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Ab-initio Modeling of Cold Gases November 11, 2009 - November 13, 2009 CECAM-ETHZ, Zurich, Switzerland Lode Pollet LMU Munich, Germany Tilman Esslinger Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland Antoine Georges College de France and Ecole Polytechnique, France, France Alejandro Muramatsu University of Stuttgart, Germany 1 Description We will first outline the state of the art of experiments on cold atoms in an optical lattice. We will then show how numerics are useful for these systems, and finally discuss how successful numerical studies have been, which is the keystone of this proposal. Since the seminal paper by Greiner et al. [1], showing the transition from the superfluid to the Mott-insulating phase in the Bose-Hubbard model, physicists have realized that modeling strongly-interacting systems in the atomic physics lab is feasible. The field had started with the theoretical prediction by Jaksch et al., showing theoretically that this model could indeed be analyzed realistically in experiments [2]. The key observation was that the atom-photon interactions could be used and controlled in such a way that the Bose-Hubbard model can be realized for a sufficiently long time and at sufficiently low temperature. Systems consisting of atoms in an optical lattice have the advantage over strongly-interacting systems of (1) being ultra-clean, (2) the interaction couplings are controllable, and (3) the type, mass and density of the atoms are controllable. Having the possibility to change the parameters of the Hamiltonian at will makes these systems prime candidates for building a quantum analog computer. On the negative side, the detection of (neutral) atoms is more difficult than detection in condensed matter physics, the temperature is relatively high (e.g., in units of the Fermi temperature for fermionic systems present experiments operate on the scale of 0.1 ), there are no phonons since the lattice is built by laser light, and there is an external harmonic trapping potential. Experimental progress has been rapid. The most recent advances include the observation of the Mott-instulating phase in the Fermi-Hubbard model [2] and the observation of the superexchange mechanism in a two-well system [3]. These experiments have mostly been explained qualitatively so far. Further progress is only possible when lower temperatures are reached and better detection schemes developed, but also when current experiments are better understood quantitatively, and this is where numerics become useful. In particular for the bosons, the theory is well understood and the numerical algorithms (Quantum Monte Carlo) very powerful. The so-called 'worm algorithm' is at present able to address the Bose-Hubbard model from first principles and for realistic system sizes [4]. Previous studies addressed individual aspects of the experiments, such as the role of the trapping potential, the role of entropy in fixing the temperature and the influence of the time-of-flight duration [5]. Fully ab-initio studies took off approximately a year ago and are still going on, with promising first results. The overall agreement is close to excellent, but it turns out that there are deviations which are not completely negligible though controllable. They hint at experimental imperfections, such as density variations, lattice laser calibration uncertainties, heating, and losses of atoms. Estimating the importance of such effects accurately has now become available thanks to the large-scale simulations. For the fermions, such numerical methods as DMFT [6] and high-temperature series expansions [7] addressed the recent observation of the Mott-insulating state. Fermions are intrinsically harder to handle experimentally than bosons. The Mott-insulating state has only been observed experimentally over the last few months [2]. Numerical studies using Dynamical Mean Field Theory (DMFT) and high-temperature series expansions have already appeared [8, 2], but finding a quantity that clearly indicated the transition is hard to find. Temperature and out-of-equilibrium effects are more serious concerns here than for the bosons. It is clear that much more numerical and experimental work is needed before consensus can be reached in the community. Numerical studies have also looked at lower temperatures, trying to see where anti-ferromagnetism sets in [8]. At these temperatures the numerical methods are no longer exact, but the approximations need further assessment. Experimental studies have also been undertaken to measure critical exponents. The critical exponent of the correlation length of the U(1) transition between a normal and a condensed three-dimensional Bose gas was measured [9]. The Berezinskii-Kosterlitz-Thouless for a two-dimensional Bose gas was also successfully studied experimentally [10]. A full numerical study taking the trapping potential, temperature, heating, and detection schemes into account is numerically challenging and largely open.Key references [1] M. Greiner, O. Mandel, T. Esslinger, T. W. Haensch, and I. Bloch, Nature 415, 39 (2002). [2] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998). [3] R. Joerdens, N. Strohmaier, K. Guenter, H. Moritz, and T. Esslinger, Nature 455, 204 (2008) ; U. Schneider et al, cond-mat/0809.1464 (2008). [4] S. Foelling et al, Nature 448, 1029 (2007), S. Trotzky et al., Science 319, no. 5861, 295 (2008). [5] N. V. Prokofev,B. V. Svistunov, and I. S. Tupitsyn, Sov. Phys. JETP 87, 310 (1998); Phys. Lett. A 238, 253 (1998). [6] L. Pollet, K. Collath, K. Van Houcke, and M. Troyer, New Journal of Physics 10, 065001 (2008); F. Gerbier et al., accepted for publication in Phys. Rev. Lett., cond-mat/0808.2212 (2008). [7] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996). [8] J. Oitmaa et al., Series Expansion Methods for Strongly Interacting Lattice Models, Cambridge University Press, Cambridge, 2006. [9] L. De Leo, C. Kollath, A. Georges, M. Ferrero, and O. Parcollet, cond-mat/0807.0790 (2008); V. W. Scarola, L. Pollet, J. Oitmaa, and M. Troyer, cond-mat/0809.3239 (2008). [10] T. Donner, S. Ritter, T. Bourdel, A. Oettl, M. Koehl, and T. Esslinger, Science 315, 1556 (2007) [11] Z. Hadzibabic, P. Krueger, M. Cheneau, B. Battelier, and J. B. Dalibard, Nature 441, 1118 (2006); New Journal of Physics 10, 045006 (200). 2 Program Day 1 - Wednesday November 11, 2009 Session 1 chair : tilman esslinger • 8:30 to 8:40 - Welcome • 8:40 to 9:15 - Presentation - Cheng Chin Emergence of mott insulating phase of ultracold atoms in an optical lattice • 9:15 to 9:40 - Presentation - Nandini Trivedi Single atom addressability and mapping the finite temperature phase diagram of the bose hubbard model • 9:40 to 10:05 - Presentation - Matthias Troyer Validating a quantum simulator • 10:05 to 10:30 - Presentation - Sebastian Huber The inverted kagome lattice: frustrated bosons without superexchange Session 2 chair : lode pollet • 11:05 to 11:30 - Presentation - Andrew Daley An atomic colour superfluid via three-body loss • 11:30 to 11:55 - Presentation - Nikolay Prokofev Diagrammatic monte carlo: what happens to the sign-problem? • 11:55 to 12:20 - Presentation - Stefan Wessel Spin liquid phase in the hubbard model on the honeycomb lattice Session 3 chair lode pollet • 14:20 to 14:55 - Presentation - Henning Moritz Studying the fermi-hubbard model with cold atoms • 14:55 to 15:20 - Presentation - Lorenzo De Leo Trapping and cooling fermionic atoms into mott and neel states • 15:20 to 15:45 - Presentation - Vito Scarola Discerning incompressible and compressible phases of cold atoms in optical lattices • 15:45 to 16:10 - Presentation - Andreas Ruegg From fermi's golden rule to rabi oscillations: dynamical unbinding transition in a periodically driven mott insulator Colloquium by randy hulet 16.45 - 18.00 Free evening Day 2 - Thursday November 12, 2009 Session 4 chair alejandro muramatsu • 8:45 to 9:20 - Presentation - Frederic Chevy Weighing a particle immersed in a fermi sea • 9:20 to 9:45 - Presentation - George Batrouni Pairing in mass and/or population imbalanced fermion systems • 9:45 to 10:10 - Presentation - Andreas Läuchli Pairing properties of population imbalanced fermions with two and three flavors Session 5 chair alejandro muramatsu • 11:00 to 11:35 - Presentation - Robert Loew Long-range interacting rydberg atoms • 11:35 to 12:00 - Presentation - Vincent Liu Cold atoms and molecules in elongated wannier orbitals • 12:00 to 12:25 - Presentation - Hans Peter Büchler Feshbach resonance in an optical lattice Session 6 chair fabian hassler • 15:00 to 15:35 - Presentation - Fabrice