# Self-consistent determination of the many-body state of ultracold bosonic atoms in a one-dimensional harmonic trap

## TL;DR

This paper investigates quantum phase fluctuations in one-dimensional ultracold bosonic gases at zero temperature using a self-consistent multiconfigurational approach, revealing a peak in phase fluctuations linked to correlation dips.

## Contribution

It introduces a self-consistent method to analyze spatial phase fluctuations and their relation to correlations in 1D Bose gases with moderate interactions.

## Key findings

- Phase fluctuations peak at specific positions, indicating correlation dips.
- The method captures the shape of orbitals and occupation amplitudes self-consistently.
- Results connect phase fluctuation behavior with interaction regimes.

## Abstract

We study zero-temperature quantum fluctuations in harmonically trapped one-dimensional interacting Bose gases, using the self-consistent multiconfigurational time-dependent Hartree method. We define $phase$ $fluctuations$ from the full single-particle density matrix by the spatial decay exponent of off-diagonal long-range order. In a regime of mesoscopic particle numbers and moderate contact couplings, we derive the spatial dependence of the amplitude of phase fluctuations, determined from the {\em self-consistently} derived shape of the field operator orbitals and Fock space orbital occupation amplitudes. It is shown that the phase fluctuations display a peak, which in turn corresponds to a dip of the first-order correlations in position space, akin to what has previously been obtained in the Tonks-Girardeau limit of very large interactions and low densities.