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arXiv:quant-ph/0512009

Lasing without inversion in a closed four-level system

Cai, Li-Feng

Published Dec 1, 2005• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.quant-ph/0512009

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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.
The LWI operation condition for an open Λ-type three level atomic system is obtained by solving the steady-state density-matrix equation with the system being driven by a strong coherent field while the inherent pumping rate and decay rate being arbitrary.It is shown that the inversions of inherent pumping rate and spontaneous decay rate replace the inversion of population,and together help to realize lasing without population inversion.Furthermore,the LWI can be realized if just either one of the two inversions is fulfilled.A schrodinger equation of three-level atomic system with appropriate conditions is analytically solved to explain the quantum interference process that leads to LWI.
Considerable attention has been directed recently to the study of lasing without the need of population inversion. The optical coherence and quantum interference associated with the light amplification may lead to interesting statistical properties in inversionless lasers. Here we analyze a laser model that consists of an ensemble of closed multi-level (three or four levels) atoms driven by a single coherent field. Unlike conventional lasers where population inversion is maintained and kept at the threshold value for arbitrary laser output, the multi-level laser analyzed here can start lasing from population inversion and evolves from population inversion into non-inversion with the increasing atomic pumping. In other words, the system makes transition from light amplification by population inversion into light amplification by coherence. On the other hand, the system can be also made to start lasing without population inversion in any state basis. In both cases, initial inversion and non-inversion, which are controlled by the ratio of spontaneous decay rates, the laser well above threshold is always maintained by lasing without inversion (light amplification by coherence), and the laser intensity fluctuations may drop below the shot noise limit. Two factors contribute to the noise reduction: first, the disappearance of the population inversion leads to the depleted atomic population in the upper lasing state, which reduces the spontaneous emission noises; second, the fast coherent cycling of electrons between excited states leads to the highly regulated absorption and emission processes. We found that the combination of these two mechanisms can lead to the noise reduction in the laser output more than 50% below the shot-noise limit.
For a four-level atomic system with a doublet of closely spaced levels, we find that, owing to the coherence that results from the vacuum of the radiation field, population trapping at excited levels and probe gain with population inversion can be achieved with weak incoherent pumping. This gain is different from both the conventional lasing gain and gain without inversion in that there exists population inversion on probe transitions but the inversion is achieved by the vacuum-induced coherence.
We provide a four-level double-V type atomic system driven by two week probe fields and two strong coupling laser beams. In the condition of resonant four-wave mixing, the two probe fields can be amplified without population inversion. Due to the fact that the two excited states are close- lying upper levels of hyperfine structure, the spontaneously generated coherence (SGC) effect must be considered. Interestingly, the amplitude of gain is sufficiently enhanced with the same parameters as those in the case without considering SGC. In addition, we find that the probe gain is sensitive to the phase of two laser fields which interact with the same lower level. To be more specific, the amplitude of gain is modulated by the phase periodically but restricted by θ (the angle between two induced dipole moments). At the same time, we also analyze the influence of the coherence pumping (strong coupling fields) detuning.