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We show that the critical temperature of a uniform dilute Bose gas increases linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.Determination of the effect of repulsive interactions on the transition temperature of a homogeneous dilute Bose gas at fixed density has had a long and controversial history [1][2][3][4][5]. While [1] predicted that the first change in the transition temperature, T c , is of order the scattering length a for the interaction between the particles, neither the sign of the effect nor its dependence on a has been obvious. Recent renormalization group studies [4] predict an increase of the critical temperature. Numerical calculations by Grüter, Ceperley, and Laloë [6], and more recently by Holzmann and Krauth [7], of the effect of interactions on the Bose-Einstein condensation transition in a uniform gas of hard sphere bosons, and approximate analytic calculations by Holzmann, Grüter, and Laloë of the dilute limit [8], have shown that the transition temperature, T c , initially rises linearly with a. The effect arises physically from the change in the energy of low momentum particles near T c [8]. Here we analyze the leading order behavior of diagrammatic perturbation theory, and argue that T c increases linearly with a. We then construct an approximate self-consistent solution of the single particle spectrum at T c which demonstrates the change in the low momentum spectrum, and which enables us to calculate the change in T c quantitatively.We consider a uniform system of identical bosons of mass m, at temperature T close to T c and use finite temperature quantum many-body perturbation theory. We assume that the range of the two-body potential is small compared to the interparticle distance n −1/3 , so that the potential can be taken to act locally and be characterized entirely by the s-wave scattering length a. Thus we work in the limit a ≪ λ, where λ = 2πh 2 /mk B T 1/2 is the thermal wavelength. (We generally use units h = k B = 1.)To compute the effects of the interactions on T c , we write the density n as a sum over Matsubara frequencies ω ν = 2πiνT (ν = 0, ±1, ±2, . . .) of the single particle Green's function, G(k,z):wherewith µ the chemical potential. The Bose-Einstein condensation transition is determined by the point where G −1 (0, 0) = 0, i.e., where Σ(0, 0) = µ. The first effect of interactions on Σ is a mean field term Σ mf = 2gn, where g = 4πh 2 a/m; the factor of two comes from including the exchange term. Such a contribution, independent of k and z has no effect on the transition temperature, as it can be simply absorbed in a redef...

We determine the critical temperature of a 3-d homogeneous system of hard-sphere Bosons by path-integral Monte Carlo simulations and finite-size scaling. At low densities, we find that the critical temperature is increased by the repulsive interactions, in the form of a power law in density with exponent 1/3: ∆TC /T0 ∼ (na 3 ) 1/3 . At high densities the result for liquid helium, namely a lower critical temperature than in the non-interacting case, is recovered. We give a microscopic explanation for the observed behavior.

We perform Ramsey spectroscopy on the ground state of ultra-cold 87 Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 ± 12 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from particle indistinguishability. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and may appear in other physical systems.In atomic clocks and other precision techniques based on atomic spin manipulation [1], a central requirement is to preserve the coherence of a state superposition over long times. Understanding how coherence decays in a given system is important for these applications, and is a touchstone of understanding its dynamics. In trapped ensembles, an inhomogeneous shift ∆(r) of the transition frequency occurs due to the trapping potential and to atomic interactions. Different atoms explore different regions of this shift landscape, and so their spins precess at different rates. This leads to dephasing at a rate determined by the characteristic inhomogeneity ∆ 0 of ∆(r) over the ensemble. Various mechanisms have been exploited to reduce this dephasing. Examples are "magic fields" that strongly reduce the field dependence for a specific transition [2,3], or the mutual compensation scheme successfully employed in ultracold 87 Rb [4], where the trap-induced inhomogeneity can be adjusted to nearly cancel the collisional mean-field inhomogeneity. All such mechanisms however, including the motional narrowing well known in nuclear magnetic resonance, have in common that the dephasing is merely slowed down, but never reversed, and the transverse polarization remains a steadily decreasing function of time.Here we present measurements on a trapped ensemble of 87 Rb atoms with two internal levels equivalent to a spin 1/2. Atomic interactions cause a spontaneous re-phasing of the spins, observed as a much longer decay time and revivals of Ramsey contrast. We are also able to extend the coherence time by more than an order of magnitude beyond the 2 to 3 s previously achieved on this system [3,5]. We explain these remarkable results by a very general mechanism based on the identical spin rotation effect (ISRE) that occurs during collisions in the forward direction between two identical particles [6] -an equivalent description can be given in terms of the exchange mean-field experienced by the atoms [7]. This effect is known to cause transient spin waves [4,[8][9][10][11][12][13][14], a deleterious phenomenon if one is interested in long coherence times. In contrast to those experiments however, we are working in a regime where both (i) the ISRE rate (exchange rate) ω ex /2π = 2 |a 01 |n/m is FIG. 1: Two classes of atoms (red and blue) precess at different rates. Their Bloch vectors were initially parallel, but have started to...