Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing, and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a nondisordered state which exhibits these incompletely understood phases. We show, using quantum Monte Carlo simulations, that we can approach the Néel temperature of the three-dimensional Hubbard model for experimentally achievable parameters. Recent experimental estimates suggest the randomness required lies in a regime where atom transport and equilibration are still robust.
Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing, and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a nondisordered state which exhibits these incompletely understood phases. We show, using quantum Monte Carlo simulations, that we can approach the Néel temperature of the three-dimensional Hubbard model for experimentally achievable parameters. Recent experimental estimates suggest the randomness required lies in a regime where atom transport and equilibration are still robust.
We study quantum phases and transitions in ultra-cold quantum gases, beyond the scope of conventional condensed matter systems. The study focuses on three major thrusts. The first thrust is the study of cold ensembles of bosonic or fermionic atoms in the higher orbital bands of optical lattices. Orbital and topological quantum physics is systematically explored for various lattice geometries, to be outlined below. The second is the low dimensional spin-imbalanced fermions in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We analyze its thermal instability towards Berezinsky-Kosterlitz-Thouless (BKT) phase transitions driven by different topological defects at finite temperature. The third is the theoretical search for a mechanism to achieve a Bose-Einstein crystal phase for bosons in the ground state. A new class of two-body interactions characterized by strong momentum-dependence is found to give rise to such a quantum state. It is different than but related to the long-debated concept of supersolidity. The first thrust forms the main part of the dissertation. Meta-stable phases of high orbital bosons and fermions have been explored for different lattice geometries such as square and bipartite lattices. Exotic Mott and superfluid phases are studied in both one and two dimensions. Quantum and thermal phase transitions, associated with time reversal symmetry breaking and their experimental signatures are discussed. In particular a quantum ``disordered" superfluid phase, beyond the mean field description, is found in one dimension. The challenging problem of probing time reversal symmetry breaking is solved. Besides, a one-dimensional fermionic optical ladder with coupled s- and p-orbitals is shown to mimic spin-orbit interactions and exhibit topological insulator and topological superconducting phases. Charge fractionalization is shown to be realizable in such an sp-orbital ladder.
Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high- T c superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.
Ultra-cold atomic gases by themselves and in combination with disorder are a highly active and innovative field of research. Since the first expenmental realization of Bose.-Elnstein condensation in 1995, ultra-cold quantum gases have become a powerful tool to study condensed matter, quantum optics, and quantum Infonnation problems. Disordered systems are been extremely difficult to study, but recent advances of ultra-cold experiments have brought about new tools and approaches to tackle these problems as well. In particular, urtra-cold quantum gases can be subject to controlled spatially disordered potentials. Breakthroughts like the seminal observation of Anderson localization in 2008 illustrate the powerful experimental control of quantum systems. There are currently two main approaches to realizing controlled disordered potentials for ultra-cold atomi gases: incommensurate '!lulti-chromatic lattices and speckle radiation. Altematlve approaches using holographic masks, rapidly oscillating laser beams and secondary lattices xJng scatterers in space are currently being studied by several groups. The sum of these innovative techniques that aim at realizing controlled disorder l'uels studies on disordered ultra-cold systems - In particular, the between interactions and disorder in non-interacting Bose- and Fenni systems, and the creation of glass states together with associated quantum phase transitions are currently attracting a lot of attention this thesis reports on the applicability and robustness of a related phenomenon called disorder-induced order. In essence, it is the process by which certain systems order when a specific type of controlled disorder is applied. In absence of disorder, the systems we consider present a contlnuous vvymmetry, e.g. a rotational U(1) symmetry as In the ferromagnetic XV model. If we apply a homogenous magnetic field along a given direction of the X I lane, all spins will align roughly in this direction. If we replace this homogenous field by a spatially randomly oscillating field in the same direction at low temperature, the system tends to avoid this external field and orders in a direction orthogonal to the field, inside the XV plane. The effect turns out to be robust enough to occur with regularly oscillating fields (e.g. staggered fields, sinuSOlda1ty oscillating fields), pseudo-random fields (realizable by uperposlng optical lattices), and random fields (as created by speckle plates), However, we stress that these disordered fields must not be dlstnbuted according to the continuous symmetry of the system but restricted to a subspace e.g. in the XV model, the spins can orient in any direction of the XV plane - and, if the disordered field is oriented WIth random angles, the system WIll not magnetize. The effect only occurs if the disorder is always along a given direction with random orientation. We study several configurations of disorder-induced order numerically and analytically, and present possible expenmental realizations for the classical XY system as an illustration of the basic Intuition of the effect IPRB 74 224448 (2006)], a system of two Raman-coupled Bose-Elnstein condensates, where disorder allows to control the relative phase of the two condensates IPRl 10030403 (2008)) superfluid BCS pairs in presence of a diatomic reservoir, where disorder fixes the complex phase of the painng function IEPl 86 26004 (2009)], and the quantum XY spin chain, where disorder leads to spontaneous magnetization in the direction orthogonat to the disordered fietd [PRA, accepted] Other systems in which we expect disorder-induced order to occur, not discussed in thiS thesis, are spinor condensates and possibly systems with synthetic gauge fields. Finally, there are reports of randomness-induced XV Ofdering in a graphene quantum Hall ferromagnet (PRl 98 156801 (2007) as well as disorder-induced ordering of superfluid 3HE-A in aerogel [JETPl84 455 (2006), Jl TP 150453 (2008).
Quantum Monte Carlo (QMC) techniques are used to provide an approximation-free investigation of the phases of the one-dimensional attractive Hubbard Hamiltonian in the presence of population imbalance. The temperature at which the ``Fulde-Ferrell-Larkin-Ovchinnikov'' (FFLO) phase is destroyed by thermal fluctuations is determined as a function of the polarization. It is shown that the presence of a confining potential does not dramatically alter the FFLO regime and that recent experiments on trapped atomic gases likely lie just within the stable temperature range.
We study s-wave superconductivity in the two-dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via a Monte Carlo approach. The method requires iterative solution of the Bogoliubov--de-Gennes equations for amplitude- and phase-fluctuating configurations of the pairing field. We establish the full thermal phase diagram of this strong-coupling problem. At low field we observe the magnetized but homogeneous ``breached pair'' superfluid phase. It reveals that Tc scales an order of magnitude below the mean-field estimate, spontaneous inhomogeneity in the field-induced magnetization, and a strong nonmonotonicity in the temperature dependence of the low-energy density of states. We compare our results to the experimental phase diagram of the imbalanced Fermi gas at unitarity. At higher field we obtain the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. The thermal transition from the FFLO phases to the normal state is strongly first order. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into the normal state. The pairing structure factor retains weak signature of finite momentum pairing to a high temperature despite the low Tc itself, while the spin-resolved density of states changes from the ``pseudogapped'' FFLO character to gapless and pseudogapped again with increasing temperature.