Gerbier Implementing artificially engineered gauge potentials in a lattice • 15:35 to 16:00 - Presentation - Iacopo Carusotto Non-equilibrium many-body physics in quantum gases of interacting photons • 16:00 to 16:25 - Presentation - Ignacio Cirac Projected entangled-pair and plaquette states Session 7 chair fabian hassler • 16:55 to 17:30 - Presentation - Simon Foelling Fully resolved optical imaging of a 2d quantum gas • 17:30 to 17:55 - Presentation - Tommaso Roscilde "escaping from the trap" : extracting bulk properties of strongly correlated systems from measurements on trapped ultracold gases • 17:55 to 18:20 - Presentation - Eugene Demler Probing many-body physics with ultracold atoms Poster session starting at 18:30 Day 3 - Friday November 13, 2009 Session 8 chair boris svistunov • 8:45 to 9:20 - Presentation - Ulrich Schneider Ultracold fermionic atoms in optical lattices: out-of-equilibrium experiments in- and • 9:20 to 9:45 - Presentation - Sebastian Schmidt Strongly correlated polaritons on a lattice • 9:45 to 10:10 - Presentation - Fabian Heidrich-Meisner The sudden expansion of interacting fermions in one dimensional optical lattices • 10:10 to 10:35 - Presentation - Kristian Baumann Observation of a non-equilibrium dicke-type quantum-phase transition Session 9 chair antoine georges • 11:05 to 11:40 - Presentation - Randy Hulet Phase diagram of a spin-imbalanced fermi gas in 1d • 11:40 to 12:05 - Presentation - Marcos Rigol breakdown of thermalization in finite one-dimensional systems • 12:05 to 12:30 - Presentation - Vladimir Gritsev Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench Session 10 chair lode pollet • 14:15 to 14:40 - Presentation - Sankar Das Sarma Localization in one-dimensional cold atomic gases • 14:40 to 15:05 - Presentation - Ehud Altman Bosons in disordered 1d traps: a new paradigm for the superfluid-insulator transition? • 15:10 to 15:35 - Presentation - Boris Svistunov Disordered commensurate bosons: 20-year-old conjectures are now theorems End of conference 3 Abstracts Emergence of Mott insulating phase of ultracold atoms in an optical lattice Cheng Chin Unviversity of Chicago, USA We present direct measurement of atomic density profiles in an optical lattice across the superfluid-Mott insulator quantum phase transition.High resolution absorption imaging is used to probe the “ wedding-cake” structure of a trapped gas as it crosses the phase boundary at finite temperature. Detailed analysis of images yields measurements of temperature and local compressibility; for the latter we observe a strong suppression deep in the Mott-insulating phase, which is recovered for the superfluid and normal phases. Furthermore, we measure spatially resolved fluctuations and correlations. Results in the superfluid, insulator and quantum critical regime will be discussed. Single atom addressability and mapping the finite temperature phase diagram of the Bose Hubbard Model Nandini Trivedi Ohio State University, USA I will discuss recent results of large scale QMC simulations of the bose Hubbard model with ~10^6 particles in a trap using the worm algorithm. I will focus on mapping the finite temperature phase diagram using kinks in the local compressibility.I will also discuss thermodynamic and frequency-dependent properties for the fermion Hubbard model with attractive and repulsive interactions, using determinantal or auxiliary field QMC plus analytic continuation methods. I will end with open questions related to the physics and computational techniques for these problems. Validating a quantum simulator Matthias Troyer Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland The inverted kagome lattice: frustrated bosons without superexchange Sebastian Huber, Ehud Altman Weizmann Institute, Israel The route to quantum magnetism in ultracold atom systems is obstructed by the difficulties of reaching low enough temperatures of the order of the superexchange coupling J. The prospect of simulating the square lattice antiferromagnet, and its expected descendant, the d-wave superconductor arouse a lot of current interest. Here we want to show how a frustrated "quantum magnet" can be obtained with bosons in an inverted kagome lattice without the need for temperatures that are much smaller than the hopping t. We discuss a possible experimental setup and the rich zoo of phases which can be expected in this system: ranging from glassy arrangements of localized states over a coexisting density-wave--superfluid phase to the exp(3 i phi) condensate. An atomic colour superfluid via three-body loss Andrew Daley University of Innsbruck, Austria We discuss how three-body loss, which is ubiquitous and typically undesirable in cold gases experiments can be used to generate an effective three-body hard-core constraint, preventing three atoms from occupying the same lattice site. This mechanism not only serves to suppress the occurance of actual three-body losses, but generates interesting many-body physics due to the effective three-body interactions.We first consider this mechanism in the context of bosonic atoms, where suppression of three-body occupation can stabilise the system with attractive two-body interactions, and gives rise to a superfluid phase of dimers. We then discuss the case of three-body loss in a three-component Fermi gas, where suppression of three-body occupation of lattice sites can stabilise phases with BCS pairing by suppressing the formation of trimers. Via a master equation treatment, we study the full dynamics including loss, both to test how well real three-body losses are suppressed, and to determine schemes to produce interesting many-body states in the presence of loss. We treat the master equation essentially exactly for 1D systems by combining time-dependent DMRG techniques with quantum trajectories methods from quantum optics. Diagrammatic Monte Carlo: what happens to the sign-problem? Nikolay Prokofev University of Massachusetts at Amherst, USA Feynman diagrams are the most celebrated and powerful tool of theoretical physics usually associated with the analytic approach. I will argue that diagrammatic expansions are also an ideal numerical tool with enormous and yet to be explored potential for solving interacting many-body systems by direct simulation of Feynman diagrams for the proper self-energies and polarization operators up to high order. Though the original series based on bare propagatorsare sign-alternating and often divergent one can determine the answer behind them by using proper series re-summation techniques and working with skeleton diagrams, i.e. by making the entire scheme self-consistent. The first results for the resonant Fermi gas and the Fermi-Hubbard model at U/t=4 away from half-filling prove that this approach is promising. Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice Stefan Wessel University of Stuttgart, Germany Employing projective quantum Monte Carlo simulations, we study the ground state phase diagram of the fermionic Hubbard model on the honeycomb lattice at half-filling. We provide evidence for a intervening phase separating the weak-coupling semi-metal and the antiferromagnetically ordered phase at strong coupling. In this intermediate interaction region, the system exhibits finite quasi-particle and spin excitation gaps, without long-range magnetic or bond-order nor superconductivity being developed. Several proposals on novel phases in related models have been put forward, whereas our simulations exhibit a spin liquid - even in the absence of magnetic frustration. Studying the Fermi-Hubbard model with cold atoms Henning Moritz ETH Zurich, In a solid material strong interactions between the electrons can lead to surprising properties. A prime example is the Mott insulator, where the strong repulsive interaction make it energetically very unfavorable to place two fermions of opposite spin on the same lattice site. Hence, a Mott insulator is characterized by insulating behavior, incompressibility and a strong reduction of double occupancy. The physics of this paradigm of strong correlations is well captured by the celebrated Hubbard model, which is widely used to describe strongly interacting electrons in a solid. In my talk I will present experiments in which we have realized theFermi-Hubbard model with ultracold atoms and investigated equilibrium and non-equilibrium properties. Due to the intrinsic purity of the experimental system we can directly compare the experimental results with theory. I will focus on precision measurements of the double occupancy, which - whencompared with DMFT or high-temperature series expansion - can serve as a thermometer. The