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Journal of Physics B Atomic Molecular and Optical Physics

Effect of interference between three-level inversions on the inversion process and amount of inversion in a four-level system

A. S. Choe, Jongmin Lee

Published Mar 28, 1998• 1 citation
Publisher

Abstract

In a four-level -system interacting with three coherent laser pulses, interference between population inversions in coupled three-level ladders is examined. The interference effect, which affects the process and the completeness of the inversion, is represented by the two-photon coherence. It is shown that, in the adiabatic passage method, the phase and the scaling factor of the two-photon coherence are zero and a constant, respectively, resulting in no interference effect, but, in the optimal detuning method, they are strongly time dependent enough to represent the interference effect to change the process and the amount of inversion significantly. In the latter method, the ratio of Rabi frequencies for the four-level inversion to be completed, which is changed by the interference effect, is obtained.

DOI
10.1088/0953-4075/31/6/006

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In a four-level -system interacting with three coherent laser pulses, interference between population inversions in coupled three-level ladders is examined. The interference effect, which affects the process and the completeness of the inversion, is represented by the two-photon coherence. It is shown that, in the adiabatic passage method, the phase and the scaling factor of the two-photon coherence are zero and a constant, respectively, resulting in no interference effect, but, in the optimal detuning method, they are strongly time dependent enough to represent the interference effect to change the process and the amount of inversion significantly. In the latter method, the ratio of Rabi frequencies for the four-level inversion to be completed, which is changed by the interference effect, is obtained.
For the purpose of an examination of coherence control, we study the dynamics of population inversion in the four-level λ system where initial populations are arbitrary coherently distributed in two lower levels. It is shown that the coherence control, which causes population transfer between the lower levels to be forbidden, is possible by using the ratio of Rabi frequencies. Under this condition, it is remarkable that the adiabatic following and the optimal detuning methods are useful to invert the four-level system completely, and it is shown that the two-photon coherences of the coupled three-level ladders are dispersive and absorptive in the former and the latter methods, respectively. From the geometrical interpretation, the Bloch vectors, describing the four-level inversions, could be defined as ones in a two-level system.
We show that optimal detuning method describing population transfer passage in a three‐level system has an essential difference from the adiabatic following passage by counterintuititive sequence of two coherent laser pulses, by examining the dressed eigenstates and the Bloch vector precessing around a torque vector. In a four‐level Λ system, population dynamics is studied for the case where, on the optimal detuning condition, two‐photon coherences causing adiabtic transfer interfere each other. For a scheme of three degenerate levels, we show a possibility of complete population inversion by the optimal detuning method.
The effect of the collisions on the control of coherent population transfer in a closed inverse YYY-type four-level system driven by three laser fields is investigated with the stimulated Raman adiabatic passage technique. An arbitrary coherent superposition between the initial state and target state can be created either by varying the Rabi frequency of the control laser field or by tuning the one-photon detunings of the pump and Stokes laser fields. When the three laser fields with nearly equal peak Rabi frequencies are each tuned to resonance with the respective transitions, the low transfer efficiency due to the nonadiabatic coupling between two degenerate adiabatic states could be enhanced dramatically with the increase of the collision-induced coherence decay rates to the value nearly comparable to the Rabi frequency of the control field. The enhanced transfer efficiency results from the collision-controlled electromagnetically induced transparency in the $\ensuremath{\Lambda}$-type three-level subsystem and electromagnetically induced absorption in the ladder-type three-level subsystem of the four-level system.
We show lasing without population inversion in a closed four-level atomic system which is no longer incoherently pumped on the transition at which lasing occurs. The four-level system can overcome some limits in the typical lambda-type and V-type three-level systems, furthermore it is possible to achieve lasing even in the absence of the inversion condition for the thermal radiation fields or of the inversion of spontaneous decay rate. We find that when the detuning of probe field is equal to that of coherent coupling field, there is a peak value along with the increase of the detuning. To explain it, we bring forward that there are adiabatic and nonadiabatic stimulated Raman processes when a three-level atomic system is interacted with two coherent fields, so there are two mechanisms influencing the change of probe field. We believe that it can explain more general lasing without inversion processes because of quantum interference induced by coherent fields.
A four-level system driven by two coherent fields is considered. It is shown that in the presence of an incoherent pump, the probe gain at a short wavelength can be achieved due to the quantum interference. Our density matrix calculation provides the conditions for probe amplification from different origins, including gain without population inversion on any state basis, gain with population inversion on the dressed-state basis and gain with population inversion on the bare-state basis. Also, by controlling the Rabi frequency of the coupling field a total change from non-inversion to inversion can be achieved which does not depend on the intensity of the incoherent pump.
We investigate the effect of collision-induced coherence on coherent population transfer with the stimulated Raman adiabatic passage technique in a double A-type four-level system with a widely separated excited doublet. It is shown that when the two pulsed lasers with Rabi frequencies nearly comparable to the energy separation of the doublet are tuned to the particular frequency where the condition for quantum interference is satisfied, the very low transfer efficiency due to the nonadiabatic coupling between the two degenerate adiabatic states could be enhanced significantly with the increase of the collisional decay rates in a moderate range. The enhanced transfer efficiency results from the weakening of the nonadiabatic coupling between the two degenerate adiabatic states realized through collision-induced destructive quantum interference.