The exact solution of the quantum Rabi Hamiltonian ĤRabi was first discovered by Braak 89 by noticing the parity symmetry in the Rabi model is sufficient to solve the Hamiltonian exactly using bosonic operators in the Bargmann space. Later, it was shown that the same solution can also be obtained from the Bogoliubov transformation. Dropping both the DSE and the counter-rotating terms (CRT) σ † â † and σâ leads to the well-known Jaynes-Cummings (JC) model as follows