far-from equilibrium dynamics of such strongly correlated systems is mostly unchartered territory and I will present experimental and theoretical results revealing the importance of higher order processes for thermalization. Trapping and Cooling Fermionic Atoms into Mott and Neel States Lorenzo De Leo Ecole polytechnique Paris, France We perform a theoretical study of a fermionic gas with two hyperfine states confined to an optical lattice. We derive a generic state diagram as a function of interaction strength, particle number, and confining potential. We discuss the central density, the double occupancy, and their derivatives as probes for the Mott state, connecting our findings to recent experiments.Using entropic arguments we compare two different strategies to reach the antiferromagnetic state in the presence of a trapping potential and propose an experimental procedure to cool fermionic atoms to the required temperatures. Discerning Incompressible and Compressible Phases of Cold Atoms in Optical Lattices Vito Scarola Virginia Polytechnic Institute and State University, USA Experiments with cold atoms trapped in optical lattices offer thepotential to realize a variety of novel phases but suffer fromsevere spatial inhomogeneity that can obscure signatures of newphases of matter and phase boundaries. Optical lattice realizationsof the Fermi-Hubbard model are of particular interest because oftheir connection to models of high temperature superconductors. Iuse a high temperature series expansion to show that compressibilityin the core of a trapped Fermi-Hubbard system is related tomeasurements of changes in double occupancy. This corecompressibility filters out edge effects, offering a direct probe ofcompressibility independent of inhomogeneity. A comparison withrecent experiments is made. From Fermi's Golden rule to Rabi oscillations: Dynamical Unbinding Transition in a Periodically Driven Mott Insulator Andreas Ruegg The University of Texas at Austin, USA Modulation spectroscopy has been used in several experiments to study cold atomic gases in optical lattices. We present analytical work on the dynamical generation of double occupancy in Fermi systems described by a single-band Hubbard model. Thereby, the amplitude of the periodic modulation (as compared to the single-particle band-width) allows us to distinguish two different regimes: For weak modulation, the rate of change in the number of doubly occupied sites is explained by a "Fermi's golden rule"-like analysis. For strong modulation, coherent Rabi oscillations between a doublon-holon pair and a singlet are expected. In this talk we show that reducing the modulation strength reveals a dynamical unbinding transition where doublon and holon are free to separate. This transition marks the boundary to the intermediate regime where both coherent and incoherent features are present. Weighing a particle immersed in a Fermi sea Frederic Chevy LKB - ENS Paris, France Recent experiments on Fermi gases with imbalanced spinpopulations have attracted considerable attention to the problem of an impurity immersed in a Fermi sea, an extension of the so-calledpolaron problem of condensed matter physics, where an electron isimmersed in a bath of (bosonic) phonons. Theoretical investigationshave demonstrated that, even in the regime of strong interactions,this "Fermi-polaron" was actually behaving like a free particle, butwith renormalized physical properties (like its chemical potentialand mass). In this talk, we will show how the latest experiments onultra-cold Fermi gases have confirmed this picture. In particular, wewill discuss how recent measurements made at ENS on the breathing mode of a spin polarized Fermi gas gave us access to the effective mass of the Fermi-polaron. Pairing in mass and/or population imbalanced Fermion systems George Batrouni , I will discuss pairing in fermionic systems on optical lattices with mass and/or population imbalance. This will be done in the context of the attractive fermionic Hubbard model using Quantum Monte Carlo methods. I will argue that, in the ground state, the dominant pairing mechanism is at nonzero center of mass momentum, i.e. FFLO. If the mass imbalance is large enough, spatial collapse of the system results. Finite temperature effects will also be discussed. Pairing properties of population imbalanced fermions with two and three flavors Andreas Läuchli Max Planck Institute for Physics of Complex Systems, Dresden, We discuss the superfluid pairing properties of attractively interacting fermions on a one-dimensional optical lattice. For the case of two flavors, we employ Bethe-Ansatz results and DMRG simulations to reveal an extended region of FFLO type pairing, where the superfluid is formed by Cooper pairs carrying finite momentum and discuss the effect of FFLO pairing on noise correlation spectra. In the case of three flavors there is competition between three different FFLO modes, which exhibits an interesting interaction and imbalance dependence. Furthermore the system is unstable towards collapse and phase separation at strong attraction, essentially due to a dynamical mass imbalance effect. Long-range interacting Rydberg atoms Robert Loew University of Stuttgart, Germany We report on a strongly interacting frozen Rydberg gas excited from a ultracold trapped ensemble of Rubidium atoms. This system can be described by a spin Hamiltonian where the long-range strong repulsive van der Waals interaction is responsible for novel manybody physics. Universal scaling behaviour due to an underlying quantum phase transition based on the socalled Rydberg blockade is observed [1,2]. [1] R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, T. Pfau "Evidence for coherent collective Rydberg excitation in the strong blockade regime" Phys. Rev. Lett.. 99, 163601 (2007). [2] R. Löw, H. Weimer, U. Raitzsch, R. Heidemann, V. Bendkowsky, B. Butscher, H. P. Büchler, and T. Pfau "Universal scaling in a strongly interacting Rydberg gas" arXiv:0902.4523 (2009). Cold atoms and molecules in elongated Wannier orbitals Vincent Liu, K. Sun and E. Zhao University of Pittsburgh, USA We show that topological phases with fractional excitations can risein two-dimensional ultracold dipolar gases on a particular class ofoptical lattices. Due to the dipolar interaction and lattice confinement, a quantum dimer model emerges naturally as the effective theory describing the low energy behaviors of these systems under well-controlled approximations. Using a nonstandard optical lattice consisting of periodically arranged double-well potentials, we identify the elongated wavefunction at each site with an ``orbital dimer'', and map the problem to dimer covering of the dual lattice. The hard core constraint of the quantum dimer model is enforced by the dipolar interactions, and the desired hierarchy of interaction energy scales is achieved by controlling the anisotropy of the orbital dimers. Experimental realization and detection of various phases are discussed. Work done in collaboration with K. Sun and E. Zhao, with support from U.S. DOE and U.S. ARO. Feshbach resonance in an optical lattice Hans Peter Büchler University of Stuttgart, Germany Cold atomic gases in optical lattices represent a perfect laboratory system for the quantum simulation of strongly correlated many-body systems described by Hubbard models. Recently, experimental and theoretical efforts focus on the observation of a Fermionic Mott insulator, and the ultimate goal towards the realization of magnetic and superconducting phases. The quantitative understanding of these experimental results and the comparison with the theoretical predictions require a precise knowledge of the parameters in the Hubbard model for cold atomic gases interacting with a Feshbach resonance. We present the solution to the two-particle problem in an optical lattice interacting via a Feshbach resonance, and provide a microscopic derivation of the parameters in the Hubbard model and the two-particle bound state energies. Implementing artificially engineered gauge potentials in a lattice Fabrice Gerbier Laboratoire Kastler Brossel, ENS, Paris, France TBA Non-equilibrium many-body physics in quantum gases of interacting photons Iacopo Carusotto Universita'' de Trento, Italy Experiments have recently started providing evidence for a variety of non-equilibrium many-body effects in gases of interacting photons in nonlinear optical cavities. In this talk, I will review the present status of the experiments as well as of their theoretical understanding. Analogies and differences with standard systems such as liquid Helium and ultracold atoms will be illustrated. New developments in the direction of exploring the peculiar phases that originate from the interplay of strong correlations with the non-equilibrium condition will be discussed. Projected Entangled-Pair and Plaquette States Ignacio Cirac, F. Mezzacapo, N. Schuch, A. Sfondrini, M. Sanz, V. Murg, M.C. Banuls, F. Verstraete Max-Plank Institute for Quantum Optics, Garching, Germany We will report on the latest numerical results using differenttechniques which combine PEPS and Monte Carlo Methods. We haveapplied those techniques to frustrated spin systems and cold atomicgases. Fully resolved optical imaging of a 2D quantum gas Simon Foelling Harvard University, USA With ultracold quantum gases, very idealized implementations of complex many-body systems can be realized in order to closely model fundamental hamiltonians. In addition, these systems can enable the realization of tools for manipulating and probing the gaswhich are not available for classical condensed matter systems. I will present our experiment that enables the preparation of a cold quantum gas in a single, strongly two-dimensional trapping potential. This potential is located a few micrometers from a glass surface, allowing for optical access with an extremely high numerical aperture. This enables us to image and manipulate the quantum gas with a resolution on the scale of 500,nm. We cangenerate optical lattices by direct projection through the lens and detect the atoms with fluorescence imaging inside the trap. In this way, we can detect individual atoms in each lattice site with high fidelity, allowing for complete site-resolved readout of the quantum state, with all degrees of freedom known for the detected atoms. "Escaping from the trap" : extracting bulk properties of strongly correlated systems from measurements on trapped ultracold gases Tommaso Roscilde ENS Lyon, France Ultracold gases trapped in optical potential enable to literally implement fundamental models of strongly correlated systems, realizing Feynman's visionary proposal of a "quantum analog simulator". Despite the high tunability of the Hamiltonians realized e.g. by ultracold bosons in optical lattices, a major drawback is represented by the high inhomogeneity of the system, due to the presence of an overall trapping potential. Here I will describe a proposal to "get rid of the trap" by performing realistic local measurements in the trap center, and by using in turn the trapping potential to achieve a fine control on the chemical potential of the system. This measurement scheme, together with conventional time-of-flight measurements, enables to characterize the phasediagram of the Hamiltonian implemented in the system without the trap and in the grand-canonical ensemble. In particular I will present the application of this method to the measurement of the detailed phase diagram of the Bose-Hubbard model on a simple lattice, as well as in an external (periodic or random) potential. Probing many-body physics with ultracold atoms Eugene Demler Harvard, USA TBA Ultracold Fermionic Atoms in optical lattices: Experiments in- and out-of-equilibrium Ulrich Schneider LMU Munich, Germany Ultracold fermionic atoms in an optical lattice represent a versatilequantum simulator for correlated electrons in a solid, as they allow for a clean and defect-free implementation of the Fermi Hubbard model with tunable perameters. In this talk, I present experimental and theoretical data concerning in- and out-of-equilibrium properties of interacting fermionic atoms in a blue detuned optical lattice, which allows for an independent control of lattice depth and additional harmonic confinement. For repulsive interactions, we studied the crossover from a metallic into a Mott insulating regime and compared our results with a DMFT calculation. In addition, I present measurements in the attractive Hubbard model, where we observed an anomalous expansion of the atomic cloud in the pseudogap regime of the BEC-BCS crossover. These measurements represent a new possible way to investigate the properties of low entropy phases using a high entropy sample. Furthermore, ultracold atoms offer the possibility to control all relevant parameters in real time during the experiment. By suddenly changing the harmonic confinement at constant lattice depth we could create a particular out-of-equilibrium situation which allows us to study transport properties of the Hubbard model. Strongly correlated polaritons on a lattice Sebastian Schmidt ETH Zurich, Switzerland Motivated by the recent success of engineering light-matter interaction in cavity QED and trapped ion systems, we investigate the superfluid-insulator transition of polaritons (i.e. quasiparticles which form through the interaction of a single bosonic mode with a quantum two-level system) as described by the Jaynes-Cummings-Hubbard model. Using a diagrammatic linked-cluster expansion in the Mott regime and a slave-boson approach in the superfluid regime we calculate quantum phase diagram,critical exponents and excitation spectra of both phases.The presence of additional conversion modes in the Mott phase and an anomaly of the sound velocity as a function of detuning in the superfluid phase signal clear deviations from Bose-Hubbard like behaviour and can be attributed to the composite nature of polaritons. The sudden expansion of interacting fermions in one dimensional optical lattices Fabian Heidrich-Meisner RWTH Aachen, Germany Time-dependent phenomena in ultracold atomic gases are currently attracting a lot of attention, as such phenomena give insights into nonequilibrium properties of interacting particles. We analyze the example of the sudden expansion of fermions in an optical lattice. Our main focus is on the case in which the initial state has a strong admixture of double occupancies. We promote the notion of quantum distillation: during the expansion, and in the presence of strongly repulsive interactions, doublons group together, forming a nearly ideal band insulator, which is metastable with a low entropy. Our analysis employs the density matrix renormalization method, and we present results for experimentally observable quantities such as the radius of the particle cloud. We suggest that the quantum distillation effect could be used for cooling purposes in experiments with two-component Fermi gases. Heidrich-Meisner, Manmana, Rigol, Muramatsu, Feiguin, Dagotto: arXiv:0903.2017 Heidrich-Meisner, Rigol, Muramatsu, Feiguin, Dagotto: Phys. Rev. A 78, 013620 (2008) Observation of a Non-Equilibrium Dicke-Type Quantum-Phase Transition Kristian Baumann ETH Zurich, Switzerland The Dicke Model describes the interaction between N two level atoms and a single electromagnetic field mode which remains a fundamental problem in quantum optics. In the thermodynamic limit the system was predicted to undergo a quantum phase transition from a normal to a superradiant phase. Here we present a non-equilibrium realization of the Dicke model in a Bose-Einstein condensate coupled to a high-finesse optical cavity. The superfluid atoms collectively coupled a far-detuned transverse pump field to an empty cavity mode. The atoms self-organize into an emergent checkerboard pattern above a critical pump power. When entering this self organized phase, the gas initially maintains phase coherence and can thus be regarded as a supersolid. Over a wide range of parameters, the boundary of this novel quantum phase is mapped out and compared to a theoretical model. This work opens up new aspects of quantum many-body physics with global interactions mediated by the cavity field. Phase Diagram of a Spin-Imbalanced Fermi Gas in 1D Randy Hulet, Yean-an Liao, Ann Sophie Rittner, Tobias Paprotta, Wenhui Li, Stefan Bauer and Erich Mueller Rice University, USA We have obtained the phase diagram of a spin-imbalanced Fermi gas and compared it with theory. Approximately 105 6Li atoms are trapped in a two-dimensional array of 1D tubes formed from a 2D optical lattice. A weak axial harmonic potential confines ~100 atoms per tube. The entire tube bundle is optically imaged, and analyzed to determine the phase boundaries. We find that the gas phase separates axially into a central partially polarized region, and outer regions that are either fully paired, for small population imbalance, or fully polarized for larger imbalance. The locations of these boundaries are in good quantitative agreement with theory. Phase separation in 1D is inverted in comparison with 3D, where the fully paired region is in the center. We are exploring the crossover from 1D to 3D by lowering the lattice depth. Finally, we also plan