On Bose-Einstein condensation in harmonic traps

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature T c of a harmonically confined Bose gas as reported in Gerbier et al., Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment. The shift in critical temperature T c with interaction strength for the homogeneous Bose gas has been the subject of numerous studies spanning almost 50 years since the first calculations of Lee and Yang [1,2]. While there is a finite shift to the chemical potential in mean-field (MF) theory, the shift of the critical temperature is zero [3]. The leading order effect is due to long-wavelength critical fluctuations and is inherently nonperturbative. Using effective field theory it was determined that the shift is T c =T 0 c can 1=3 , where n is the particle number density, a is the s-wave scattering length, and c is a constant of order unity [4]. Until recently, results for the value of c disagreed by an order of magnitude and even sign, as summarized in Fig. 1

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“…This effect can be seen more clearly by calculating the critical temperature . The latter is obtained as usual [17,30,31] by setting in Eq. (23) equal to zero, thus (24) This result enabled us to investigate the effects of the and alpha on .…”

Section: Thermodynamic Parametersmentioning

confidence: 99%

“…(27). In the thermodynamic limit, as the asymptotic value of the heat capacity is given by: (31) in calculating (31) the asymptotic expansion of is used, for all value of the function behaves like itself.…”

Section: Formentioning

confidence: 99%