Spin critical opalescence in zero-temperature Bose-Einstein condensates
Department of Physics, Temple University - Philadelphia, PA 19122, USA
2 T-4, Theory division, Los Alamos National Laboratory - Los Alamos, NM 87545, USA
Accepted: 5 January 2012
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 point 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.
PACS: 67.85.Fg – Multicomponent condensates; spinor condensates / 67.85.-d – Ultracold gases, trapped gases / 64.70.Tg – Quantum phase transitions
© EPLA, 2012