Variational results for the Rabi Hamiltonian

Abstract

We present simple two-and three-parameter variational calculations for the Rabi Hamiltonian. The importance of symmetry in the anstitze is stressed. The numerical results indicate that our anstitze provide accurate approximations both to the groundstate energy and wavefunction and to the first excited state if the two-boson energy significantly exceeds the level splitting.

High-order connected moments expansion for the Rabi Hamiltonian

“…Table 1 shows the ground-state energy of the Rabi Hamiltonian for several values of N and for the same set of parameters chosen by Bishop et al [30]. Present results are ½¼¿ Unauthenticated Download Date | 5/12/18 5:15 AM more accurate than those obtained earlier and will be a useful benchmark for the investigation of the convergence properties of the CMX.…”

Rabi model beyond the rotating-wave approximation: Generation of photons from vacuum through decoherence

“…a (a † ) is the annihilation (creation) operator of the EM field, σ z = |e e| − |g g| and σ + = |e g| (σ − = σ † + ) are atomic operators, with |g and |e denoting the ground and excited atomic states, respectively. Although largely studied over the last decades, up to now its exact analytical solution is lacking and only numerical [2,3,4,5] and approximate analytical solutions are available [6,7,8], despite the conjecture by Reik and Doucha [9] that an exact solution of RH in terms of known functions is possible. The most used analytical approach to RH is to make the rotate wave approximation (RWA), where the antirotating term g a † σ + + aσ − is neglected , since in the weak coupling regime g/ω 1, small detuning |∆| ω (∆ = ω 0 − ω), and weak field amplitude its contribution to the evolution of the system is quite small [10,11].…”

Time evolution of the Rabi Hamiltonian from the unexcited vacuum

“…Reik and others [12] have adapted Judd's method [11] for the Jahn-Teller system for use with the Rabi Hamiltonian. Here, the Hamiltonian is translated into the Bargmann representation [13] Variational results have also been provided by Bishop et al [14] and by Benivegna and Messina [15]. The latter method also permits perturbative corrections, allowing the exact results to be approached.…”