Conserved excitation number and U(1)-symmetry operators for the anti-rotating (anti-Jaynes-Cummings) term of the Rabi Hamiltonian

Abstract

+ hω0sz+ hg (ˆa+ ˆa†)(s++ s−)(1a) where ω, ˆa, ˆa† are the quantized field mode angular frequency, annihilation and creation operators, while ω0, sz, s+, s− are the atomic state transition angular frequency and operators. We have used σx= s−+ s+ and expressed the free field mode Hamiltonian in the symmetrized normal and anti-normal order form