Dynamical crossover between the infinite-volume and empty-lattice limits of ultra-cold fermions in 1D optical lattices

TL;DR

This paper investigates the fundamental differences between two thermodynamic limits in ultra-cold fermionic systems in 1D optical lattices, revealing a smooth crossover in transport behavior that can be experimentally tested.

Contribution

It introduces a detailed analysis of the crossover between infinite-volume and empty-lattice limits in ultra-cold fermions, highlighting their distinct transport properties.

Findings

Finite steady-state current in the infinite-volume limit.

No steady-state current in the empty-lattice limit.

Smooth crossover between the two limits with changing initial filling.

Abstract

Unlike typical condensed-matter systems, ultra-cold atoms loaded into optical lattices allow separate control of both the particle number and system size. As a consequence, there are two distinct "thermodynamic" limits that can be defined for these systems: i) "infinite-volume limit" at constant finite density, and ii) "empty-lattice limit" at constant particle number. To probe the difference between these two limits and their crossover, we consider a partially occupied lattice and study the transport of non-interacting fermions and fermions interacting at the mean-field level into the unoccupied region. In the infinite-volume limit, a finite steady-state current emerges. On the other hand, in the empty-lattice limit there is no finite steady-state current. By changing the initial filling, we find a smooth crossover between the two limits. Our predictions may be verified using available experimental tools and demonstrate a fundamental difference between isolated small systems such as ultra-cold atoms and conventional condensed-matter systems.