Bosonic and fermionic transport phenomena of ultra-cold atoms in 1D optical lattices

TL;DR

This paper investigates the transport behavior of non-interacting ultra-cold bosons and fermions in 1D optical lattices, revealing distinct steady-state and oscillatory dynamics driven by quantum statistics.

Contribution

It provides the first detailed comparison of bosonic and fermionic transport phenomena in 1D optical lattices using the micro-canonical approach.

Findings

Fermions develop a finite steady-state current similar to nanoscale electronic transport.

Bosons exhibit oscillatory currents that decay to zero in the thermodynamic limit.

Particle number fluctuations differ significantly due to quantum statistics.

Abstract

Using the micro-canonical picture of transport -- a framework ideally suited to describe the dynamics of closed quantum systems such as ultra-cold atom experiments -- we show that the exact dynamics of non-interacting fermions and bosons exhibit very different transport properties when the system is set out of equilibrium by removing the particles from half of the lattice. We find that fermions rapidly develop a finite quasi steady-state current reminiscent of electronic transport in nanoscale systems. This result is robust -- it occurs with or without a harmonic confining potential and at zero or finite temperature. The zero-temperature bosonic current instead exhibits strong oscillatory behavior that decays into a steady-state of zero current only in the thermodynamic limit. These differences appear most strikingly in the different particle number fluctuations on half of the lattice as a consequence of the spin statistics. These predictions can be readily verified experimentally.