to investigate the nature of the partially polarized phase, which is predicted to be a modulated FFLO superfluid. Breakdown of thermalization in finite one-dimensional systems Marcos Rigol Georgetown University, USA Little more than fifty years ago, Fermi, Pasta, and Ulam (FPU) set up a numerical experiment to prove the ergodic hypothesis for a one-dimensional lattice of harmonic oscillators when nonlinear couplings were added. Much to their surprise, the system exhibited long-time periodic dynamics with no signals of ergodic behavior. Those results motivated intense research, which ultimately gave rise to the modern chaos theory and to a better understanding of the basic principles of classical statistical mechanics. More recently, experiments with ultracold gases in one-dimensional geometries have challenged our understanding of the quantum domain. After bringing a nearly isolated system out of equilibrium, no signals of relaxation to the expected thermal equilibrium distribution were observed. Some of those results can be understood in the framework of integrable quantum systems, but then it remains the question of why thermalization did not occur even when the system was supposed to be far from integrability. In the latter regime, thermalization is expected to occur and can be understood on the basis of the eigenstate thermalization hypothesis. In this talk, we utilize quantum quenches to describe how the transition between thermalization and its absence occurs in finite one-dimensional lattices. We find the latter to be a smooth process in which the predictions of standard statistical mechanics continuously worsen as one approaches the integrable point. We establish a direct connection between the presence or absence of thermalization and the validity or failure of the eigenstate thermalization hypothesis, respectively. Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench Vladimir Gritsev Universite de Fribourg, Switzerland We study the unitary time evolution of antiferromagnetic order in anisotropic Heisenberg chains that are initially prepared in a pure quantum state far from equilibrium. Our analysis indicates that the antiferromagnetic order imprinted in the initial state vanishes exponentially. Depending on the anisotropy parameter, oscillatory or non-oscillatory relaxation dynamics is observed. Furthermore, the corresponding relaxation time exhibits a at the critical point, in contrast to the usual notion of critical slowing down, from which a maximum is expected. P. Barmettler et al, Phys. Rev. Lett. 102, 130603 (2009) Localization in one-dimensional cold atomic gases Sankar Das Sarma University of Maryland, USA Bosons in disordered 1d traps: a new paradigm for the superfluid-insulator transition? Ehud Altman Weizmann Institute of Science, Israel Ultracold bosons in one dimensional traps are typically weakly interacting, whereas the disorder potential generated e.g. by microfabricated "atomchips", is highly tunable. How is superfluidity destroyed in such a system with increasing disorder strength? Giamarchi and Schulz famously describe one possible transition [Europhys. Lett. 3, 1287 (1987)] . However their analysis is perturbative and strictly valid only for weak disorder and tunable interactions, opposite of the natural regime of cold atoms. Using a strong randomness RG approach we show that the transition in a typical atomic system is very different than the weak disorder scenario. In marked contrast to the latter, it occurs at a non universal value of the correlation exponent (Luttinger parameter). Rather, the critical point is marked by universal mezoscopic fluctuations in physical observables including the critical current and the correlation exponent. We show how signatures of the transition may be detected with interference experiments. Disordered Commensurate Bosons: 20-Year-Old Conjectures Are Now Theorems Boris Svistunov, V. Gurarie, L. Pollet, N.V. Prokof'ev, and M. Troyer University of Massachusetts at Amherst, USA We prove the theorem of inclusions stating that in the presence of generic bounded disorder there exist rare, but arbitrarily large, regions of the competing phase across the generic transition line. We argue that the only non-generic phase transitions are the Griffiths-type ones, driven by rare regions in which disorder emulates some regular external perturbation. An immediate implication of the theorem of inclusions is the absence of direct superfluid-to-gapped-insulator quantum phase transitions. With an enhanced version of the theorem of inclusions we prove finite compressibility (and thus relevance of disorder) on the critical line of superfluid to Bose glass transition. The exceptional role of the Griffiths-type transitions implies that the transition from Mott insulator to any gapless insulator should be inevitably of this type.Quantum dynamics in ultracold atomic gases Corinna Kollath Ecole Polytechnique, Switzerland Recent experimental developments increased the interest in quantum systems far from equilibrium. In particular, the good tunability of ultracold quantum gases now allows for a rapid change of the system parameters and the observation of the subsequent quantumevolution decoupled from the environment. For example the non-adiabatic dynamics across thesuperfluid-Mott-insulating phase transition has been realized inbosonic gases confined to optical lattices. The theoretical description of these time-dependent phenomena is very involved. We discuss the response of these strongly correlated quantum systems to differentparameter changes as a change in their interaction strength. DYNAMICS OF BOSONS IN OPTICAL LATTICES IN THE PRESENCE OF MODULATED TRAPS Rosario Fazio Scuola Normale Superiore, Pisa, Italy I will present our results on the behavior of bosons in optical lattices confined in time-dependent traps. I first consider the case of dipole oscillations induced by displacing the trap center of a few lattice sites [2]. Depending on the system parameters this motion can vary from undamped to overdamped. The dipole oscillations as a function of the lattice displacement, the particle density and the strength of interparticle interactions were studied by means of DMRG calculations. I will then present the case in which the frequency of the trap is modulated periodically in time [2] allowing to probe the dynamical compressibility of the system. Also in this case the results of the DMRG calculation will be compared with experiments. 4 Posters Diagrammatic Monte Carlo method for bosonic impurity problems Peter Anders Institute for Theoretical Physics, Switzerland We present a continuous-time Monte Carlo method for bosonic impurity models which allows the study of bosonic lattice models within the recently developed bosonic dynamical mean field (B- DMFT) framework. The method is based on a Monte Carlo sampling of a perturbation expansion in the hybridization functions as well as the condensate wave function. It allows us to solve the B-DMFT equations and to calculate the Green’ s function for various temperatures and coupling parameters. As an application we present the finite temperature B-DMFT phase diagram for the bosonic Hubbard model on the Bethe lattice. Dynamical simulations of infinite chains using Matrix Product States Mari-Carmen Banuls, M. B. Hastings, F. Verstraete and J. I. Cirac Max Planck Insitute of Quantum Optics, Garching, Germany Techniques based on Matrix Product States, as DMRG, have provenextremely successful for the numerical simulation of ground states inthe case of one dimensional systems. When the quantities of interestare not static, but one wants to simulate out-of-equilibrium dynamics,the applicability of such methods is limited to very short times, ingeneral.We propose a new method, based on a transverse contraction ofthe tensor network, which allows the calculation of time dependentexpectation values and dynamical correlation functions for infinitetranslationally invariant chains to much longer times than any otherexisting method. The technique is applicable to a broad range ofproblems, including finite systems, and also periodic infinite chainsand impurity models, among others. M.C. Banuls, M. B. Hastings, F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 102, 240603 (2009). Observation of a Self-Organized Quantum Phase Kristian Baumann, C. Guerlin, F. Brennecke, T. Esslinger ETH Zurich, Switzerland We experimentally investigate a non-equilibrium quantum phase transition in an open system formed by a Bose-Einstein condensate and an ultrahigh-finesse optical cavity. The superfluid atoms collectively couple a transverse pump field, formed by a standing-wave