Quantum optics of dielectrics in momentum-space

Yair Dimant, Shimon Levit

We develop a path integral approach for analyzing the stationary light propagation in general dielectric media. The Hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle with spin-orbit coupling and position dependent mass. After appropriate ordering several path integral representations of a solution are constructed. First we keep the propagation of the polarization degrees of freedom in an operator form integrated over paths in a coordinate space. The use of spin 1 coherent states allows representing this part as a path integral over such states. Finally a path integral in a transversal momentum space with explicit transversality enforced at every time slice is also given. As an example the geometrical optics limit is discussed and the ray equation is recovered together with the Rytov rotation of the polarization vector.

Stephen Mark Barnett

Roy J. Glauber, Maciej Lewenstein

Koji Usami

An approach is described for observing quantum features of micron-sized spinning objects. Specifically, we consider a birefringent (uniaxial positive) dielectric object in the shape of an oblate (i.e., frisbee-like) symmetric top. It can be trapped in the air, its extraordinary axis can be aligned, and its angular momentum along the extraordinary axis can be stabilized, all optically. We show that the angular momentum quantum noise of the object perpendicular to the gigantic angular momentum along the extraordinary axis can be measured as a linear birefringent phase shift of a probe laser in an analogous fashion to the spin quantum nondemolition (QND) measurement in atomic physics.

M. Ducloy

Hamid Reza Hamedi, Vassilios Yannopapas, Emmanuel Paspalakis

Abstract The light–matter interaction for a four‐level double‐V‐type quantum system interacting with a pair of weak probe fields while located near a 2D array of metal‐coated dielectric nanospheres is studied. A situation is considered in which one of the probe field carries an optical vortex, that is, an electromagnetic field with optical angular momentum, and the other probe field has no vortex. It is demonstrated that due to the phase sensitivity of the closed‐loop double V‐type quantum system, the linear and nonlinear susceptibility of the non‐vortex probe beam depends on the azimuthal angle and orbital angular momentum (OAM) of the vortex probe beam. This feature is missing in an open four‐level double V‐type quantum system interacting with free‐space vacuum, as no quantum interference occurs in this case. The azimuthal dependence of optical susceptibility of the quantum system is used to determine the regions of spatially structured transparency.