  We investigate the quantum optical torque on an atom interacting with an
inhomogeneous electromagnetic environment described by the most general linear
constitutive relations. The atom is modeled as a two-level system prepared in
an arbitrary initial energy state. Using the Heisenberg equation of motion
(HEM) and under the Markov approximation, we show that the optical torque has a
resonant and non-resonant part, associated respectively with a
spontaneous-emission process and Casimir-type interactions with the quantum
vacuum, which can both be written explicitly in terms of the system Green
function. Our formulation is valid for any inhomogeneous, dissipative,
dispersive, nonreciprocal, and bianisotropic structure. We apply this general
theory to a scenario in which the atom interacts with a material characterized
by strong nonreciprocity and modal unidirectionality. In this case, the main
decay channel of the atom energy is represented by the unidirectional surface
waves launched at the nonreciprocal material-vacuum interface. To provide
relevant physical insight into the role of these unidirectional surface waves
in the emergence of non-trivial optical torque, we derive closed-form
expressions for the induced torque under the quasi-static approximation.
Finally, we investigate the equilibrium states of the atom polarization, along
which the atom spontaneously tends to align due to the action of the torque.
Our theoretical predictions may be experimentally tested with cold Rydberg
atoms and superconducting qubits near a nonreciprocal material. We believe that
our general theory may find broad application in the context of nano-mechanical
and bio-mechanical systems.
