Photonic topological insulator plates violate Lorentz reciprocity, which leads to a directionality of surfaceguided modes. This in-plane directionality can be imprinted via an applied magnetic field. On the basis of macroscopic quantum electrodynamics in nonreciprocal media, we show that two photonic topological insulator surfaces are subject to a tunable, magnetic-field-dependent Casimir torque. Due to the directionality, this torque exhibits a unique 2π periodicity, in contradistinction to the Casimir torques encountered for reciprocal uniaxial birefringent media or corrugated surfaces which are π periodic. Remarkably, the torque direction and strength can be externally driven in situ by simply applying a magnetic field on the system, and we show that this can be exploited to induce a control of the rotation of small objects. Our predictions are relevant for nanooptomechanical experiments and devices.

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 nonresonant 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 three-dimensional 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 nontrivial optical torque, we derive closed-form expressions for the induced torque under the quasistatic 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 nanomechanical and biomechanical systems.

We investigate the quantum recoil force acting on an excited atom close to the surface of a nonreciprocal photonic topological insulator (PTI). The main atomic emission channel is the unidirectional surface plasmon propagating at the PTI-vacuum interface, and we show that it enables a spontaneous lateral recoil force that scales at short distances as 1/d^4, where d is the atom-PTI separation. Remarkably, the sign of the recoil force is polarization and orientation independent, and it occurs in a translation-invariant homogeneous system in thermal equilibrium. Surprisingly, the recoil force persists for very small values of the gyration pseudovector, which, for a biased plasma, corresponds to very low cyclotron frequencies. The ultrastrong recoil force is rooted in the quasihyperbolic dispersion of the surface plasmons. We consider both an initially excited atom and a continuous pump scenario, the latter giving rise to a steady lateral force whose direction can be changed at will by simply varying the orientation of the biasing magnetic field. Our predictions may be tested in experiments with cold Rydberg atoms and superconducting qubits.