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Annual Meeting Optical Society of America

Long-lived states of the quantized field in a laser

Julio R. Gea-Banacloche

Published Jan 1, 1990• 0 citations
Publisher

Abstract

The lifetimes of different pure states of the quantized field in a single-mode laser (Scully-Lamb model) are considered. For operation high above threshold, I have shown number states to have extremely short lifetimes: Long lifetimes require coherent superpositions of neighboring number states with a width of the order of the square root of the average photon number. Thus, the long-lived states approach classical states. I propose a definition of the lifetime, which is found to be maximized by states that resemble the conventional Glauber coherent states, although they are slightly narrower in photon-number distribution. This is in contrast to the steadystate photon-number distribution for an ensemble of identical lasers (as given by the diagonal steady-state density matrix), which is wider than a coherent state. Possible interpretations and implications of these results are discussed.

DOI
10.1364/oam.1990.tunn3

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The lifetimes of different pure states of the quantized field in a single-mode laser (Scully-Lamb model) are considered. For operation high above threshold, I have shown number states to have extremely short lifetimes: Long lifetimes require coherent superpositions of neighboring number states with a width of the order of the square root of the average photon number. Thus, the long-lived states approach classical states. I propose a definition of the lifetime, which is found to be maximized by states that resemble the conventional Glauber coherent states, although they are slightly narrower in photon-number distribution. This is in contrast to the steadystate photon-number distribution for an ensemble of identical lasers (as given by the diagonal steady-state density matrix), which is wider than a coherent state. Possible interpretations and implications of these results are discussed.
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The rate at which pure initial states satisfying the detailed balance condition on the photon number states deteriorate into mixtures in the decoherence process is computed for a laser field above threshold in the Scully-Lamb laser model. In steady-state laser operation, the field state suggested by Scully and Lamb is shown to be the least increase of the error area in the complex amplitude plane, thus becoming the most stable field state among the squeezed states characterized by the phase order parameter Δ.
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.
The quantum-statistical properties of the optical field of a two-mode laser with two coupled transitions have been studied by means of a generalization of the Scully and Lamb theory. The photon number distribution and the mode intensity distribution are obtained in the steady state for a system of homogeneously broadened atoms in resonance with the laser field. It is shown that the mode-coupling constant $\ensuremath{\xi}$ is unity and that near threshold the results of earlier treatments are recovered. Furthermore, it is shown that certain limit measures for the relative intensity fluctuations predicted by the semiclassical Fokker-Planck treatments based on the third-order theory are valid even in the limit of arbitrarily high gain levels.