Quasi-one dimensional degenerate Bose gas

TL;DR

This paper analytically investigates density and phase fluctuations in a quasi-one-dimensional degenerate Bose gas, revealing multiple peaks in the dynamic structure factor and discussing the conditions for true condensation.

Contribution

It provides an analytical framework for understanding fluctuations and coherence in quasi-1D Bose gases, extending prior experimental and theoretical work.

Findings

Multiple peaks in the dynamic structure factor due to discrete energy spectrum

Long-duration Bragg pulses can resolve these peaks

Current MIT experiment conditions do not produce a true condensate, but it can be achieved with parameter adjustments

Abstract

Motivated by the MIT experiment [Gorlitz {\em et al.}, Phys. Rev. Lett. {\bf 87}, 130402 (2001)], we analytically study the effect of density and phase fluctuations on various observables in a quasi one-dimensional degenerate Bose gases. Quantizing the Gross-Pitaevskii Hamiltonian and diagonalize it in terms of the normal modes associated with the density and phase fluctuations of a quasi-one dimensional Bose gas. We calculate dynamic structure factor $S(q,\omega)$ from low-energy condensate density fluctuations and find that there are multiple peaks in $S(q,\omega)$ for a given momentum $q$ due to the discrete energy spectrum. These multiple peaks can be resolved by a two-photon Bragg pulse with a long duration which transfer the momentum to the system. We calculate the momentum transferred $ P_z(t)$ by using the phase-density representation of the Bose order parameter. We also calculate the single-particle density matrix, phase coherence length, and momentum distribution by taking care of the phase fluctuations upto fourth-order term as well as the density fluctuations. Our studies on coherence properties shows that 1D Bose gases of MIT experiment do not form a true condensate, but it can be obtained by a moderate changes of the current experimental parameters.