Spin and density self-ordering in dynamic polarization gradients fields

We study the zero-temperature quantum phase diagram for a two-component Bose-Einstein condensate in an optical cavity. The two atomic spin states are Raman coupled by two transverse orthogonally polarized, blue-detuned plane-wave lasers inducing a repulsive cavity potential. For a weak pump the lasers favor a state with homogeneous density and predefined uniform spin direction. When one pump laser is polarized parallel to the cavity mode polarization, the photons coherently scattered into the resonator induce a polarization gradient along the cavity axis, which mediates long-range density-density, spin-density, and spin-spin interactions. We show that the coupled atom-cavity system implements central aspects of the t-J-V-W model with a rich phase diagram. At the mean-field limit we identify at least four qualitatively distinct density- and spin-ordered phases including ferromagnetic and antiferromagnetic order along the cavity axis, which can be controlled via the pump strength and detuning. Real-time observation of amplitude and phase of the emitted fields bears strong signatures of the realized phase and allows for real-time determination of phase transition lines. Together with measurements of the population imbalance, most properties of the phase diagram can be reconstructed.

Automated summary

In this study, we investigate the zero-temperature quantum phase diagram of a two-component Bose-Einstein condensate in an optical cavity. The coupled atom-cavity system demonstrates key aspects of the t-J-V-W model, showcasing a rich phase diagram with multiple density and spin-ordered phases that can be controlled through pump strength and detuning. Real-time observation of emitted fields can provide strong signatures of the realized phase and facilitate the determination of phase transition lines.