Effect of the counterrotating-wave terms on the spontaneous emission from a multilevel atom

Abstract

The spontaneous decay of a multilevel atom interacting with the electromagnetic field in free space is investigated with a unitary transformation method, which is introduced in order to include all rotating and counter-rotating terms in the Hamiltonian. By using the ground state of the total Hamiltonian, the evolution of the effective decay rate and the energy shift are calculated. When the atomic transition frequency is smaller than the central frequency of the spectrum, the Zeno effect dominates, and if the atomic transition frequency is larger than the central frequency, the anti-Zeno effect will dominate. The time evolution of the energy shift is obtained. The counter-rotating terms lead to a shift toward the low frequency region for the frequency distribution of the emitted photon.

Quantum anti-Zeno effect without rotating wave approximation

“…Recently it was recognized [10,11] that the theoretical prediction [8] for the reservoir-enhanced decay phenomena may be based on the rotating wave approximation (RWA) [3], where the counter-rotating terms are neglected as they are high-frequency oscillating. A quite natural question follows as to whether the existence of the QAZE really relies on the counter-rotating term, which is usually ignored in many applications since it possesses high-frequency oscillation in the interaction picture.…”

Control of the Lamb shift by a driving field

“…As the interaction Hamiltonian H 1 contains the counterrotating terms, we follow the unitary transformation approach presented in [12] and [13]. This approach allows us to make the unitary transformation so that the interaction part has the same form as under the RWA.…”

“…In the regular approach to dealing with the quantum interference phenomenon, rotating wave approximation (RWA) is often made. Recently, a unitary transformation approach has been proposed to solve for the influence of the counter-rotating terms on the dynamic evolution of the atom in the short time limit [12,13]. In this paper we apply this method to a laser-driven atomic system and show how the Lamb shift can be affected by the quantum interference between the two-photon channel of the original energy levels and the new channels opened by the pumping laser.…”

Quantum interference due to energy shifts and its effect on spontaneous emission

“…In these studies, the main focus was on the interference between the decay rates of the two levels (real parts of the dynamical equations), while the imaginary parts (phase changes) in the dynamical equations, which result in the energy shift, were neglected under the long time limit and the Markov approximation [1,2]. In the single-transition case, the imaginary parts lead to the dynamic energy shift and eventually result in the energy shift in the long time limit [9][10][11]. During the dynamical process, especially in the initial evolution period, the imaginary parts and the real parts are correlated, that is to say, the dynamic energy shifts and the decay rates are correlated [9,10].…”

“…In the single-transition case, the imaginary parts lead to the dynamic energy shift and eventually result in the energy shift in the long time limit [9][10][11]. During the dynamical process, especially in the initial evolution period, the imaginary parts and the real parts are correlated, that is to say, the dynamic energy shifts and the decay rates are correlated [9,10]. It is natural to ask, what is the quantum interference resulting from the energy shifts, and what is the effect of the dynamic energy shift (the imaginary part) on the decay rate (the real part), including the quantum interference between the two decay rates?…”