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Physical Review A

Noise reduction, lasing without inversion, and pump statistics in coherently prepared λ quantum-beat media

Miguel Orszag, Shi-Yao Zhu, János A. Bergou, Marlan O. Scully

Published Apr 1, 1992• 8 citations
Publisher

Abstract

Amplitude-noise reduction and diminished losses are found in a laser system in which the lower level of the usual two-level atom is replaced by a coherently prepared doublet, i.e., a \ensuremath{\lambda} quantum-beat configuration. The role of atomic coherence between the various levels and regular pumping is investigated. When a portion of the output signal is reflected from a phase-conjugate mirror and reinjected into the laser, the locking phase can be altered and a large phase-noise reduction can be obtained.

DOI
10.1103/physreva.45.4872

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 14, 2000•0 citations
Amplitude-noise reduction and diminished losses are found in a laser system in which the lower level of the usual two-level atom is replaced by a coherently prepared doublet, i.e., a \ensuremath{\lambda} quantum-beat configuration. The role of atomic coherence between the various levels and regular pumping is investigated. When a portion of the output signal is reflected from a phase-conjugate mirror and reinjected into the laser, the locking phase can be altered and a large phase-noise reduction can be obtained.
We present the quantum theory of a two-mode Lambda-type three level quantum-beat laser with injected atomic coherences. The lower two levels are coupled by an external classical field. The master equation and the Fokker–Planck equation are derived. Phases of the two modes are locked to a value depending on the phase of the external field, the phase of the injected coherence and the population of the lower two levels. Lasing without inversion and without threshold is found for both modes with and without injected coherences. Applying the appropriate initial atomic coherences one can switch intensities between the two modes, as well as bifurcation and multiple branching can be found when coherences among all levels are present. It is also possible to find phase bistability at a fixed intensity for one of the two modes, when high pump is applied. Strong intensity and phase noise reduction can be found in one of the modes at the expense of increased noises in the other one. Near Poissonian noise can be achieved. This research was supported by a grant of the Office of Naval Research.
A quantum theory of a \ensuremath{\Lambda}-type three-level single-mode quantum-beat laser with injected atomic coherences and with an external microwave field, which coherently drives the lower two nearly degenerate levels, is studied. A master equation for the field-density operator and the photon statistics is derived. The laser operation is analyzed in terms of the coefficients of the Fokker-Planck equation of the laser field. Noninversion lasing is found in both cases: without and with injected atomic coherences. At the same time, in the latter case large quantum-noise reduction is found, and for particular initial parameter choices the laser field is very near to a coherent state with exactly Poissonian photon-number distribution and near-Poissonian phase distribution.
We show that the nonlinear dynamics of the active atoms in conventionally pumped multilevel laser systems can lead to output intensity fluctuations significantly below the shot noise level1,2 (see also Refs, 3-5). Our calculations are based on the standard model of the laser which assumes a large number of atoms resonantly coupled to a single lasing mode. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through pumping as the key process leading to this dynamic pump noise reduction. It is required that (i) the pump rates be comparable to the decay rates of the atom, and (ii) we have a closed repumping cycle, and a constant number of atoms. We find that the results are closely related to recent calculations based on the assumption of an external regular pump6 (for noise reduction in semiconductor lasers, see Ref. 7).
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.
Based on the standard laser model of a large number N of model atoms resonantly coupled to a single lasing mode, we show that the nonlinear dynamics of the active atoms of the laser can lead to output-intensity fluctuations significantly reduced below the shot-noise level. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through the pumping as the key process leading to this dynamic-pump-noise reduction. This process has been neglected in most of the standard treatments of the laser so far. We find that the results are closely related to recent calculations based on the assumption of an external regular pump. For the widely used four-level model of the active atoms, the intensity noise can be reduced 50% below the shot-noise level. Generalizing the model to an m-level system, we find a quantum-noise reduction by a factor of 1/2m/(m-1)(m\ensuremath{\ge}3), leading to perfect output-intensity noise reduction in the limit of a large number of intermediate steps in the recycling process of the active atoms. Finally, we demonstrate that the bandwidth of the noise reduction can be significantly enhanced using a nonlinear absorber in the cavity.
When pumping produces atomic coherence on working levels or atomic polarization two-level atom can generate the light without inversion. In such systems one- and two-photon generation of the light is considered for the laser and micromaser operation. Using Lamb-Scully model generalized for coherent pumping statistics of the light is considered. Two-photon laser operation is found to be phase squeezed and perfect noise reduction can be achieved. In maser a set of steady state of subpoissian photon statistics is found. For these states the noise reduction up to 60 percent can be obtained if inversion is zero. Phase squeezing in micromaser is found.