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arXiv:1412.3472 · Physical Review A

Effect of impurities on the transition temperature of a dilute dipolar trapped Bose gas

H. Yavari, Elaheh Afsaneh

Published Jan 2, 2013• 3 citations
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Abstract

By using a two-fluid model the effect of impurities on the transition temperature of a dipolar trapped Bose gas is investigated. By treating Gaussian spatial correlation for impurities from the interaction modified spectra of the system, the formula for the shift of the transition temperature is derived. The shift of the transition temperature contains essentially three contributions due to contact, dipole-dipole, and impurity interactions. Applying our results to dipolar Bose gases shows that the shift of the transition temperature due to impurities could be measured for an isotropic trap (dipole-dipole contribution is zero) and the Feshbach resonance technique (contact potential contribution is negligible).

DOI
10.1103/physreva.87.013601

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By using a two-fluid model the effect of impurities on the transition temperature of a dipolar trapped Bose gas is investigated. By treating Gaussian spatial correlation for impurities from the interaction modified spectra of the system, the formula for the shift of the transition temperature is derived. The shift of the transition temperature contains essentially three contributions due to contact, dipole-dipole, and impurity interactions. Applying our results to dipolar Bose gases shows that the shift of the transition temperature due to impurities could be measured for an isotropic trap (dipole-dipole contribution is zero) and the Feshbach resonance technique (contact potential contribution is negligible).
The effects of impurity and Bose-Fermi interactions on the transition temperature of a dipolar Bose–Einstein condensation in trapped Bose-Fermi mixture, by using the two-fluid model, are investigated. The shift of the transition temperature consists of four contributions due to contact, Bose-Fermi, dipole-dipole, and impurity interactions. We will show that in the presence of an anisotropic trap, the Bose-Fermi correction to the shift of transition temperature due to the excitation spectra of the thermal part is independent of anisotropy factor. Applying our results to trapped Bose-Fermi mixtures shows that, by knowing the impurity effect, the shift of the transition temperature due to Bose-Fermi interaction could be measured for isotropic trap (dipole-dipole contributions is zero) and Feshbach resonance technique (contact potential contribution is negligible).
We investigate the effects of long-ranged dipole-dipole potential on the transition temperature of a weakly interacting Bose gas. We apply the two-fluid model to derive the energy spectra of the thermal and the condensate parts. From the interaction modified spectra of the system, the formula for the shift of transition temperature was derived. Compared to the conventional weakly interacting Bose system with contact potential only where thermal effect is larger, we find that the condensate effect is about two times that of the thermal part in the dipolar system. Due to the relative smallness of dipole-dipole interaction with respect to the contact interaction in current dipolar Bose-Einstein condensation, we suggest to measure the dipolar effect by tuning the scattering length to negligible small by the Feshbach resonance technique.
We report a theoretical study of the transition temperature of a trapped interacting dilute Bose gas. The system is treated like a two-fluid model consisting of a thermal component and a condensate component. Through the calculation of the energy spectra, the origins of various effects on the transition temperature are derived. We found that the interactive shift is affected by both the thermal component and the condensate component. The latter effect, which is about 34% of the former, has never been reported so far. With these two effects, our calculated interactive shift agrees very well with the recent measurement.
We consider a dilute gas of dipole moments in an arbitrary harmonic trap and treat both the short-range, isotropic $\ensuremath{\delta}$ interaction and the long-range, anisotropic dipole-dipole interaction perturbatively. In this way, we calculate the leading shift of the critical temperature with respect to that of an ideal gas as a function of the relative orientation of the dipole moments with respect to the harmonic trap axes. In particular, we determine those magic angles, where the dipolar shift of the Bose-Einstein condensation temperature vanishes. Furthermore, we show for the parameters of the ongoing 52Cr^{52}\mathrm{Cr}52Cr BEC experiment of Pfau and co-workers that this dipolar shift can be enhanced by increasing the number of particles, the geometrical mean trap frequency, and the anisotropy of the trap.
We report measurements of the Bose-Einstein condensate critical temperature shift due to dipolar interactions, employing samples of ultracold erbium atoms which feature significant (magnetic) dipole-dipole interactions in addition to tunable contact interactions. Using a highly prolate harmonic trapping potential, we observe a clear dependence of the critical temperature on the orientation of the dipoles relative to the trap axis. Our results are in good agreement with mean-field theory for a range of contact interaction strengths. This work creates an opportunity for further investigations into beyond-mean-field effects and the finite-temperature phase diagram in the more strongly dipolar regime where supersolid and droplet states emerge.