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

TL;DR

This paper investigates the shift in Bose-Einstein condensation temperature for trapped interacting bosons using large-N theories, addressing higher-order corrections and proposing a phenomenological model to improve predictions in various interaction regimes.

Contribution

It introduces large-N based theories combined with the local density approximation to evaluate higher-order $T_c$ shifts and proposes a phenomenological model to reconcile theoretical predictions with experimental data.

Findings

Large-N theories provide quantitative predictions for $T_c$ shifts.

LOAF theory accurately captures $T_c$ shift in weak interactions.

A phenomenological model improves predictions in stronger interactions.

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.