Abstract
We use the coordinate Bethe ansatz to study the Lieb–Liniger model of a one-dimensional gas of bosons on a finite-sized ring interacting via an attractive delta-function potential. We calculate zero-temperature correlation functions for seven particles in the vicinity of the crossover to a localized solitonic state and study the dynamics of a system of four particles quenched to attractive interactions from the ideal-gas ground state. We determine the time evolution of correlation functions, as well as their temporal averages, and discuss the role of bound states in shaping the postquench correlations and relaxation dynamics.
Highlights
In Refs. [32, 33] we developed a methodology for the calculation of equilibrium and nonequilibrium correlation functions of the repulsively interacting Lieb–Liniger gas based on the semi-analytical evaluation of matrix elements between the eigenstates of the Lieb–Liniger Hamiltonian given by the coordinate Bethe ansatz
To better understand the eigenstate contributions to the nonequilibrium dynamics following a quench to attractive interactions, we focus on quenches of N = 4 particles from the ideal-gas ground state to attractive and repulsive interactions with γ = ±40, and plot in Fig. 4 the populations |C{λj}|2 of the contributing eigenstates against their energies E{λj}
We have studied the nonequilibrium dynamics of the one-dimensional Bose gas following a quantum quench from the noninteracting ground state to attractive interaction strengths γ < 0
Summary
The near-perfect isolation and exquisite control possible for many experimental parameters in ultra-cold atomic gases has enabled the study of nonequilibrium dynamics of closed many-body quantum systems [1]. [32, 33] we developed a methodology for the calculation of equilibrium and nonequilibrium correlation functions of the repulsively interacting Lieb–Liniger gas based on the semi-analytical evaluation of matrix elements between the eigenstates of the Lieb–Liniger Hamiltonian given by the coordinate Bethe ansatz We extend this approach to the attractively interacting gas, for which the Bethe rapidities that characterize the eigenstates are in general complex-valued, indicating the presence of multiparticle bound states. We apply our method to calculate results for the time evolution of correlation functions following a quench to attractive interactions from the ideal-gas ground state, for a system of four particles.
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