Correlation properties of a one-dimensional repulsive Bose gas at finite temperature

Abstract

We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the one-body density matrix are calculated as a function of the interaction strength and temperature with the exact ab-initio Path Integral Monte Carlo method. We explore all possible gas regimes from weak to strong interactions and from low to high temperatures. We provide a detailed comparison with a number of theories, such as perturbative (Bogoliubov and decoherent classical), effective (Luttinger Liquid) and exact (ground-state and thermal Bethe Ansatz) ones. Our Monte Carlo results exhibit an excellent agreement with the tractable limits and provide a fundamental benchmark for future observations which can be achieved in atomic gases, cavity quantum-electrodynamic and superconducting-circuit platforms.

Scattering by harmonically trapped 2D quantum gas near and around the critical regime

“…Using the terms for the Bose particles: recently reported for repusive 1-d bose gases at finite temperature for interacting case in [68]. The detection of the pair correlation function Bose gas can be achieved through various methods such as spatially resolved in situ single-atom counting, as suggested in [69], standard absorption imaging [48,64], time-of-flight measurements [64,70], etc.…”

Exact results of dynamical structure factor of Lieb–Liniger model

“…The Lieb-Liniger model describes N spinless bosons with a contact interaction in a line [12]. As one of the simplest quantum integrable models, it has been extensively studied on a variety of aspects, including thermodynamic properties and quantum criticality [24,25], quantum quench dynamics [26][27][28][29][30][31][32][33], static correlation functions [34][35][36] and dynamical correlation functions [21,22,[37][38][39][40][41][42][43][44][45][46] etc. A quantum integrable system amenable to the Yang-Baxter equation does promise exactly solvability, however it is hardly to carry out an investigation into correlations naively from the Bethe wavefunction at a many-body level [9,10].…”