Coherence, Correlations, and Collisions: What One Learns about Bose-Einstein Condensates from Their Decay

Abstract

We have used three-body recombination rates as a sensitive probe of the statistical correlations between atoms in Bose-Einstein condensates (BEC) and in ultracold noncondensed dilute atomic gases. We infer that density fluctuations are suppressed in the BEC samples. We measured the three-body recombination rate constants for condensates and cold noncondensates from number loss in the F 1, m f 21 hyperfine state of 87 Rb. The ratio of these is 7.4͑2.6͒ which agrees with the theoretical factor of 3! and demonstrates that condensate atoms are less bunched than noncondensate atoms.[S0031-9007(97)03611-9] PACS numbers: 03.75.Fi, 05.30.Jp, 32.80.Pj, 42.50.Dv The onset of Bose-Einstein condensation (BEC) is defined by the sudden accumulation of many bosons in a single quantum state. The symmetry property of bosons is such that if a gas is indeed composed of many identical bosons all occupying the same single-particle state, the gas will exhibit a collection of correlation properties known as coherence. While most early experiments on dilute-gas BEC [1-3] have shown good quantitative agreement with the simple physical model of macroscopic occupation of a single state, no dilute-gas experiment explicitly addressed the issue of coherence in the condensate until the striking observation by Andrews et al. [4] of first-order coherence in a sodium condensate. In this paper we describe collision-rate measurements that probe the higher-order coherence properties of thermal and Bose-condensed rubidium atoms [5]. In particular, the coherence of the BEC ground state is contrasted with the chaotic fluctuations of the ultracold noncondensed states.The correlation properties of degenerate samples of ideal bosons have already been extensively studied in the context of quantum optics [6]. In fact, the close analogies between the macroscopically occupied state of a laser beam (characterized as a "coherent state") and that of a Bose condensate have prompted the use of the term "atom laser" to describe some aspects of BEC [7]. Quantum optics teaches that a laser beam is described by a quantum field that exhibits both (i) "first-order coherence," meaning that a measurement of the phase of the field at one point in space and time may be used to predict the phase of the field at some other point [8] and (ii) "higher-order coherences," meaning in essence that the intensity fluctuations in a coherent sample are suppressed relative to those in a thermal sample with the same mean intensity.The analog of intensity fluctuations in a beam of photons is density fluctuations in a gas of atoms. For example, Fig. 1(a) shows the calculated [9] three-body correlation function for a gas of thermal (i.e., noncondensed) bosons. Note that there is an enhanced probability for finding three bosons close together. The same physics accounts for short-time photon bunching in a thermal light beam (the Hanbury-Brown-Twiss effect [10]), for the two-atom bunching that has been observed in beams of ultracold (but not condensed) atoms [11], and for three-pion correla...

Macroscopic quantum information processing using spin coherent states

“…There is no twobody scattering term, K a , in (36) because such collisions are forbidden due to conservation of energy and angular momentum selection rules [46]. For BECs in standard (non-atom chip) magneto-optical traps, the three-body recombination is typically the dominant effect as shown in [45], with an estimated value of L a = 5.8(1.9) × 10 −30 cm 6 s −1 . However, this is due to the relatively high density of BECs in this configuration, and in atom chips the densities are much lower making this a less serious effect.…”

Revivals in an attractive Bose-Einstein condensate in a double-well potential and their decoherence

“…The main source of three-body losses is the recombination of condensed atoms, discussed in details in both theoretical [25,26] and experimental [27,28] works. Our study of three- body losses is just a simple extension of the previous subsection.…”

“…where z (n) (t) is the solution of Newton equation with initial conditions z 0 = z (n) 0 defined in (27) and dz dt | t=0 = 0. The comparison between our approximation (28) and the numerical solution of the Bose-Hubbard model is presented in Fig.…”

Density fluctuations in a quasi-one-dimensional Bose gas as observed in free expansion

“…This is related to the fact that the characteristic length over which the particles bunching vanishes (i.e. g (2) (0) = 1) decreases with increasing temperature. Eventually, this length becomes smaller than the spatial resolution of the imaging system and the bunching effect cannot be visible any more.…”

“…And indeed, very soon after observation of trapped atomic condensates the first order coherence of such systems, manifesting itself in the ability to produce the interference fringes in a two-slit experiment, had been proven [1] experimentally. Higher order correlations leading to atom bunching were established from collisions and three-body losses [2]. Although the Glauber coherence theory introduced to characterize correlations of quantum electromagnetic field is well established now, the issue of coherence of a matter field is still under intensive investigation.…”