Finite-temperature phase diagram and collective modes of coherently coupled Bose mixtures
Phys. Rev. A 113, 043310 – Published 9 April, 2026
DOI: https://doi.org/10.1103/l529-9544
Abstract
We investigate the ferromagnetic-paramagnetic phase transition in coherently (Rabi-)coupled Bose-Einstein condensates at zero and finite temperatures, exploring different routes to the transition by tuning the Rabi coupling or increasing the temperature at a fixed coupling. Using the Hartree-Fock-Bogoliubov theory within the Popov approximation, we map out the finite-temperature phase diagram of a three-dimensional homogeneous condensate. The critical line is identified from the softening of the spin gap, which at finite temperature does not strictly close but exhibits a discernible minimum. Magnetization and the spin dispersion branch reveal the progressive suppression of the ferromagnetic order with increasing temperature. In quasi-one-dimensional harmonic traps, the transition, driven by Rabi coupling, does not correspond to a sharply defined critical point. To this end, we use the softening of the spin breathing mode as an operational indicator of the transition, whose minimum shifts to lower coupling strengths with increasing temperature. Notably, the thermally driven transition causes monotonic hardening of all the spin modes. For both coupling and the temperature-driven transition, the hybridized “density” modes in the ferromagnetic phase acquire more density character while approaching the critical point.
