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Physical Review A

Observation of the ‘‘Brownian motion’’ of the electric field in a laser

M. R. Young, Surendra Singh

Published Feb 1, 1987• 23 citations
Publisher

Abstract

Critical dynamics of the laser field near the threshold of oscillation is investigated and observation of the Brownian motion of the electric field amplitude driven by quantum noise is reported. Experimental results agree well with the nonlinear oscillator model of the laser.
DOI
10.1103/physreva.35.1453

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Calculations on the Hanle effect in a J - J:i atomic transition are performed for laser fields with a) Brownian motion phase diffusion b) Gaussian amplitude fluctuations and c) fluctuating real and imaginary parts of the laser electric field amplitude (chaotic field model). We use the Fokker-Planck operator approach to stochastic differential equations. The zero-field level-crossing dip broadens at high laser intensity significantly less so as the laser bandwidth increases or if the amp]itu(le fluctuates.
A quantum theory for noise in the steady state of the laser oscillator above threshold is presented. The concept of operator noise source is introduced. A simple laser model operating in a single mode with resonant frequency tuned to the center of the material line is considered. The resonance linewidth of the inverted material is collision-broadened, and assumed to be much broader than the cold-cavity width. We restrict ourselves to one type of collision. The quantum description of this laser model leads to nonlinear operator equations. These are linearized, but this linearization is justified only for operation "sufficiently" above threshold. The first- and second-order Glauber functions and the expectation value of the field commutator are derived for the field inside the laser cavity. These results are compared with the predictions of a "semiclassical" theory in which the classical equations contain noise sources such that properties of the field below threshold are correctly predicted. Our results differ by certain terms from the results of this semiclassical theory. These terms are too small to have been detected experimentally.
A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For the associated Fokker-Planck equation we do a perturbation theory which has terms presenting dynamics similar to that satisfied by the probability amplitude in Quantum Theory even though the physical interpretation be classical. In particular classical observables present expected values that coincide with those calculated using Quantum Mechanics.
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As a continuation of a previous paper [J.-M. Liu, Z. Phys. B 57, 85 (1984)], the present paper is about the dynamical threshold phenomena in the system of a single-mode one-photon laser driven by an external coherent field. The values for the dynamical threshold exponents and amplitudes near the various thresholds are theoretically predicted. As shown, the characteristic time goes to infinity as the control parameters of the system approach each of these thresholds, and the influence of the existence of the absorbing atoms in the laser cavity on the dynamical threshold phenomena in the system is definite.