Critical temperature of trapped interacting bosons from large-N based theories

Abstract

Ultracold atoms provide clues to an important many-body problem regarding the dependence of Bose-Einstein condensation (BEC) transition temperature $T_c$ on interactions. However, cold atoms are trapped in harmonic potentials and theoretical evaluations of the $T_c$ shift of trapped interacting Bose gases are challenging. While previous predictions of the leading-order shift have been confirmed, more recent experiments exhibit higher-order corrections beyond available mean-field theories. By implementing two large-N based theories with the local density approximation (LDA), we extract next-order corrections of the $T_c$ shift. The leading-order large-N theory produces results quantitatively different from the latest experimental data. The leading-order auxiliary field (LOAF) theory containing both normal and anomalous density fields captures the $T_c$ shift accurately in the weak interaction regime. However, the LOAF theory shows incompatible behavior with the LDA and forcing the LDA leads to density discontinuities in the trap profiles. We present a phenomenological model based on the LOAF theory, which repairs the incompatibility and provides a prediction of the $T_c$ shift in stronger interaction regime.

11 pages, 3 figures

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Using photoemission spectroscopy to probe a strongly interacting Fermi gas
• Effects of Interactions on the Critical Temperature of a Trapped Bose Gas
• Non-perturbative predictions for cold atom Bose gases with tunable interactions
• Large-N approximation for single- and two-component dilute Bose gases
• Equation of state and contact of a strongly interacting Bose gas in the normal state
• Interaction effects on atomic laboratory trapped Bose-Einstein condensates

Cited by in corpus (1)

• Thermodynamics and structural transition of binary atomic Bose-Fermi mixtures in box or harmonic potentials: A path-integral study