laser beam, to an empty cavity mode. Above a critical pump intensity the cavity field builds up in a Dicke-type phase transition accompanied by self-organization of the atoms in an emergent checkerboard pattern. The Bose-Einstein condensate acquires a density modulation reflecting a reduced symmetry compared to the underlying mode structure of the cavity and pump field. When entering the self-organized phase the gas initially maintains its first-order spatial coherence, and can thus be regarded as a supersolid, similar to those proposed for two-component systems. Thereafter dephasing sets in, yet it is possible to retrieve a Bose-Einstein condensate when lowering the pump intensity again. For a wide range of parameters the boundary of this novel self-organizedquantum phase is mapped out and compared to a theoretical model. This work opens up new aspects of quantum many-body physics with global interactions, and provides the first experimental realization of an effective Dicke Hamiltonian including counter-rotating coupling terms. Variational wave functions for Mott insulators Federico Becca International School for Advanced Studies (SISSA) and CNR-DEMOCRITOS IOM, Italy We give a review of recent developments on the possibility to have a faithful representation of strongly correlated systems by using improved variational wave functions. In particular, we focus the attention on the bosonic Hubbard model, where the numerically exact solution is known by Monte Carlo simulations, which allow us to assess the variational accuracy. We show how it is possible to describe the superfluid-insulator transition by using the Gutzwiller wave function supplemented with a long-range Jastrow factor. An appealing interpretation in terms of the binding-unbinding Kosterlitz-Thouless transition is obtained through the mapping onto a classical model. Finally, the case with long-range interactions will be also briefly discussed. Polar Molecules with Three-Body Interactions on the Honeycomb Lattice Lars Bonnes Institute for Theoretical Physics III, University of Stuttgart, Germany Motivated by a recent proposal on using polar molecules in optical lattices driven by microwave fields to induce strong three-body interactions (H. P. B"uchler et al., Nature Physics 3, 726 (2007)), we analyze the quantum phase diagram of the boson Hubbard model with nearest neighbor three- and two-body repulsions using quantum Monte Carlo simulations. In particular, we consider a honeycomb lattice, where three-body repulsions lead to degenerate classical regions at various unconventional lattice fillings. Furthermore, we consider the interplay of twoand three-body repulsions for the experimentally relevant parameter regime, and find evidence for an cascaded transition to the checkerboard solid for finite two-body repulsions. Cavity Optomechanics with a Bose-Einstein Condensate Ferdinand Brennecke, K. Baumann, C. Guerlin, S. Leinss, S. Ritter, T. Donner, T. Esslinger ETH Zurich, In our experiment we couple a Bose-Einstein condensate with anultrahigh-finesse optical cavity. The tremendous degree of control over atomic gases achieved in Bose-Einstein Condensates combined with the rich field of cavity quantum electrodynamics opens access to a wealth of new physics. In the dispersive regime, our system realizes a model of cavity optomechanics. This research field typically studies the coupling of the mechanical motion of one of the cavity mirrors to the light field. In our case, the mechanical oscillator is given by a coherent density modulation of the atomic cloud. We have observed this density modulation and strong optical nonlinearities, present at the single photon level. Furthermore our mechanical oscillator naturally starts inits ground state, from which a single motional excitation can cause a shift of the cavity resonance on the order of the cavity linewidth. Our system is promising to study the quantum regime of cavity optomechanics. Multi-particle composites in density-imbalanced quantum fluids Evgeni Burovski, Giuliano Orso and Thierry Jolicoeur LPTMS, Universite Paris-Sud, France We consider two-component one-dimensional quantum gases with density imbalance. While generically such fluids are two-component Luttinger liquids, we show that if the ratio of the densities is a rational number, p/q, and mass asymmetry between components is sufficiently strong, one of the two eigenmodes acquires a gap. The gapped phase corresponds to (algebraic) ordering of (p+q)-particle composites. In particular, for attractive mixtures, this implies that the superconducting (FFLO) correlations are destroyed. We illustrate our predictions analytically for a dipolar gas and numerically for the fermionic Hubbard model with hopping asymmetry. arXiv:0904.0569 arXiv:0907.1533 Three Species Fermi Gas in 2D Optical Lattice with Dynamic Constraint Soon-Yong Chang University of Innsbruck, Austria We present analysis of the attractively interacting three species Fermi gas in the 2D optical lattice with the dynamically imposed three body constraint by using a variational many body method. We discuss crossing of symmetries in the ground state and the pairing. We also discuss experimental implications. Single site addressability in optical lattices Marc Cheneau Max Planck Institute for Quantum Optics, Germany xperiments with optical lattices have so far suffered from an important drawback: it has been impossible to probe or to manipulate the atoms at the level of a single lattice site, while maintaining a sufficiently tight spacing to allow for a nearest neighbour coupling through tunnelling. For quantum processing, this means that only simple algorithms have been implemented, in which the same operation was applied to all pairs of qubits. In condensed matter-like experiments, this lack of a local probe also constitutes a severe limitation as dilute gases are intrinsically inhomogeneous (trapped), meaning that any measurement performed on a macroscopic scale inevitably leads to a blurred, incomplete characterisation of the system. Our new experimental setup allows for single site addressability of bosonic atoms in a tight optical lattice, thanks to a specially designed lens system with a resolution smaller than the lattice spacing. Using this new tool, it is possible to observe and manipulate density, spin structure, and correlations at the scale of a lattice site. This will allow us to investigate steady-state and dynamical properties of low-dimensional systems, such as spin-charge separation, which were out of reach of previous experiments. We also plan to engineer fast, high-fidelity, quantum gates and to build massively entangled systems as a resource for quantum computation. Effects of Ground Hyperfine Energy Separation on Quantum Computation and Frequency Standard GOPAL DIXIT TECHNICAL UNIVERSITY MUNICH, Germany The quantum information processing (QIP) is one of the interesting areas in physics which is gaining momentum both in theoretical and experimental fronts in the recent days. The single valence ions, particularly the ones with 2S1/2 ground state are being chosen for QIP studies [1] to encode qubits into the ground state hyperfine levels. These levels are chosen due to their relatively long lifetimes against spontaneous decay rates and long phase coherence because of their small energy separations. The hyperfine studies help us understanding the nuclear structure of an atom and its influence on the short range wavefunctions. Recently trapped and laser cooled ions are excellent candidates for many high precision measurements [2, 3]. Due to the decoupling of the internal states caused by the collisions and Doppler shifts, trapped and laser-cooled ions have been regarded as nearly isolated quantum systems [4]. Therefore, precise measurements of hyperfine transition frequencies of several species of trapped ions have been performed, which lead to develop the better frequency standard in microwave and optical frequency regions [5-7]. Experiments on singly ionized trapped and laser-cooled cadmium (Cd+1) ions and zinc (Zn +1) have raised their potential for applications in quantum computing and information processing [8]. Besides, both the ions are promising candidate for new frequency standard in microwave region [5]. It is, therefore, of great importance to have precise study of the hyperfine energy separations of ground as well as few excited states of those ions. However, rare accurate ab initio many-body estimations are available in literature of these properties. Here I will present about the above applications and our recent studies [8, 9] of these properties using highly correlated relativistic coupled cluster technique using single, double and partial triple excitations. Contributions of different correlation effects, like core-core, core-polarization and core-valence correlations, will be discussed in details. 