones in artificial magnetic fields in systems of ultra-cold bosons in optical lattices. Also, I elucidate on differences between effects of magnetic field in solids and the artificial magnetic field in optical lattices, which can be controlled on much higher level leading to effects not possible in condensed matter physics. T. P. Polak, T. A. Zaleski, Phys. Rev. A 87, 033614 (2013)

Compact mixture of degenerate quantum gases
(Katerine Posso-Trujillo, Holger Ahlers, Ernst M. Rasel, and Naceur Gaaloul)
Recent proposals in atom optics rely on long-lived samples of ultra-cold matter. Having compact sources (no more than mm range in radius) is necessary to prevent decoherence over long times and more strictly dephasing due to the spatial extension of the sample. A possible solution is to use the $\delta$-kick technique to collimate the expanding BEC source, however this technique has to be adapted to the case of a quantum mixture. During this talk, we will provide a clear method for preparing a mixture of 85Rb/87Rb which stays compact for several seconds. The recipe includes the production of a miscible and stable mixture of the two Rb isotopes. The $\delta$-kick cooling of both with realistic parameters of magnetic fields used, and laser beams.

Dynamical generation of nontrivial lattices for topologically insulating states
(O. Dutta, A.Przysiężna, M.Lewenstein)
Non-trivial lattice geometries are at the heart of many exotic phenomena in solid-state physics such as topologically insulating states. Therefore search of materials with non-trivial lattice geometries is an important aspect of present research directions in solid-state physics. In the field of ultracold gases, there are ongoing studies to create such lattices artificially by using optical means. We theoretically propose a general method of creating non-trivial lattice geometries dynamically. We study a mixture of strongly attractive two-species fermions trapped in a square optical lattice and show that the strong interaction induces emergence of non-trivial lattice structures by self-organization of the ultracold gas. The lattice generated this way can host topologically insulating states such as Quantum Anomalous Hall states and/or Quantum Spin Hall states. Our theoretical considerations are supported by investigation of necessary experimental conditions to realize such states. We believe that our proposal opens up another fascinating route for experimental and theoretical studies of systems where particles live in interaction-induced emergent structures with exotic dispersion relations. The method is very general and can be extended to other lattice structures. Moreover our proposal gives potential facilitation for the experimental realization of topological insulator. Namely it does not involve additional optical components other than the ones needed for creating the parent lattice.

Trapping cold neutral atoms with a nanofiber for a hybrid quantum system
(S. Ravets, J.E. Hoffman, F. Fatemi, G. Beadie, P. Kordell, S.L. Rolston, L.A. Orozco)
Optical nanofibers show great promise in the design, integration, and interconnection of nanophotonic devices. When the diameter of the waveguide becomes smaller than the wavelength, there exists an intense evanescent component propagating outside of the waveguide, providing a platform for probing non-linear physics or light-matter interaction. We explore uses of atoms trapped in the evanescent optical field near a 500-nm diameter nanofiber for the creation of a hybrid quantum system by magnetically coupling to a superconducting circuit. In this talk, we demonstrate transmissions greater than 99.9% for the fundamental mode and 97% for the first family of excited modes through an optical nanofiber. We achieve efficient guidance by selecting the adapted fiber and by controlling the taper angle, allowing us to better meet adiabaticity. We present a novel spectrogram measurement of mode beating during the fiber pull that allows characterization of the modes excited.

Stationary stated of trapped spin-orbit coupled condensates
(Emmi Ruokokoski, J. A. M. Huhtam"aki, M. M"ottonen)
In the presence of Rashba-Dresselhaus-type spin-orbit coupling, the low-energy stationary states of pseudospin-1 Bose-Einstein condensates exhibit exotic nature. In our studies we found that for experimentally feasible parameters and strong spin-orbit coupling, the ground state is a square vortex lattice irrespective of the nature of the spin-dependent interactions. For weak spin-orbit coupling, the lowest-energy state may host a single vortex. Furthermore, we showed that the distinct stationary states can be observed experimentally by standard time-of-flight spin-independent absorption imaging.

