Repulsive to attractive interaction quenches of 1D Bose gas in a harmonic trap

TL;DR

This paper investigates the dynamics of one-dimensional trapped bosons undergoing a quench from repulsive to attractive interactions, focusing on the breathing modes of the super-Tonks-Girardeau state using spectral analysis and approximate models.

Contribution

It introduces a spectral approach to analyze the eigenstates and breathing dynamics of 1D Bose gases after interaction quenches, employing finite-dimensional approximations and contrasting methods.

Findings

Breathing frequency depends on the energy difference between specific eigenstates.

Spectral analysis reveals the nature of excited eigenstates in the quenched system.

Approximate models effectively capture the dynamics of the super-Tonks-Girardeau state.

Abstract

We consider quantum quenches of harmonically trapped one-dimensional bosons from repulsive to attractive interactions, and the resulting breathing dynamics of the so-called `super-Tonks-Girardeau' (sTG) state. This state is highly excited compared to the ground state of the attractive gas, and is the lowest eigenstate where the particles are not bound or clustered. We analyze the dynamics from a spectral point of view, identifying the relevant eigenstates of the interacting trapped many-body system, and analyzing the nature of these quantum eigenstates. To obtain explicit eigenspectra, we use Hamiltonians with finite-dimensional Hilbert spaces to approximate the Lieb-Liniger system. We employ two very different approximate approaches: an expansion in a truncated single-particle harmonic-trap basis and a lattice (Bose-Hubbard) model. We show how the breathing frequency, identified with the energy difference between the sTG state and another particular eigenstate, varies with interaction.