1. R. Ozeri et al., Phys. Rev. A 75, 042329 (2007). 2. P. K. Ghosh, Ion Traps: Oxford Science Publications (Oxford: Clarendon) (1995). 3. D. J. Wineland and W. M. Itano, Phys. Today 40, 34 (1987). 4. U. Tanaka et al., Phys. Rev. A 53, 3982 (1996). 5. U. Tanaka et al., Appl. Phys. B 78, 43-47 (2004). 6. B. M. Jelenkovic et al., Phys. Rev. A 74, 022505 (2006). 7. K. Matsubara et al., Appl. Phys. B 76, 209 (2003). 8. B.B. Blinov, D.L. Moehring, L.M. Duan and C. Monroe, Nature (London) 428, 153 (2004) 8. Gopal Dixit et al., Phys. Rev. A 77, 012718 (2008). 9. Gopal Dixit et al., J. Phys. B 41, 025001 (2008). DMFT simulations of ultracold fermions in optical lattices Elena Gorelik University of Mainz, Germany Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal, repulsive on-site interactions U>0. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory usingmultigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., should beaccessible to experiments. In addition, we present spectral functions and discuss the properties of a novel "semi-compressible" state observed for large U near half filling. We also present first results for two-flavor systems in a harmonic potential using a QMC implementation of the real-space DMFT approach. In particular, we show the gradual melting of a central antiferromagnetic phase with increasing temperature in 2 dimensions. Equilibrium and out of equilibrium studies of ultracold fermions in an optical lattice Daniel Greif ETH Zurich, Switzerland In our experiment we use a two component Fermi gas in a 3D optical lattice to realize the Fermi-Hubbard model. This clean approach offers the advantage of posing well defined questions and accessing clean probes. Here we present recent measurements of equilibrium and out of equilibrium properties of this model system. Tuning the interaction via a Feshbach resonance over a broad range we investigate the crossover from a metallic to Mott insulating state. This is signaled by a drastic reduction of double occupancy and the appearance of a gapped mode in the doublon spectrum probed by lattice modulation. The resolution in double occupancy of our most recent measurements allows for precise comparison with both DMFT calculations and high-temperature series expansions. The remarkable agreement allows us to determine the temperature, which reaches values on the order of the tunneling energy T~t. If the lattice modulation is sufficiently weak, the increase of doublons with time is well captured by linear response theory. In this regime the buildup rate of doublons is a measure for equilibrium properties such as the temperature sensitive local spin ordering, which could in principle be used to detect anti-ferromagnetic ordering. For long modulation times the system is driven into a far from equilibrium state with many additional doublons. We show that the dominant decay mechanism is a high-order scattering process and the doublon lifetime depends exponentially on the ratio of onsite interaction to tunneling energy. Creating and modifying Feshbach resonances with rf radiation Thomas Hanna, Adam Kaufman, Russell Anderson, David Hall, Eite Tiesinga and Paul S. Julienne NIST, USA We have developed a method for studying the modification of scattering properties of atoms in the vicinity of a Feshbach resonance, including the effects of strong rf radiation for which multiphoton effects are significant. Apart from known atomic properties, only three input parameters are required to construct a complete model of Feshbach resonances: the singlet and triplet scattering lengths, and the coefficient of the long range van der Waals potential. We apply our technique to collisions of 87Rb, which has several resonances around 9 G and 18 G. As the rf frequency or amplitude change, the bound states causing the different resonances can be coupled together, leading to rich variation of the scattering properties with magnetic field, and rf frequency and amplitude. Our calculations quantitatively reproduce experimental data for 87Rb. We also study the creation and manipulation of 6Li resonances with rf radiation, and suggest regimes in which rf could be a useful tool for manipulating scattering properties. The BCS-BEC crossover and the disappearance of FFLO-correlations in a spin-imbalanced, one-dimensional Fermi gas Fabian Heidrich-Meisner, A.E. Feiguin, U. Schollwoeck, W. Zwerger RWTH Aachen, Germany We present a numerical study of the one-dimensional BCS-BEC crossover of a spin-imbalanced Fermi gas. The crossover is described by the Bose-Fermi resonance model in a real space representation. Our main interest is in the behavior of the pair correlations, which, in the BCS limit, are of the Fulde-Ferrell-Larkin-Ovchinnikov type, while in the BEC limit, a superfluid of diatomic molecules forms that exhibits quasi-condensation at zero momentum. We use the density matrix renormalization group method to compute the phase diagram as a function of the detuning of the molecular level and the polarization. As a main result, we show that FFLO-like correlations disappear well below full polarization close to the resonance. The critical polarization depends on both the detuning and the filling. Preprint arXiv:0908.3074 Momentum distribution, renormalization factor, and effective mass of the two-dimensional electron gas Markus Holzmann LPTL, Jussieu, Paris, France We calculate the momentum distribution of the Fermi liquidphase of the homogeneous, two-dimensional electron gas. We showthat, close to the Fermi surface, the momentum distribution ofa finite system with $N$ electrons approaches itsthermodynamic limit slowly, with leading order correctionsscaling as $N^-1/4$. These corrections dominate theextrapolation of the renormalization factor, $Z$, and thesingle particle effective mass, $m^*$, to the infinite systemsize. We show how convergence can be improved analytically. Inthe range $1 le r_s le 10$, we get a lower renormalizationfactor $Z$ and a higher effective mass, $m^*>m$, compared tothe perturbative RPA values. M. Holzmann, B. Bernu, V. Olevano, R.M. Martin, and D.M. Ceperley, Phys. Rev. B 79, 041308(R) (2009). Diagrammatic Monte Carlo for the Hubbard Model Evgeny Kozik ETH Zurich, United Kingdom We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Using perturbative Feynman diagrams (rather than skeleton, or ``bold-line'', graphs) for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory. We find that going from single site to large clusters is essential for obtaining the same level of accuracy as provided by DiagMC. Fermionic Projected Entangled Pair States Christina Kraus Max-Planck Institut für Quantenoptik, Garching, Germany We introduce a family of states, the fPEPS, which describes fermionic systems on lattices in arbitrary spatial dimensions. It constitutes the natural extension of another family of states, the PEPS, whichefficiently approximate ground and thermal states of spin systems with short-range interactions. We give an explicit mapping between those families, which allows us to extend previous simulation methodsto fermionic systems. We also show that fPEPS naturally arise as exact ground states of certain fermionic Hamiltonians. We give an example of such a Hamiltonian, exhibiting criticality while obeyingan area law. Luttinger liquid of trimers in Fermi gases with unequal masses Giuliano Orso, Evgeni Burovksi, and Thierry Jolicoeur LPTMS, University of Paris South, France An experimentally hot topic in the field of ultra-cold atoms is the study of Fermi mixtures where the standard BCS pairing mechanism is frustrated. Can a gas be superfluid if the number of up and down fermions is different ? What is the nature of superfluidity when pairing occurs between two different species, say Li-K ?In this respect, one dimensional (1D) systems are particularly interesting. First they stabilize exotic phases that are extremely fragile in higher dimensions, like the celebrated Fulde Ferrell Larkin Ovchinnikov (FFLO) state. Second, powerful numerical methods allow to go beyond mean field theories and unveil new effects. Here I present some recent theoretical work [1] on attractive fermions in a 1D optical lattice with unequal tunneling rates, corresponding to different effective masses for the two components. In the presence of mass asymmetry, the microscopic model is no longer integrable and multi-particle bound states appear. Here I will focus on trimers, namely