Spin critical opalescence in zero temperature Bose-Einstein Condensates

TL;DR

This paper explores the critical spin opalescence phenomenon in zero-temperature Bose-Einstein condensates, revealing long-range spin fluctuations and suppressed density fluctuations near a special scattering length condition.

Contribution

It introduces an effective spin model to describe phase transitions in BECs and identifies conditions for critical spin fluctuations at zero temperature.

Findings

Long-range spin fluctuations occur at the transition point.

Density fluctuations are suppressed near the special scattering length condition.

Critical opalescence manifests in impurity atom waves at zero temperature.

Abstract

Cold atom developments suggest the prospect of measuring scaling properties and long-range fluctuations of continuous phase transitions at zero-temperature. We discuss the conditions for characterizing the phase separation of Bose-Einstein condensates of boson atoms in two distinct hyperfine spin states. The mean-field description breaks down as the system approaches the transition from the miscible side. An effective spin description clarifies the ferromagnetic nature of the transition. We show that a difference in the scattering lengths for the bosons in the same spin state leads to an effective internal magnetic field. The conditions at which the internal magnetic field vanishes (i.e., equal values of the like-boson scattering lengths) is a special point. We show that the long range density fluctuations are suppressed near that point while the effective spin exhibits the long-range fluctuations that characterize critical points. The zero-temperature system exhibits critical opalescence with respect to long wavelength waves of impurity atoms that interact with the bosons in a spin-dependent manner.