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arXiv:1308.2095 · Physical Review Letters

Observation of Transverse Bose-Einstein Condensation via Hanbury Brown–Twiss Correlations

RuGway Wu, Andrew Manning, Sean S. Hodgman, R. G. Dall, Andrew G. Truscott, Timothy O. Lamberton, Karen V. Kheruntsyan

Published Aug 27, 2013• 15 citations
arXivHTMLPDF

Abstract

A fundamental property of a three-dimensional Bose-Einstein condensate is long-range coherence; however, in systems of lower dimensionality, not only is the long-range coherence destroyed but additional states of matter are predicted to exist. One such state is a "transverse condensate," first predicted by van Druten and Ketterle [Phys. Rev. Lett. 79, 549 (1997)], in which the gas condenses in the transverse dimensions of a highly anisotropic trap while remaining thermal in the longitudinal dimension. Here, we detect the transition from a three-dimensional thermal gas to a gas undergoing transverse condensation by probing Hanbury Brown-Twiss correlations.

DOI
10.1103/physrevlett.111.093601

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•Jan 1, 2004•0 citations
A fundamental property of a three-dimensional Bose-Einstein condensate is long-range coherence; however, in systems of lower dimensionality, not only is the long-range coherence destroyed but additional states of matter are predicted to exist. One such state is a "transverse condensate," first predicted by van Druten and Ketterle [Phys. Rev. Lett. 79, 549 (1997)], in which the gas condenses in the transverse dimensions of a highly anisotropic trap while remaining thermal in the longitudinal dimension. Here, we detect the transition from a three-dimensional thermal gas to a gas undergoing transverse condensation by probing Hanbury Brown-Twiss correlations.
Phase transitions are ubiquitous in our three-dimensional world. By contrast, most conventional transitions do not occur in infinite uniform low-dimensional systems because of the increased role of thermal fluctuations. The crossover between these situations constitutes an important issue, dramatically illustrated by Bose-Einstein condensation: a gas strongly confined along one direction of space may condense along this direction without exhibiting true long-range order in the perpendicular plane. Here we explore transverse condensation for an atomic gas confined in a novel trapping geometry, with a flat in-plane bottom, and we relate it to the onset of an extended (yet of finite-range) in-plane coherence. By quench crossing the transition, we observe topological defects with a mean number satisfying the universal scaling law predicted by Kibble-Zurek mechanism. The approach described can be extended to investigate the topological phase transitions that take place in planar quantum fluids. Interacting quantum many-body systems in low dimensions is an active research area in ultra-cold gases. Here, Chomaz et al.study the dimensional crossover of Bose–Einstein condensation and observe the emergence of phase coherence in an ultra-cold quasi-2D Bose gas confined to a flat-bottom trapping potential.
A major advance in understanding the behavior of light was to describe the coherence of a light source by using correlation functions that define the spatio-temporal relationship between pairs and larger groups of photons. Correlations are also a fundamental property of matter. We performed simultaneous measurement of the second- and third-order correlation functions for atoms. Atom bunching in the arrival time for pairs and triplets of thermal atoms just above the Bose-Einstein condensation (BEC) temperature was observed. At lower temperatures, we demonstrated conclusively the long-range coherence of the BEC for correlation functions to third order, which supports the prediction that like coherent light, a BEC possesses long-range coherence to all orders.
The Hanbury Brown-Twiss experiment has proved to be an effective means of measuring two-point correlation function of identical particles. We analyze experimental observation of stripes formation of a phase fluctuating Bose-Einstein condensates in a highly elongated 3D traps [Dettmer {\em et al.}, Phys. Rev. Lett. {\bf 87}, 160406 (2001)] by means of axial two-point correlation functions. We also predict that the stripes are present in quasi-1D Bose gas in the mean-field as well as in the hard-core bosons regimes. These stripes can be realized by measuring the axial two-point correlation functions by using the Bragg interferometric method which is similar to the original Hanbury Brown and Twiss experimental setup.
We have observed the Bose-Einstein condensation of an atomic gas in the (quasi)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion of the condensate. The critical temperature agrees with the theoretical prediction for a uniform Bose gas. The momentum distribution of a noncondensed quantum-degenerate gas is also clearly distinct from the conventional case of a harmonically trapped sample and close to the expected distribution in a uniform system. We confirm the coherence of our condensate in a matter-wave interference experiment. Our experiments open many new possibilities for fundamental studies of many-body physics.
The fact that two-dimensional interacting trapped systems do not undergo Bose-Einstein Condensation (BEC) in the thermodynamic limit, though rigorously proved, is somewhat mysterious because all relevant limiting cases (zero temperature, small atom numbers, noninteracting particles) suggest otherwise. We study the possibility of condensation in finite trapped two-dimensional systems. We first consider the ideal gas, which incorporates the inhomogeneity and finite size of experimental systems and can be solved exactly. A semiclassical self-consistent approximation gives us a feel for the temperature scales; diagonalization of the one-body density matrix confirms that the condensation is into a single state. We squeeze a three-dimensional system and see how it crosses over into two dimensions. Mean-field theory, our main tool for the study of interacting systems, prescribes coupled equations for the condensate and the thermal cloud: the condensate receives a full quantum-mechanical treatment, while the noncondensate is described by different schemes of varying sophistication. We analyze the T = 0 case and its approach to the thermodynamic limit, finding a criterion for the dimensionality crossover and obtaining the coupling constant of the two-dimensional system that results from squeezing a three-dimensional trap. We next apply a semiclassical Hartree-Fock approximation to purely two-dimensional finite gases and find that they can be described either with or without a condensate; this continues to be true in the thermodynamic limit. The condensed solutions have a lower free energy at all temperatures but neglect the presence of phonons within the system and cease to exist when we allow for this possibility. The uncondensed solutions, in turn, are valid under a more rigorous scheme but have consistency problems of their own. Path-integral Monte Carlo simulations provide an essentially exact description of finite interacting gases and enable us to study highly anisotropic systems at finite temperature. We find that our two-dimensional Hartree-Fock solutions accurately mimic the surface density profile and predict the condensate fraction of these systems; the equivalent interaction parameter is smaller than that dictated by the T = 0 analysis. We conclude that, in two-dimensional isotropic finite trapped systems and in highly compressed three-dimensional gases, there is a phenomenon resembling a condensation into a single state.