Artificial gauge fields in extra dimensions
(Julius Ruseckas, Gediminas Juzelūnas, Ian Spielman, Alessio Celi, Pietro Massignan, Maciej Lewenstein)
Recently it was suggested to extend the dimension of optical lattices by using atomic internal degrees of freedom as an extra dimension [1]. Here we demonstrate that one can engineer a two-dimensional lattice with nonzero synthetic magnetic flux using atoms in a standard one-dimensional optical lattice. The additional dimension appears due to laser-assisted transitions between the atomic sub-levels in the ground state manifold. The synthetic magnetic flux is generated by a combination of an ordinary tunnelling in the real space and laser-assisted transitions characterised by the complex amplitudes in the extra dimension. A distinctive feature of the proposed scheme is the sharp boundaries in the extra dimension, a feature that is difficult to implement for the atoms in optical lattices in the real-space. The boundaries of the extra dimension can be closed down using additional laser-assisted transitions. Closing the boundaries of the extra dimensions leads to a remarkably simple realisation of the fractional (Hofstadter butterfly-type) spectrum.

Universal Superfluid Transition and Transport Properties of Two-Dimensional Dirty Bosons
(Giuseppe Carleo, Guilhem Boeris, Markus Holzmann, and Laurent Sanchez-Palencia)
We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, using large-scale finite temperature quantum Monte Carlo simulations. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior and strictly vanishes only at zero temperature. Our results do not show any evidence of a finite-temperature localization transition, and point towards the existence of Bose bad-metal phase as a precursor of the Bose-glass phase.

Precision measurement of ultracold collisions in 87Rb
(A.I. Sidorov)
We employ a BEC prepared in a superposition of two hyperfine states (|1> = |F = 1,m=−1> and |2> = |F = 2, m=+1>) for precision measurement of s-wave scattering lengths and the energy of the most weakly bound state (25 MHz) in 87Rb molecules. Long-lasting collective oscillations are excited via the transfer of a small fraction of atoms to state |2> and conveniently described by an effective 1D treatment. We fit the temporal dependence of the oscillating BEC width with GPE simulations using a converging iteration procedure. Accurate measurements of the axial trap frequency and of the state |2> oscillations make possible a measurement of the ratio a12/a11 = 0.97616(16) and of the inter-state scattering length a12 = 98.006(16)a0. To measure the intra-state scattering length a22 we perform two Ramsey interferometric sequences with variable areas of the first pulse (pi/10 and pi/2). By fitting the GPE simulations to the evolution of Ramsey fringes we extract the value a22 = 95.44(7)a0. We employ the radiofrequency-induced association of condensed atoms in states |1> and |2> at magnetic fields < 3.5 G to measure the energy of the most weakly bound state and provide data to improve parameters of the 87Rb molecular potentials.

Beyond pure state entanglement for atomic ensembles
(Julia Stasińska, Simone Paganelli, Anna Sanpera)
We analyze multipartite entanglement between atomic ensembles within quantum matter-light interfaces. In our proposal, a polarized light beam crosses sequentially several polarized atomic ensembles impinging on each of them at a given angle. These angles are crucial parameters for shaping the entanglement since they are directly connected to the appropriate combinations of the collective atomic spins that are squeezed. We exploit such a scheme to go beyond the pure state paradigm proposing realistic experimental settings to address multipartite mixed state entanglement in continuous variables.

Detection of Fisher information for mesoscopic quantum states
(Helmut Strobel, Wolfgang Muessel, Daniel Linnemann, Luca Pezze, Eike Nicklas, Jiri Tomkovic, Ion Stroescu, Maxime Joos, David B. Hume, Augusto Smerzi, Markus K. Oberthaler)
A very general classification of quantum states is the quantum Fisher information. It can be calculated from the density matrix which is experimentally accessible by state tomography. For a mesoscopic number of particles full state tomography with the necessary precision cannot be implemented in our system. Instead, we use the fact that the Fisher information is the key parameter quantifying possible sensitivity beyond the standard quantum limit in a phase estimation protocol. We will present the realization of collective states of binary Bose-Einstein condensates with about 350 atoms and the analysis of their interferometric performance which gives a lower bound on the Fisher information. Our method is able to show that the Fisher information surpasses the shot-noise limit in a regime where no spin squeezing is present and thus reveals multiparticle entanglement.

