Diagonalization of the Rabi Hamiltonian by means of a unitary transformation

Valerii Vladimirovich Val'kov

Dean Lee, Nathan Salwen, Daniel Lee

Andrey Pereverzev, Eric R. Bittner

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonalizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges.

H. M. Moya-Cessa, A. Vidiella-Barranco, José Antonio Roversi +1 more

We present a method of treating the problem of the interaction of a single trapped ion with laser beams based on successive applications of unitary transformations onto the Hamiltonian. This allows the diagonalization of the Hamiltonian, by means of recursive relations, without performing the Lamb-Dicke approximation.

V. Yu. Kuliev

Vassilios Fessatidis, Jay D. Mancini, Samuel P. Bowen