### 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.