Interplay of Density and Phase Fluctuations in Ultracold One-dimensional Bose Gases

The relative importance of density and phase fluctuations in ultracold one dimensional atomic Bose gases is investigated. By defining appropriate characteristic temperatures for their respective onset, a broad experimental regime is found, where density fluctuations set in at a lower temperature than phase fluctuations. This is in stark contrast to the usual experimental regime explored up to now, in which phase fluctuations are largely decoupled from density fluctuations, a regime also recovered in this work as a limiting case. Observation of the novel regime of dominant density fluctuations is shown to be well within current experimental capabilities for both $^{23}Na$ and $^{87}Rb$, requiring relatively low temperatures, small atom numbers and moderate aspect ratios.Comment: Expanded experimental discussion, modified Fig.

Basis-dependent dynamics of trapped Bose-Einstein condensates and analogies with semi-classical laser theory

We present a consistent second order perturbation theory for the lowest-lying condensed modes of very small, weakly-interacting Bose-Einstein condensates in terms of bare particle eigenstates in a harmonic trap. After presenting our general approach, we focus on explicit expressions for a simple three-level system, mainly in order to discuss the analogy of a single condensate occupying two modes of a trap with the semi-classical theory for two-mode photon lasers. A subsequent renormalization of the single-particle energies to include the dressing imposed by mean fields demonstrates clearly the consistency of our treatment with other kinetic approaches.Comment: 2 Modified Sections: (i) Analogy between 2-mode BEC and Semi-classical laser theory (ii) Links to other kinetic theories made more explicit. European Physical Journal D (accepted for publication): Laser Cooling and Quantum Gas Sectio

Spatial Correlation Functions of one-dimensional Bose gases at Equilibrium

The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly-interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore,the change in both coherence length and shape of the correlation function, from gaussian to exponential, with increasing temperature is quantified. Moreover, the presented results for higher order correlation functions are shown to be in agreeement with existing predictions. Appropriate consideration of density-density correlations is shown to facilitate a precise determination of quasi-condensate density profiles, providing an alternative approach to the bimodal density fits typically used experimentally

Phase coherence in quasicondensate experiments: an ab initio analysis via the stochastic Gross-Pitaevskii equation

We perform an ab initio analysis of the temperature dependence of the phase coherence length of finite temperature, quasi-one-dimensional Bose gases measured in the experiments of Richard et al. (Phys. Rev. Lett. 91, 010405 (2003)) and Hugbart et al. (Eur. Phys. J. D 35, 155-163 (2005)), finding very good agreement across the entire observed temperature range ($0.8<T/T_{\phi}<28$). Our analysis is based on the one-dimensional stochastic Gross-Pitaevskii equation, modified to self-consistently account for transverse, quasi-one-dimensional effects, thus making it a valid model in the regime $\mu ~ few \hbar \omega_\perp$. We also numerically implement an alternative identification of $T_{\phi}$, based on direct analysis of the distribution of phases in a stochastic treatment.Comment: Amended manuscript with improved agreement to experiment, following some additional clarifications by Mathilde Hugbart and Fabrice Gerbier and useful comments by the reviewer; accepted for publication in Physical Review