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

Abstract: In this article we apply algebraic operator ordering property of the basic atom and field operators to construct and prove conservation of the excitation number operator of the anti-rotating (anti-Jaynes-Cummings) component of the quantum Rabi model. The corresponding U(1) and parity symmetry operators have also been derived in explicit form.