Casimir-Lifshitz force for nonreciprocal media and applications to photonic topological insulators

Abstract

Based on the theory of macroscopic quantum electrodynamics, we generalize the expression of the Casimir force for nonreciprocal media. The essential ingredient of this result is the Green's tensor between two nonreciprocal semi-infinite slabs including a reflexion matrix with four coefficients that mixes optical polarizations. This Green's tensor does not obey Lorentz's reciprocity and thus violates time-reversal symmetry. The general result for the Casimir force is analyzed in the retarded and nonretarded limits, concentrating on the influences arising from reflections with or without change of polarization. In a second step we apply our general result to a photonic topological insulator whose nonreciprocity stems from an anisotropic permittivity tensor, namely InSb. We show that there is a regime for the distance between the slabs where the magnitude of the Casimir force is tunable by an external magnetic field. Furthermore the strength of this tuning depends on the orientation of the magnetic field with respect to the slab surfaces.The conductivity tensor Q from Eq. (3) and the Green's tensor from Eq. (6) are related by µ 0 ω d 3 s d 3 s G (r, s, ω)·ℜ Q s, s , ω ·G * T r , s , ω = ℑ G r, r , ω , (9)

Fluctuation-induced forces on an atom near a photonic topological material

“…The Casimir-Polder force acting on atoms located close to the surface of a material body is of longstanding and current interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], and is of considerable practical importance in a variety of physical, biological and chemical processes. For planar surfaces, the normal component of the force has been extensively investigated both theoretically and experimentally [18].…”

Maxwell eigenmode approach to the Casimir-Lifshitz torque

“…Our approach does not depend on approximations such as weak anisotropy or neglecting retardation effects, and can be generalized to other types of media, such as metamaterials [34], multiferroics [35], topological matter [41], biaxial materials [31], and non-reciprocal materials [42]. The recently reported measurements of the Casimir torque [20] should instigate further investigations for which this result is of considerable importance.…”

Quest for Casimir repulsion between Chern-Simons surfaces

“…The reflection and transmission matrices for each of the subsystems satisfy (16). This allows us to show that (17), (20) and (21) together with the identity det (…”

“…Let us take one of the subsystems, say I, and consider it as a composite system consisting of two interfaces at z = 0 and z = − separated by a dielectric. Then, r I can be expressed through the scattering matrices at the interfaces by using the formula on the line above (20) (with obvious modifications). The dependence on is given by analogs of Eqs.…”