Quantum dynamics and entanglement of a 1D Fermi gas released from a trap

TL;DR

This paper studies the nonequilibrium entanglement dynamics of a 1D Fermi gas released from traps, revealing universal behaviors and analytical relations between entanglement entropy and particle fluctuations during expansion.

Contribution

It provides analytical results for entanglement entropy evolution in 1D Fermi gases after trap release, highlighting universal scaling laws and differences between trap types.

Findings

Entanglement entropy exhibits a universal small-time logarithmic growth.

Expansion from hard-wall traps shows a specific entropy-variance relation.

Entanglement dynamics from harmonic traps can be described by a global rescaling of initial entropy.

Abstract

We investigate the entanglement properties of the nonequilibrium dynamics of one-dimensional noninteracting Fermi gases released from a trap. The gas of N particles is initially in the ground state within hard-wall or harmonic traps, then it expands after dropping the trap. We compute the time dependence of the von Neumann and Renyi entanglement entropies and the particle fluctuations of spatial intervals around the original trap, in the limit of a large number N of particles. The results for these observables apply to one-dimensional gases of impenetrable bosons as well. We identify different dynamical regimes at small and large times, depending also on the initial condition, whether it is that of a hard-wall or harmonic trap. In particular, we analytically show that the expansion from hard-wall traps is characterized by the asymptotic small-time behavior $S \approx (1/3)\ln(1/t)$ of the von Neumann entanglement entropy, and the relation $S\approx \pi^2 V/3$ where V is the particle variance, which are analogous to the equilibrium behaviors whose leading logarithms are essentially determined by the corresponding conformal field theory with central charge $c=1$. The time dependence of the entanglement entropy of extended regions during the expansion from harmonic traps shows the remarkable property that it can be expressed as a global time-dependent rescaling of the space dependence of the initial equilibrium entanglement entropy.