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Physical Review A

Strong intracavity and output laser noise reduction via initial atomic coherence

C. Saavedra, J. C. Retamal, Christoph H. Keitel

Published May 1, 1997• 11 citations
Publisher

Abstract

We study a nonlinear semiclassical and fully quantum-mechanical theory of a laser with an active medium of three-level atoms that may be initially prepared in a coherent superposition and interact with a classical external electromagnetic field. In particular, we determine the intracavity and output photon statistics of the laser light in a broad range of parameters. We find an inner sub-Poissonian statistics with a Mandel parameter close to the minimal value -1 when the laser is operating with initially prepared atoms, off resonant, and without inversion of the populations. In another regime, with, however, less favorable intracavity statistics, we find squeezing in the intensity output fluctuations of 80%, which is well above the present state of art noise reduction for this kind of coherently driven laser system.

DOI
10.1103/physreva.55.3802

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Physical Review A•Jul 1, 1989•45 citations
We study a nonlinear semiclassical and fully quantum-mechanical theory of a laser with an active medium of three-level atoms that may be initially prepared in a coherent superposition and interact with a classical external electromagnetic field. In particular, we determine the intracavity and output photon statistics of the laser light in a broad range of parameters. We find an inner sub-Poissonian statistics with a Mandel parameter close to the minimal value -1 when the laser is operating with initially prepared atoms, off resonant, and without inversion of the populations. In another regime, with, however, less favorable intracavity statistics, we find squeezing in the intensity output fluctuations of 80%, which is well above the present state of art noise reduction for this kind of coherently driven laser system.
We present a detailed analysis of the noise properties of a potential lasing scheme employing a coherently driven three-level system in the \ensuremath{\Lambda} configuration inside an optical cavity. We derive expressions for the steady-state laser intensity and the width of the intensity fluctuations and show that the output fields exhibit sub-Poissonian statistics for suitable operating conditions. The fundamental mechanism responsible for noise suppression is identified as increased intensity dissipation inside the cavity through emission and absorption by the atoms, which counteracts the intensity fluctuations.
Abstract We investigate the quantum statistical and squeezing properties of radiation generated by a coherently driven three-level laser system coupled to a squeezed vacuum reservoir. The analysis is carried out using c-number Langevin equations for normally ordered operator moments, allowing a transparent description of the interplay among atomic coherence, coherent driving, and reservoir-induced correlations. We show that significant quadrature squeezing can be achieved under appropriate conditions, with the degree of squeezing strongly influenced by the linear gain coefficient of the squeezed-vacuum reservoir, the strength of the coherent driving, and the initial atomic preparation. In particular, we find that maximal initial atomic coherence alone does not lead to squeezing in the absence of coherent driving, highlighting the essential role of phase-sensitive amplification. The results further reveal a shift of optimal squeezing toward lower values of the atomic coherence parameter and higher values of the driving strength as the gain and reservoir squeezing increase. In addition, we demonstrate the coexistence of strong quadrature squeezing with super-Poissonian photon statistics, reflecting the distinct roles of phase-sensitive and intensity fluctuations. The squeezing spectrum is also analyzed to provide frequency-resolved insight into noise suppression, directly relevant to homodyne-detection measurements. These findings clarify the trade-off between coherent excitation, which enhances phase-sensitive correlations, and photon population growth, which tends to increase intensity fluctuations, and they highlight parameter regimes where strong nonclassical effects can be realized under parameter regimes consistent with experimentally demonstrated cavity-QED and squeezed-light implementations.
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.
The influence of injected atomic coherence on a laser's operation is discussed by analyzing the semiclassical equations of motion of this system. Both stationary-steady-state and time-dependent regimes of operation are investigated. We present the dependence of the stationary laser intensity and phase on the external parameters (population inversion, amplitude of atomic coherence, and detuning). For small cavity-field detuning and large atomic coherence, both frequency and phase locking occurs. The laser frequency is locked to the atomic frequency, and the phase is locked to a value determined primarily by the phase of the atomic coherence. Under certain conditions, in the inverted regime, the output intensity is an ssS-shaped function of the atomic coherence, leading to the possibility of a bistable behavior. However, only a portion of the bistable curve gives stable stationary operation, and in critical points (the location of which depends crucially on the external parameters) time-dependent instabilities branch away. When the detuning is larger than a critical value there is neither phase nor frequency locking. We find that the time-dependent behavior of the laser intensity in this case is oscillatory (quasiperiodic), and show that there is a stable limit cycle in the phase plane of the quadratures. There is a small parameter region where a stationary steady state and an oscillatory state may coexist. We also consider the nonlinear quantum theory of a laser with injected atomic coherence, and include the effect of pumping statistics. We derive the Fokker-Planck equation for the P representation, and express the noise in terms of moments. We find that in the steady state the intensity noise can be suppressed below the shot-noise limit but that the phase fluctuations are not affected by pump regularity. For nonzero detuning, we find that transient squeezing of the phase fluctuations is possible.
We investigate the transient and the steady-state behaviour of the photon statistics of a single-atom laser, consisting of a three-level Λ system, driven by an incoherent external pump field and strongly coupled to a single mode of an optical cavity. For several limiting cases we are able to obtain analytical results. A comparison with standard multi-atom laser theory reveals a surprisingly good agreement down to very small intracavity photon numbers. Under appropriate operating conditions a calculation of the second-order intensity correlation function yields sub-Poissonian statistics as well as strong antibunching induced by the nonlinear dynamics of the atom.
A quantum theory of a two-level single-mode laser with injected atomic coherence is developed by generalizing the Scully-Lamb laser theory to a form appropriate for the analysis of a coherently pumped laser. We assume that the active atoms are prepared initially in a coherent superposition of the upper and lower levels, and we derive the master equation for the field density operator by treating the interaction of the laser field with many active atoms simultaneously. It is shown that the photon-number distribution can be exactly Poissonian. The laser operation is analyzed in terms of the Fokker-Planck equation for the laser field. Both the intensity and phase diffusion coefficients are phase sensitive and, for stable laser operation, become much smaller than those of an ordinary laser. Consequently, the injected atomic coherence reduces both the photon-number noise and phase noise simultaneously. The intensity diffusion coefficient can vanish exactly, and at the same time the phase diffusion coefficient can become very small. This leads to spontaneous-emission noise quenching in the photon-number distribution, and the laser field can become very close to a coherent state. A scheme to generate the proper form of the initial atomic coherence necessary for the quantum noise quenching is proposed and analyzed.