Equilibration Rates and Negative Absolute Temperatures for Ultracold Atoms in Optical Lattices

Abstract

As highly tunable interacting systems, cold atoms in optical lattices are ideal to realize and observe negative absolute temperatures, T<0. We show theoretically that, by reversing the confining potential, stable superfluid condensates at finite momentum and T<0 can be created with low entropy production for attractive bosons. They may serve as "smoking gun" signatures of equilibrated T<0. For fermions, we analyze the time scales needed to equilibrate to T<0. For moderate interactions, the equilibration time is proportional to the square of the radius of the cloud and grows with increasing interaction strengths as atoms and energy are transported by diffusive processes.

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

“…7 in SI ). Negative temperatures describe equilibrated systems with population inversion and are well defined for systems like the Hubbard model where the energy has an upper bound [35]. They have been observed in spin systems [33] and localized ultracold atoms [34].…”

Thermodynamic laws in isolated systems

“…We thank Michele Campisi for directing our attention to Eq. (14). We thank Oliver Penrose for bringing Eq.…”

“…By contrast, the definition (E) adopted here implies that two systems cannot be in thermal equilibrium unless they are in contact, reflecting the fact that it seems meaningless to speak of thermal equilibrium if two systems are unable to exchange energy. 14 One may try to rescue the idea of using temperature to identify equivalence classes of systems in thermal equilibrium-and, thus, of demanding that systems with the same temperature are in thermal equilibrium-by broadening the definition of "thermal equilibrium" to include both "actual" thermal equilibrium, in the sense of definition (E) above, and "potential" thermal equilibrium: Two systems are in potential thermal equilibrium if they are not in thermal contact, but there would be no net energy transfer between the systems if they were brought into (hypothetical) thermal contact. One could then demand that two systems with the same temperature are in actual or potential thermal equilibrium.…”

“…Thus, demanding that two systems with the same temperature must be in thermal equilibrium is not a feasible extension of the zeroth law. 14 If we uphold the definition (E), but still wish to uniquely label equivalence classes of systems in thermal equilibrium (and thus in thermal contact), we are confronted with the difficult task of always assigning different temperatures to systems not in thermal contact. 15 The situation differs for systems coupled to an infinite heat bath and described by the canonical ensemble.…”

“…Mathematically, the microcanonical density operator of many systems can be obtained from the canonical density operator via an inverse Laplace transformation. quantum heat engines [2,13,14] and the realizability of dark energy analogs in quantum systems [2].…”