three-body bound state made of one light and two heavy fermions. I will first present the solution of the three-body problem, yielding the binding energy and the effective mass of a single trimer. I will then show that, undercertain conditions, trimers can dramatically affect the properties of a many-body system, leading to a suppression of FFLO correlations and topological changes in the grand-canonical phase diagram. Experimental signatures of trimers in cold atoms experiments will be discussed. [1] G. Orso, E. Burovski and T. Jolicoeur, arXiv:0907.1533 Superfluid Transition of an interacting Bose gas in a random potential: a Path Integral Monte Carlo study Sebastiano Pilati The Abdus Salam International Centre for Theoretical Physics, Italy We study the superfluid transition of an Interacting Bose gas in thepresence of correlated disorder using Path Integral Monte Carlo techniques based on the Worm Algorithm. Disorder is introduced into the system by a 3D speckle potential whose intensity and correlation length can be varied at will. We determine the critical temperature, chemical potential and density as a function of the disorder intensity. We observe that disorder causes a reduction of the critical temperature. This effect diminishes for increasing inter-particle repulsion. In the regime of strong disorder, we show the behavior of the density profiles, of the condensate and of the superfluid fraction as a function of the temperature and of the interaction strength. We observe that in the weakly interacting limit the gas localizes in the deepest wells on the external field and has no long-range order. Strong inter-particle repulsion can delocalize the system and increase the superfluid component. Finally, we study the equation of state of the exotic normal phase that we observe at low temperatures in the presence of strong disorder. Pfaffian state(s) simulation in Spin-1 Optical Lattices Matteo Rizzi, L. Mazza, M. Rizzi, M. Lewenstein, J.I. Cirac Max Planck Institut für Quantenoptik - Garching, Germany We investigate the possibility of simulating bosons subject to an infinite three-body contact repulsion, and to an external magnetic field, with experimentally feasible cold atoms setups. The need for three local degrees of freedom drives the attention to spin-1 atomic Mott insulator with filling factor 1. A proper perturbative treatment, and a coupling to auxiliary F=2 ancillas, allows to identify a regime where the mapping holds. Such a scheme can be used to investigate Pfaffian states, introduced in the context of Quantum Hall effect by Moore and Read. They indeed arise if particles are constrained to be not more than two in a single place. They are known to support non-abelian topological excitations; moreover, they are claimed to be the underlying pairing mechanism in p+ip superconductors. Their bosonic version displays a QH filling factor u=1, i.e. one particle for each quantum of magnetic flux. Up to now, the long quest for them has not yet produced experimental fingerprints. At dilute enough limit of our discretized system, topological properties are conserved. With the help of Chern numbers and ground state degeneracy, we show that even increasing the magnetic field these properties should not be abruptly washed out. The proposed scheme thus opens a route towards the study of exotic states and non-abelian quasi-excitations with cold atomic quantum simulators. Probing a Mott insulator of cold atoms by dynamically generating double occupancy Andreas Ruegg, S. D. Huber The University of Texas at Austin, USA Modulation spectroscopy has been used in several experiments to study cold atomic gases in optical lattices. We present analytical work on the dynamical generation of double occupancy in Fermi systems and propose a "Fermi's golden rule"-like expression to quantify the rate of change in the number of doubly occupied sites due to a periodic modulation of the hopping amplitude. Using different approximative methods we aim at a qualitative understanding of this rate in a wide parameter regime. We find that conclusive evidence for a Mott phase can be inferred from such a measurement. Spectral functions of one-dimensional quantum liquids Mikhail Zvonarev LPTMS, France I will report on a theoretical progress in understanding the spectral properties of one-dimensional quantum liquids. While for small energy and momentum transferred the spectral properties are explained (with notably exceptions) by the Luttinger model, their description at arbitrary energy/momentum remained an open problem until very recently. The situation changed in the last three years, and at present there exist several theories explaining the spectral properties of 1D systems away from the Luttinger Liquid regime. I will discuss these theories and some open questions. 5 Participant List Organizers Esslinger, Tilman Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland Georges, Antoine College de France and Ecole Polytechnique, France, France Muramatsu, Alejandro University of Stuttgart, Germany Pollet, Lode LMU Munich, Germany Altman, Ehud - Weizmann Institute of Science, Israel Anders, Peter - Institute for Theoretical Physics, Switzerland Banuls, Mari-Carmen - Max Planck Insitute of Quantum Optics, Garching, Germany Batrouni, George - , Baumann, Kristian - ETH Zurich, Switzerland Becca, Federico - International School for Advanced Studies (SISSA) and CNR-DEMOCRITOS IOM, Italy Blatter, Gianni - Theoretische Physik, ETH Zurich, Bonnes, Lars - Institute for Theoretical Physics III, University of Stuttgart, Germany Brennecke, Ferdinand - ETH Zurich, Büchler, Hans Peter - University of Stuttgart, Germany Buhmann, Jonathan - Institute for Theoretical Physics, ETH Zürich, Switzerland Burovski, Evgeni - LPTMS, Universite Paris-Sud, France Carusotto, Iacopo - Universita'' de Trento, Italy Chang, Soon-Yong - University of Innsbruck, Austria Cheneau, Marc - Max Planck Institute for Quantum Optics, Germany Chevy, Frederic - LKB - ENS Paris, France Chin, Cheng - Unviversity of Chicago, USA Cirac, Ignacio - Max-Plank Institute for Quantum Optics, Garching, Germany Daley, Andrew - University of Innsbruck, Austria Das Sarma, Sankar - University of Maryland, USA De Leo, Lorenzo - Ecole polytechnique Paris, France Demler, Eugene - Harvard, USA DIXIT, GOPAL - TECHNICAL UNIVERSITY MUNICH, Germany Fischer, Mark - ETH Zürich, Switzerland Foelling, Simon - Harvard University, USA Gerbier, Fabrice - Laboratoire Kastler Brossel, ENS, Paris, France Gorelik, Elena - University of Mainz, Germany Greif, Daniel - ETH Zurich, Switzerland Gritsev, Vladimir - Universite de Fribourg, Switzerland Gupta, Jyotsana - Max Planck Institute for Polymer Research Mainz, Germany Hanna, Thomas - NIST, USA Hassler, Fabian - ETH Zurich, Switzerland Heidrich-Meisner, Fabian - RWTH Aachen, Germany Holzmann, Markus - LPTL, Jussieu, Paris, France Huber, Sebastian - Weizmann Institute, Israel Hulet, Randy - Rice University, USA Jordens, Robert - ETH Zurich, Switzerland Kollath, Corinna - Ecole Polytechnique, Switzerland Kozik, Evgeny - ETH Zurich, United Kingdom Kraus, Christina - Max-Planck Institut für Quantenoptik, Garching, Germany Läuchli , Andreas - Max Planck Institute for Physics of Complex Systems, Dresden, Liu, Vincent - University of Pittsburgh, USA Loew, Robert - University of Stuttgart, Germany Ma, Ping Nang - ETH Zurich, Switzerland McCulloch , Ian - University of Queensland, Australia Moritz, Henning - ETH Zurich, Orso, Giuliano - LPTMS, University of Paris South, France Pilati, Sebastiano - The Abdus Salam International Centre for Theoretical Physics, Italy Prokofev, Nikolay - University of Massachusetts at Amherst, USA Rigol, Marcos - Georgetown University, USA Rizzi, Matteo - Max Planck Institut für Quantenoptik - Garching, Germany Roscilde, Tommaso - ENS Lyon, France Ruegg, Andreas - The University of Texas at Austin, USA Scarola, Vito - Virginia Polytechnic Institute and State University, USA Schmidt, Sebastian - ETH Zurich, Switzerland Schneider, Ulrich - LMU Munich, Germany Sigrist, Manfred - Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland Strohmaier, Niels - ETH Zurich, Switzerland Svistunov , Boris - University of Massachusetts at Amherst, USA Tarruell, Leticia - Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland Theiler, Barbara - ETH Zurich, Switzerland Tiecke, Tobias - University of Amsterdam, The Netherlands Trivedi, Nandini - Ohio State University, USA Troyer, Matthias - Swiss Federal Institute of Technology Zurich (ETHZ), Switzerland Werner, Philipp - ETH Zurich, Switzerland Wessel, Stefan - University of Stuttgart, Germany Zvonarev, Mikhail - LPTMS, France