Synthetic spin-orbit coupling mediated by a bosonic environment

We study a mobile quantum impurity, possessing internal rotational degrees of freedom, confined to a ring in the presence of a many-particle bosonic bath. By considering the recently introduced rotating polaron problem, we define the Hamiltonian and examine the energy spectrum. The weak-coupling regime is studied by means of a variational ansatz in the truncated Fock space. The corresponding spectrum indicates that there emerges a coupling between the internal and orbital angular momenta of the impurity as a consequence of the phonon exchange. We interpret the coupling as a phonon-mediated spin-orbit coupling and quantify it by using a correlation function between the internal and the orbital angular momentum operators. The strong-coupling regime is investigated within the Pekar approach, and it is shown that the correlation function of the ground state shows a kink at a critical coupling, that is explained by a sharp transition from the noninteracting state to the states that exhibit strong interaction with the surroundings. The results might find applications in such fields as spintronics or topological insulators where spin-orbit coupling is of crucial importance.