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arXiv:cond-mat/0105525 · Physical Review Letters

Observation of Phase Fluctuations in Elongated Bose-Einstein Condensates

S. Dettmer, D. Hellweg, Pasi Ryytty, J. Arlt, Wolfgang A. Ertmer, K. Sengstock, Dmitry S. Petrov, Gora V. Shlyapnikov, H. Kreutzmann, Luis Santos, Maciej Lewenstein

Published Oct 1, 2001• 306 citations
arXivHTMLPDF

Abstract

The occurrence of phase fluctuations due to thermal excitations in Bose-Einstein condensates (BECs) is studied for a variety of temperatures and trap geometries. We observe the statistical nature of the appearance of phase fluctuations and characterize the dependence of their average value on temperature, number of particles, and the trapping potential. We find pronounced phase fluctuations for condensates in very elongated traps in a broad temperature range. The results are of great importance for the realization of BEC in quasi-1D geometries, for matter wave interferometry with BECs, as well as for coherence properties of guided atom laser beams.

DOI
10.1103/physrevlett.87.160406

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The occurrence of phase fluctuations due to thermal excitations in Bose-Einstein condensates (BECs) is studied for a variety of temperatures and trap geometries. We observe the statistical nature of the appearance of phase fluctuations and characterize the dependence of their average value on temperature, number of particles, and the trapping potential. We find pronounced phase fluctuations for condensates in very elongated traps in a broad temperature range. The results are of great importance for the realization of BEC in quasi-1D geometries, for matter wave interferometry with BECs, as well as for coherence properties of guided atom laser beams.
We investigate the phase fluctuations of a Bose-Einstein condensate in one- (1D) and three-dimensional (3D) elongated harmonic traps with the help of the numerical simulation using classical field approximation. By calculating the eigenvalues of the one-dimensional single-particle density matrix we show that the phase fluctuations of a Bose-Einstein Condensate in a 1D system are due to the thermal low-energy excitations. We find that the phase fluctuations depend on the temperature as has been predicted [Phys. Rev. Lett. 85, 3745 (2000), Phys. Rev. Lett. 87, 050404 (2001)]. Finally we show that the phase coherence length of a condensate in a harmonic trap depends on the aspect ratio of anisotropy (geometry) of the trap. We determine the border between the 3D and quasi-one-dimensional systems by calculating the phase coherence length of the condensate.
Summary form only given. We have systematically studied BECs of /sup 87/Rb atoms in the regime of phase-fluctuating condensates. We observe the phase fluctuations by measuring the density distribution of the released cloud after ballistic expansion. By varying the temperature, the number of atoms in the condensate and the aspect ratio of the trapping potential, we studied the continuous transition from the usual 3D regime, where phase fluctuations are low, into the regime of strong phase fluctuations in the condensate. To determine the amount of phase fluctuations experimentally, we measured the formation and structure of stripes in the atomic density distribution after ballistic expansion as a function of the above mentioned parameters. The appearance of stripes after switching off the trapping fields can be understood as conversion of phase fluctuations respect. phase gradients into axial velocity fields and consecutive density distributions. These results are in good agreement with theoretical and numerical studies and set clear limitations on applications of BECs e.g. in interferometric measurements.
An elongated trap potential for cold atoms is designed based on a quadrupole-Ioffe configuration. Phase fluctuations in a Bose–Einstein condensate (BEC), which is confined by the trap, are studied. We simulate the atom density distribution induced by fluctuation after time of flight from this elongated trap potential and study the temperature measurement method related to the distribution. Furthermore, taking advantage of the tight confinement and radio frequency dressing technique, we propose a double well potential for splitting BECs. Our results are helpful for improving understanding of low-dimensional quantum gases and provide important guidance for atomic interferometry.
Fluctuations are fundamental in physics and important for understanding and characterizing phase transitions. In this spirit, the phase transition to the Bose-Einstein condensate (BEC) is of specific importance. Whereas fluctuations of the condensate particle number in atomic BECs have been studied in continuous systems, experimental and theoretical studies for lattice systems were so far missing. Here, we explore the condensate particle number fluctuations in an optical lattice BEC across the phase transition in a combined experimental and theoretical study. We present both experimental data using ultracold ^{87}Rb atoms and numerical simulations based on a hybrid approach combining the Bogoliubov quasiparticle framework with a master equation analysis for modeling the system. We find strongly anomalous fluctuations, where the variance of the condensate number δN_{BEC}^{2} scales with the total atom number as N^{1+γ} with an exponent around γ_{theo}=0.74(10) and γ_{exp}=0.62(9), which we attribute to the 2D/3D crossover geometry. Our Letter highlights the importance of the trap geometry on the character of fluctuations and on fundamental quantum mechanical properties.