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arXiv:cond-mat/0505039 · Physical Review A

Interplay of density and phase fluctuations in ultracold one-dimensional Bose gases

Nick P. Proukakis

Published Feb 7, 2006• 12 citations
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Abstract

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 regime of dominant density fluctuations is shown to be well within current experimental capabilities for both $^{23}\mathrm{Na}$ and $^{87}\mathrm{Rb}$, requiring relatively low temperatures, small atom numbers, and moderate aspect ratios.

DOI
10.1103/physreva.73.023605

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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 regime of dominant density fluctuations is shown to be well within current experimental capabilities for both 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb, requiring relatively low temperatures, small atom numbers, and moderate aspect ratios.
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 regime of dominant density fluctuations is shown to be well within current experimental capabilities for both 23Na and 87Rb, requiring relatively low temperatures, small atom numbers, and moderate aspect ratios.
Quantum critical matter has already been studied in many systems, including cold atomic gases. We report the observation of a universal behaviour of ultracold quantum critical Bose gases in a one-dimensional optical lattice. In the quantum critical region above the Berezinskii-Kosterlitz-Thouless transition, the relative phase fluctuations between neighboring subcondensates and spatial phase fluctuations of quasi-2D subcondensates coexist. We study the density probability distribution function when both these two phase fluctuations are considered. A universal exponential density probability distribution is demonstrated experimentally, which agrees well with a simple theoretical model by considering these two phase fluctuations.
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,ω)S(q,\omega)S(q,ω) from low-energy condensate density fluctuations and find that there are multiple peaks in S(q,ω)S(q,\omega)S(q,ω) for a given momentum qqq 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.
Summary form only given. Phase transitions are among the most dramatic phenomena in nature. Minute variations in the conditions controlling a system trigger a fundamental change of its properties. In the critical regime near a second-order phase transition point the fluctuations of the order parameter are so dominant that they completely govern the behaviour of the system on all length scales. The correlation length of the ultracold gas measures the characteristic length scale of these fluctuations and diverges at the critical temperature. Using cold atomic gases, we have directly observed critical fluctuations of the order parameter near the phase transition of Bose-Einstein condensation. From the divergence of the correlation length of the order parameter versus temperature we have determined its critical exponent v. Despite our densities being ten orders of magnitude smaller and our interactions considerably weaker, we find a remarkable similarity to case of the lambda-transition of helium-4.
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,ω)S(q,ω)S(q,ω) from low-energy condensate density fluctuations and find that there are multiple peaks in S(q,ω)S(q,ω)S(q,ω) for a given momentum qqq 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.