Cooling Atomic Gases With Disorder

Abstract

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 threedimensional 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. [5,6]. Ultracold atomic gases offer the opportunity to emulate these fundamental issues using optical speckle [7,8], impurities [9], or a quasiperiodic optical lattice [10,11] to introduce randomness. In the bosonic case, the competition between strong interactions and strong disorder has been studied in the context of the elusive Bose glass phase [7,9,11], while for fermions, a recent experiment has explored disorder-induced localization in the three-dimensional (3D) Hubbard model of strongly interacting fermions [12].In this paper, we explore the thermodynamics of interacting, disordered systems and suggest that, in addition to studies of the many-body phenomena noted above, preparing a gas in a random potential might be exploited to cool the atoms. Specifically, we show using an unbiased numerical method that one can lower the temperature and access the regime with long-range magnetic order by adiabatically decreasing the randomness in the chemical potential or hopping energies of the Hubbard Hamiltonian. The achievement of new quantum phases in cold atom experiments largely depends on the reduction of the entropy per particle. The success of our proposal requires that the gas would have to be cooled (e.g. evaporatively) after the disorder is in place. We will return in the

Cooling quantum gases with entropy localization

“…Once the atoms at the edges are separated from the center, one can think about other modifications depending on the particular system at hand. For example, [17] introduced another cooling technique by adiabatically ramping down the disorder with the aim of reaching the Néel temperature, however, the technique was not sufficient on its own and required an additional scheme to reduce the entropy initially. Our cooling mechanism is a promising candidate for this pre-cooling.…”

“…In discussing 'cooling' of cold atomic systems, the relevant quantity is often entropy rather than temperature [9][10][11][12][13][14][15][16][17][18]. Temperature can be radically reduced by adiabatically changing system parameters [19][20][21][22] (for example the depth of an optical lattice), but, there is no utility in lowering the temperature if the other energy scales in the system are commensurably reduced.…”

Multitude of phases in correlated lattice fermion systems with spin-dependent disorder

“…This, together with recently developed methods for cooling [14] and detecting antiferromagnetic correlations [8][9][10][11][12][13]15], will make it possible to explore correlated lattice fermions in the presence of spin-dependent disorder experimentally and to test our predictions.…”

“…Furthermore, it is now even possible to observe antiferromagnetic correlations [8][9][10][11][12][13]. Together with a theoretically proposed new cooling method [14], this allows experiments with ultracold atoms to be performed at temperatures at which antiferromagnetic order in a finite system appears, i.e., where the correlation length reaches the size of the system [15]. These developments motivated us to extend our previous work on correlated lattice fermions with spin-dependent disorder [16,17] to the case with antiferromagnetic long-range order (AF-LRO).…”

Properties of the superfluid in the disordered Bose-Hubbard model

“…For bosons, where interactions play a crucial role, the disordered Bose-Hubbard model (DBHM) allows one to study the interplay between correlation and disorder. Ever since the seminal work of Fisher et al [1], this model has received a lot of attention and its properties have been explored using renormalization-group (RG) approaches and numerical techniques, as well as experiment [1][2][3][4][5][6][7][8][9][10][11].…”