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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...

We present a comprehensive study of the frequency shifts associated with the lattice potential in a Sr lattice clock by comparing two such clocks with a frequency stability reaching 5×10(-17) after a 1 h integration time. We put the first experimental upper bound on the multipolar M1 and E2 interactions, significantly smaller than the recently predicted theoretical upper limit, and give a 30-fold improved upper limit on the effect of hyperpolarizability. Finally, we report on the first observation of the vector and tensor shifts in a Sr lattice clock. Combining these measurements, we show that all known lattice related perturbations will not affect the clock accuracy down to the 10(-17) level, even for lattices as deep as 150 recoil energies.