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

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.

6 pages, 5 figures

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• Waiting time distributions of noninteracting fermions on a tight-binding chain
• Entanglement entropy in dynamic quantum-coherent conductors
• Nonequilibrium relaxation transport of ultracold atoms
• Interaction-induced conducting-nonconducting transition of ultra-cold atoms in 1D optical lattices
• Transport with ultracold atoms at constant density
• Controlling Transport of Ultra-Cold Atoms in 1D Optical Lattices with Artificial Gauge Fields
• Relaxation Dynamics of Meso-Reservoirs
• Phase-induced transport in atomic gases: from superfluid to Mott insulator
• Matter-wave propagation in optical lattices: geometrical and flat-band effects
• Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems