Quasiparticle spinors in light-matter interactions: generalized Jaynes-Cummings and antiJaynes-Cummings models

Abstract

Seeking a clear understanding of the physical nature of quasiparticle excitations formed in the JaynesCummings and antiJaynes-Cummings interaction mechanisms in the quantum Rabi model, we have introduced appropriate composite atom-field dynamical operators which characterize the algebraic structure of the quantum state space of a quasiparticle excitation. We identify the dynamical operators as generalized atom-field angular momentum operators comprising state annihilation , creation, coherence, population inversion and Casimir operators, which generate a closed generalized SU(2) Lie algebra and satisfy the fermion anticommutation relations of a spinor. We therefore interpret the atom-field quasiparticle excitations in the quantum Rabi interaction as quasiparticle spinors. We establish that the algebraically complete quasiparticle spinor Hamiltonian automatically incorporates an intrinsic atom-field excitation number correlation operator component, yielding generalized Jaynes-Cummings Hamiltonian H = H + ¯h(ω0 − ω)ˆa † asˆ +s−, antiJaynes-Cummings Hamiltonian H = H − ¯h(ω0 + ω)ˆa † asˆ −s+ and Rabi Hamiltonian HR = 1 2 (H+H), where H , H are the standard Jaynes-Cummings and antiJaynes-Cummings Hamiltonians. A quasiparticle spinor, identified as JC-spinor or antiJC-spinor, may be interpreted as a generalized spin- 1 2 particle specified by an infinite spectrum of integer and half-integer quantum numbers and an infinite spectrum of photon-carrying spin-up and spin-down qubit states for field mode photon numbers n = 0, 1, 2, 3, ..., ∞. The Hamiltonian generates a general time evolving entangled state vector describing Rabi oscillations between the qubit state vectors. Expressing the time evolving state vector as a superposition of entangled state eigenvectors reveals a frequency-shift phenomenon associated with the atom-field excitation correlation energy. Considering the atom initially in a spin-up and spin-down superposition state or the field mode initially in a coherent state, the dynamical evolution of the state population inversion, coherence and the fluctuations is characterized by quantum collapses and revivals due to interference of oscillations with different Rabi frequencies.