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Physical Review A

Λ-type lasers and masers: Lasing without inversion and a vector model

Ning Lü

Published Apr 1, 1992• 5 citations
Publisher

Abstract

We show that the problem of a \ensuremath{\Lambda}-type (and also a V-type) three-level single-mode laser (maser) is isomorphic to that of a two-level single-mode laser (maser) under the conditions of energy-level degeneracy and equal decay rates. This correspondence reveals that lasing without population inversion can occur in the \ensuremath{\Lambda}-type system with or without an initial atomic coherence, and also gives immediately the master equation of the laser (maser) field. We analyze in detail the operational and noise properties of a \ensuremath{\Lambda}-type laser using a Fokker-Planck approach. We also present a vector model to visualize the population trapping and the absorption and emission processes in such a laser (maser) system.

DOI
10.1103/physreva.45.5011

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We show that the problem of a \ensuremath{\Lambda}-type (and also a V-type) three-level single-mode laser (maser) is isomorphic to that of a two-level single-mode laser (maser) under the conditions of energy-level degeneracy and equal decay rates. This correspondence reveals that lasing without population inversion can occur in the \ensuremath{\Lambda}-type system with or without an initial atomic coherence, and also gives immediately the master equation of the laser (maser) field. We analyze in detail the operational and noise properties of a \ensuremath{\Lambda}-type laser using a Fokker-Planck approach. We also present a vector model to visualize the population trapping and the absorption and emission processes in such a laser (maser) system.
We derive the master equations for the fields in the one-mode \ensuremath{\Lambda}-type micromaser and laser with injected atoms in a superposition of their states. In terms of effective parameters, these equations are equivalent to those for a two-level micromaser and laser. The interference terms in the master equations may cancel the absorption terms independent of statistical properties of the field. Due to the atomic coherence between the two degenerate lower levels, the generation of field states with sub-Poissonian photon statistics is possible in the micromaser without the need for a population inversion. If an equivalent level system is used in a laser operating without population inversion it can produce field states with Poisson distributions of the photon number.
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.
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.
The master equation for the field in the two-mode \ensuremath{\Lambda} laser with atoms injected in a superposition of their states is presented, and lasing without population inversion is studied from this vantage. An explicit expression for the steady-state photon distribution is derived under the conditions of detailed balance and no injected coherence. We study the photon statistics, as well as the decay of off-diagonal density-matrix elements and the linewidths of the two laser modes. The effect of an injected atomic coherence on the amplification of light is examined. It is shown that the interference terms in the master equation cancel the absorption terms if the field in each mode is in a coherent state and the conditions for atomic trapping are fulfilled. Numerical calculations demonstrate the buildup of lasing without inversion from the vacuum state of the field.
Noninversion lasing is investigated in \ensuremath{\Lambda}-type three-level atomic systems that are coupled to two modes of the electromagnetic field. As a result of an external field driving the transition between the lower two closely spaced levels, laser action can be achieved in both modes simultaneously at arbitrarily small initial upper-level population (lasing without inversion) provided the pumping rate exceeds a certain threshold. The relative phase of the two modes is locked to a particular value controlled by the phase of the external field. In addition, new regimes of the laser operation arise when initial coherences between various atomic levels are also injected into the resonator. Firstly, laser action can be achieved in both modes at arbitrarily small pumping (no threshold). Secondly, the injected atomic coherence can control competition between the modes, and result in a variety of multistable steady-state behavior illustrating the very sensitive dynamics of the system.
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.