| dc.description.abstract | This paper presents a precise algebraic and physical framework for studying the dynamics and practical
applications of the quantum Rabi model. We redefine the quantum Rabi interaction in terms of polariton
and anti-polariton qubits generated by the Jaynes-Cummings and anti-Jaynes-Cummings interactions,
respectively. The formation of a polariton qubit involves absorption or emission of positive energy photon
by the field mode, while the formation of an anti-polariton qubit involves absorption or emission of
negative energy photon by the field mode, triggered by initial emission or absorption of positive energy
photon by the atom. A polariton or anti-polariton qubit is a two-state quantized particle specified by
two state vectors, Hamiltonian, conserved excitation number, identity, state transition, U(1)-symmetry,
parity-symmetry, SU(2)/U(1)-symmetry and SU(1, 1)/U(1)-symmetry operators. Superpositions of the
qubit state vectors provide the eigenvectors and energy eigenvalues of the respective Hamiltonians. The
polariton or anti-polariton qubit state transition operator defined within the two-dimensional subspace
spanned by the qubit state vectors has algebraic properties equivalent to the algebraic properties of
an atomic spin state transition operator (Pauli matrix) σx, leading to a photospin interpretation of a
polariton or anti-polariton qubit. Dynamical evolution describing Rabi oscillations between qubit states
is easily evaluated and basic features of the dynamics are determined explicitly. The similarity of polariton
and anti-polariton qubits to the atomic spin qubits, i.e., the photospin picture, naturally leads to the
introduction of a quantum Rabi optical lattice as a geometrical framework for studying the dynamics and
physical properties of systems of interacting polariton and anti-polariton qubits. | en_US |
