Session D4: Simulations Meet Experiments on Ultracold Quantum Gases

Pairing states of a one-dimensional spin imbalanced Fermi gas accross a Feshbach resonance

A description of the BCS-BEC crossover in one dimension that properly accounts for the coexistence of fermions and bound pairs can be achieved in the framework of the Bose-Fermi resonance model, in which two fermions in an open channel couple resonantly to a diatomic molecule in the closed channel. In the case of a gas with spin imbalance, pairing correlations consistent with a phase of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type dominate a wide parameter range on the BCS side of the resonance. In the BEC regime, the FFLO correlations are suppressed, leading to a Bose-Fermi mixture consisting of a conventional bosonic superfluid in the molecular channel immersed into a gas of fermions that is either partially or fully polarized. I will present results of a comprehensive numerical study of this model using the density matrix renormalization group method, and determine the dependence of the critical polarization on filling and detuning. [F. Heidrich-Meisner, A.E. Feiguin, U. Schollwoeck, W.Z werger, Phys. Rev. A81, 023629 (2010)]   

Quantum Simulations with Ultracold Bosons in Optical Lattices and Superlattices

Ultracold quantum gases in optical lattices have opened a new window for understanding strongly correlated many-body systems. They especially allow for ab-initio tests of fundamental condensed matter theories. In the presentation, I will discuss several examples, where static phases and non-equilibrium evolutions of ultracold quantum gases are compared to theoretical simulations. Among the examples that will be discussed are the measurement of the critical temperature for superfluidity in the vicinity of the quantum phase transition from a superfluid to a Mott insulator and the observation of a reentrant phase transition between superfluid and Mott insulating phases in a columnar superlattice. Finally, I will report on experimental and theoretical results that shed light on the question how isolated, strongly interacting quantum systems, can locally appear as if the system has equilibrated globally.   

Trapping, cooling and probing fermionic atoms into the Mott and Neel states

A new form of quantum condensed matter physics has emerged from the study of ultra-cold fermionic atoms in optical lattices. Experiments have recently reached the incompressible Mott regime. Detailed comparison to theory and computational studies at intermediate temperatures have validated the concept of optical lattice emulation of many-body fermionic systems. Cooling these systems deeper into the quantum degenerate regime, and devising new spectroscopic probes to investigate physical issues of interest such as quasiparticle properties, are key challenges in this context. The presentation will be based in part on the following references: L. De Leo, C.Kollath, A.Georges, M.Ferrero and O.Parcollet Phys. Rev. Lett. 101, 210403(2008); J.-S. Bernier et al. Phys. Rev. A 79, 061601 (2009); R. J\"ordens et al. Phys. Rev. Lett. 104, 180401 (2010); J.-S. Bernier et al., Phys. Rev. A 81, 063618 (2010); L. De Leo et al., arXiv:1009.2761   

Generalized Thermalization in Integrable Systems

Once only of theoretical interest, integrable models of one-dimensional quantum many-body systems can now be realized with ultracold gases. The possibility of controlling the effective dimensionality and the degree of isolation in the experiments have allowed access to the quasi-1D regime and to the long coherence times necessary to realize integrable models. In general, in integrable quantum systems that are far from equilibrium, observables cannot relax to the usual thermal expectation values. This is because of the constraints imposed by the non-trivial set of conserved quantities that make these systems integrable. Experimentally, relaxation of an observable to a non-thermal expectation value was recently observed in a cold-atom system close to integrability. At integrability, it is natural to describe the observables after relaxation by an updated statistical mechanical ensemble: the generalized Gibbs ensemble (GGE), which is constructed by maximizing the entropy subject to the integrability constraints. In recent studies, the GGE has been found to accurately describe various observables in the steady state of integrable systems, but a microscopic understanding of its origin and applicability remains elusive. In this talk, we review some of the early results on this topic and discuss the justification of the GGE based on a generalized view of the eigenstate thermalization hypothesis, which was originally introduced to explain thermalization in nonintegrable systems. {\bf References:}\\[4pt] [1] M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. {\bf 98}, 050405 (2007).\\[0pt] [2] M. Rigol, A. Muramatsu, and M. Olshanii, Phys. Rev. A {\bf 74}, 053616 (2006).\\[0pt] [3] A. C. Cassidy, C. W. Clark, and M. Rigol, arXiv:1008.4794.   

A quantitative analysis of small atomic systems

Ultracold atoms in an optical lattice provide a unique toolbox for emulating the prototypical models of condensed matter physics. Before the optical lattice system can be trusted as a quantum simulator however, it needs to be validated and benchmarked against known results, for which quantum Monte Carlo simulations are ideally suited. In this talk, an overview of recent numerical studies of ultracold bosonic and fermionic systems in an optical lattice will be given, starting with a full comparison based on experimental time-of-flight images of bosons in an optical lattice and ab-initio simulations. Next, the advantages of single-site resolution detection tools will be highlighted. Finally, the temperature and entropy in present experiments on fermions in an optical lattice will be estimated, and the full thermodynamics on approach to the Neel temperature will be presented. Nearest-neighbor spin-spin correlations are shown to be useful for thermometry.