Photospins in the quantum Rabi model

Abstract

This article provides a systematic interpretation of the quantum Rabi model as a model of photospins formed in the atom-field Jaynes-Cummings and anti-Jaynes-Cummings interaction mechanisms. A photospin is a quantized photon-carrying two-state quasiparticle mode specified by two qubit state vectors, state eigenvectors, energy eigenvalues and well defined dynamical and symmetry operators. The algebraic properties of a photospin are exactly the same as the algebraic properties of a two-state atomic spin (spin- 1 2 particle). The time evolving photospin qubit state vectors describe exact Rabi oscillations between the qubit states, while the corresponding time evolving density operator reveals that the geometric configuration of the photospin state space is a circle of unit radius in the yz-plane. The internal dynamics of a Jaynes-Cummings interaction generated photospin (rotating photospin) is characterized by red-sideband transitions specified by frequency detuning δ = ω0 − ω, while the internal dynamics of an anti-Jaynes-Cummings interaction generated photospin (antirotating photospin) is characterized by blue-sideband transitions specified by frequency detuning δ = ω0 + ω. The simple algebraic properties of a photospin allow formulation of exactly solved models of interacting photospins on Jaynes-Cummings and anti-Jaynes-Cummings optical lattices. The physical property that a photospin state transition operator has eigenvalues ±1 in the eigenstate basis provides models of interacting photospins equivalent to one-dimensional Curie-Weiss or Ising models of interacting spins on a linear crystal lattice. Time evolving state vectors of two interacting photospins have been determined exactly as entangled nonorthogonal state vectors, which have wide applications in quantum information processing, quantum computation, quantum teleportation and communication, quantum state tomography and related quantum technologies.