Double Universality of a Quantum Phase Transition in Spinor Condensates: Modification of the Kibble-Żurek Mechanism by a Conservation Law
(Tomasz Świsłocki, Emilia Witkowska, Jacek Dziarmaga, and Michał Matuszewski)
We consider a phase transition from an antiferromagnetic to a phase separated ground state in a spin-1 Bose-Einstein condensate of ultracold atoms. We demonstrate the occurrence of two scaling laws, for the number of spin domain seeds just after the phase transition, and for the number of spin domains in the final, stable configuration. Only the first scaling can be explained by the standard Kibble-Żurek mechanism. We explain the occurrence of two scaling laws by a model including postselection of spin domains due to the conservation of condensate magnetization.

High-temperature pulsed supersonic source of cadmium molecular beam: Towards production of entangled cadmium atoms.
(Tomasz Urbanczyk, Jaroslaw Koperski )
Recently, in the Group of Molecular Spectroscopy and Quantum Information at Jagiellonian University, the high-temperature pulsed supersonic source of cadmium molecular beam was developed and successfully tested [1]. The source, which can operate in temperatures up to 1000K, is a crucial part of an experiment in which entangled cadmium atom pairs are produced by photodissociation of ((^111)Cd)_2 cadmium dimers in a process of stimulated Raman transition (SRT) and detected in two-step excitation-ionisation (TPEI) process [2]. During the talk the main idea of the experiment as well as the recent progresses in its realization will be discussed. By choosing of appropriate working parameters of the source (e.g., temperature, nozzle diameter and pressure of the carrier gas it can be used in production of different cadmium complexes [i.e., those including Cd_2 and CdRg (Rg=rare gas)] in ground electronic energy state ready for spectroscopic research. The presentation will also include results of rotational spectroscopy of Cd_2 and CdAr dimers. Plans for the future will also be presented. [1] T. Urbanczyk, J. Koperski, Rev. Sci. Instrum. 83 (2012) 083114. [2] T. Urbanczyk, M. Strojecki, M. Krosnicki, J. Koperski, Opt. Appl. 42 (2011) 433.

Accurate effective Hamiltonians via unitary flow in Floquet space
(Albert Verdeny Vilalta, Andreas Mielke and Florian Mintert)
Periodically driven quantum systems can be effectively described by a time-independent Hamiltonian provided that the driving is sufficiently fast. The suitable driving of a system allows one to simulate essentially any desired Hamiltonian. However, the identification of such effective Hamiltonians for given driving parameters is a big theoretical challenge. We present a systematic construction of effective Hamiltonians of periodically driven quantum systems and its application to shaken optical lattices. With this, we are able to explain the experimentally observed deviation of expected suppression of tunneling of ultra-cold atoms and describe an optimal scheme to simulate flat-band systems, a paradigm of strong correlations. The static effective Hamiltonian and the actual periodically time-dependent Hamiltonian are related to each other by a periodic unitary transformation that needs to be identified. We pursue this with Floquet theory and relate time-dependence of a Hamiltonian with an interaction of the associated Floquet operator. This allows us to translate the quest for effective Hamiltonians to the identification of a transformation that brings the Floquet operator into a non-interacting form. With the method of flow equations we show that this can be done systematically in a high frequency expansion, so that we can identify effective Hamiltonians with desired accuracy.

Theory for twin matter waves experiments
(T. Wasak, P. Szańkowski, J. Chwedeńczuk, M. Trippenbach)
We review the Bogoliubov theory in the context of recent experiments, where atoms are scattered from a Bose-Einstein Condensate into two well-separated regions. We find the full dynamics of the pair-production process, calculate the correlation functions and show that the system is ideally number-squeezed. We calculate the Fisher information to show how the entanglement between the atoms from the two regions changes in time. We then apply our theory to the "twin-beam" experiment described in R. Bucker et al., Nat. Phys. 7, 608 (2011).