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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Coherent population trapping beyond the rotating-wave approximation

Boris G. Matisov, I. E. Mazets, Laurentius Windholz

Published Aug 1, 1995• 6 citations
Publisher

Abstract

We consider the case of interaction of a three-level atom with a high intensity pulse electromagnetic field. Rabi frequencies are assumed to be of the order of the transition frequency or greater. We demonstrate that coherent population trapping exists even in such a case when the usual rotating-wave approximation is no longer valid. However, a certain condition on the phases of electromagnetic wave components has to be satisfied in order to make coherent population trapping possible. This condition is specific for the strong field case in contrast to the case where the rotating-wave approximation is valid. Also we point out some elements for which a model of an atom with a finite number of levels may still be valid while the rotating-wave approximation breaks down.

DOI
10.1088/1355-5111/7/4/001

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Journal of Physics Communications•Apr 17, 2018•3 citations
We consider the case of interaction of a three-level atom with a high intensity pulse electromagnetic field. Rabi frequencies are assumed to be of the order of the transition frequency or greater. We demonstrate that coherent population trapping exists even in such a case when the usual rotating-wave approximation is no longer valid. However, a certain condition on the phases of electromagnetic wave components has to be satisfied in order to make coherent population trapping possible. This condition is specific for the strong field case in contrast to the case where the rotating-wave approximation is valid. Also we point out some elements for which a model of an atom with a finite number of levels may still be valid while the rotating-wave approximation breaks down.
We investigate the interaction of a multilevel atom with a short femtosecond optical pulse beyond the scope of the rotating-wave approximation. We consider the behavior of a three-level atom under the action of two optical pulses resonant with two allowed transitions and a two-level atom under the action of a resonant optical pulse. It is shown that the imaginary part of the off-diagonal elements of the density matrix oscillates with high frequency due to the counter-rotating terms. It is shown also that an effective time-dependent addition to the Rabi frequency exists, which is of importance for ultrashort optical pulses.
One of the simplest models involving the atom-field interaction is the coupling of a single two-level atom with single-mode optical field. Under the rotating wave approximation, this problem is reduced to a form that can be solved exactly. But the approximation is only valid when the two levels are resonant or nearly resonant with the applied electromagnetic radiation. Here we present an analytical solution without the rotating wave approximation and applicable to general atom-field interaction far away from the resonance. We find that there exists remarkable influence of the initial phase of optical field on the Rabi oscillations and Rabi splitting, and this issue cannot be explored in the context of the rotating wave approximation. Due to the retention of the counter-rotating terms, higher-order harmonic appears during the Rabi splitting. The analytical solution suggests a way to regulate and control the quantum dynamics of a two-level atom and allows for exploring more essential features of the atom-field interaction.
We explore extended $\ensuremath{\Lambda}$ systems driven by two resonant laser fields in a strong regime characterized by the fact that the Rabi frequencies are much bigger than the difference between the two field frequencies. We show that a specific coherent superposition of the lower states is trapped during the dynamics. This extended trapped state is different from the trapped state usually encountered in the rotating-wave-approximation regime. We show the robustness of this trapping in the sense that it is stable with respect to significant deviations of the field parameters (frequencies and amplitudes).
The poulation transfer and coherent population trapping of a three-level atom interacting with few cycle pulse train are studied.The density matrix equation in interation picture is numerical solved without rotating wave approximation.The research indicates that if a three-level atom interacts with a few cycle pulse train,the population transfer of level and the coherence of ground state will be gradual accumulated.When the repetition frequency of pulses is integer points of the ground-state splitting,the three atom interacts with pulse train can be seen as the atom interacts with two tenoning frequency of the frequency comb.So the system will be in the dark state and reach coherent population trapping.If the parameters of few-cycle pulse are appropriately selected,the coherence of three-level system will evolute into stable value in 0.5 nanosecond.The coherent population trapping in the three-level is generated.Comparing with the pulse that the pulse width is 100 femtoseconds,the build-up time of coherent population trapping by few cycle pulse train is shortened two orders of magnitude.When the ground-state splitting is wided enough and the carrier frequency of pulse is ω=(ω1+ω2)/2,where,are the atomic transition frequency,the doppler frequency shift that is aroused by the movement of atom won't destroy the coherent population trapping of atom.The reason is that all tenoning frequencies of the frequency comb have the same frequency shift,so the condition of coherent population trapping is still meeted.
The trapping states of a quantum system occupy a very special place in quantum optics. Here, we propose a method to realize the population trapping (PT) in a two-level atom driven by a carrier envelope phase (CEP) locked laser pulse. We present detailed numerical results on the influence of CEP in different detuned atoms beyond the rotating wave approximation and find the population is strongly dependent on CEP, the detuning and the Rabi frequency. This allows us to choose proper parameters to realize three specific trapping states: upper trapping state, half trapping state and lower trapping state. To explain the fantastic influence of CEP, we present an analytical solution under weak-field approximation, which is consistent with the numerical solution. We further define the action quantity of the pulse acting on the atom as the integral for the interaction Hamiltonian and find the population varies approximatively linearly with the action quantity. This investigation provides directive significance for achieving PT at arbitrary quantum states and insightful schemes to regulate and control the quantum dynamics of atoms via accurately controlled optical field, and the results could be beneficial for applications to laser cooling, isotope separation and so on.