Dynamical fermionization in a one-dimensional Bose-Fermi mixture

TL;DR

This paper demonstrates that a strongly interacting Bose-Fermi mixture in one dimension exhibits dynamical fermionization after trap release, with momentum distributions evolving to match initial density profiles, confirmed analytically and numerically.

Contribution

It provides an analytical proof and numerical confirmation that Bose-Fermi mixtures show dynamical fermionization, extending previous results to mixed systems.

Findings

Momentum distribution approaches initial density profile after trap release.

Dynamical fermionization observed in Bose-Fermi mixtures.

Similar dynamics occur under trap frequency quenches.

Abstract

After release from the trap the momentum distribution of an impenetrable gas asymptotically approaches that of a spinless noninteracting Fermi gas in the initial trap. This phenomenon is called dynamical fermionization and, very recently, has been experimentally confirmed in the case of the Lieb-Liniger model in the Tonks-Girardeau regime. We prove analytically and confirm numerically that following the removal of axial confinement the strongly interacting Bose-Fermi mixture exhibits dynamical fermionization and the asymptotical momentum distribution of each component has the same shape as its density profile at $t=0$. Under a sudden change of the trap frequency to a new non-zero value the dynamics of both fermionic and bosonic momentum distributions presents characteristics which are similar to the case of single component bosons experiencing a similar quench. Our results are derived using a product representation for the correlation functions which, in addition to analytical considerations, can be implemented numerically very easily with complexity which scales polynomially in the number of particles.