Spin relaxation in a polariton fluid: Quantum hydrodynamic approach

Cavity polaritons, the elementary excitations appearing in quantum microcavities in the strong-coupling regime, reveal clear signatures of quantum collective behavior. The combination of unique spin structure and strong nonlinear response opens the possibility of direct experimental observation of a plethora of nontrivial optical polarization phenomena. Spin relaxation processes are of crucial importance here. However, a mathematical formalism for their coherent description is still absent. In the present paper, based on the quantum hydrodynamics approach for a two-component liquid, we derive the set of the corresponding equations where both energy and spin relaxation terms appear naturally. We analyze in detail how these terms affect the dynamics of spinor polariton droplets in the external magnetic field and the dispersion of elementary excitations of a uniform polariton condensate. Although we focus on the case of cavity polaritons, our approach can be applied to other cases of spinor bosonic condensates, where the processes of spin relaxation play a major role.