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Time correlations and squeezing phenomena in lasers

Alexander M. Khazanov, Gennady A. Koganov, R. Shuker

Published May 8, 1994• 0 citations
OpenAlex

Abstract

The conventional way of studying laser noise assumes analytic solution of the quantum problem for the laser field coupled to the active medium. A number of the laser schemes have been discussed, and predictions for noise reduction and for the squeezed state of field have been made.1 On the basis of first principies of the quantum mechanies, the conventional approach exhibits the relatively rare situation in which the quantum equations admit compact analytic solution. At the same time, the difficulty in interpreting the results seems to be unresolved. Specifically, it is very difficult lo determine the relative contribution of each physical source of noise to the final fluctuation result.

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The conventional way of studying laser noise assumes analytic solution of the quantum problem for the laser field coupled to the active medium. A number of the laser schemes have been discussed, and predictions for noise reduction and for the squeezed state of field have been made.1 On the basis of first principies of the quantum mechanies, the conventional approach exhibits the relatively rare situation in which the quantum equations admit compact analytic solution. At the same time, the difficulty in interpreting the results seems to be unresolved. Specifically, it is very difficult lo determine the relative contribution of each physical source of noise to the final fluctuation result.
We summarize the basic problems in laser coherence and the concepts and techniques needed to solve them. Special techniques needed to handle partition noise in semiconductor lasers will be touched on. We address the problem of how a self-sustained oscillator works. Why is the laser line so narrow? Why does a small amount of noise produce a broadening of the line as opposed to additive side bands? What is the role of zero point oscillations and spontaneous emission in determining the line width? In what sense can the transition to a lasing state be described as a phase transition? The concepts used to deal with the response of a laser system involve a quasi-Markoffian description. This in turn validates a quantum regression theorem which relates the spectrum of the noise to the transport response even in a system far from equilibrium. A significant simplification is made by introducing non-commuting (quantum) noise sources. The techniques required in the solution of laser noise problems involve a multi-time correspondence between quantum variables and c-number random variables that reduces a quantum stochastic problem to a classical stochastic problem. Adiabatic elimination is used to eliminate the fast variables to obtain a reduced problem for the fields alone or the fields and some total atomic variables (total inversion and polarization). Reduction to a rotating wave version of the van der Pol oscillator and numerical solution of the Fokker-Planck equation yields (a) the line shape (b) the spectrum of intensity fluctuations and (c) the distribution of photocounts observed over some time interval. Comparison of theoretical results with later experiments will be presented.
We showed in Section 5.2 of the present chapter that according to quantum theory the value of the electric field of an electromagnetic wave could not be predicted to arbitrarily high precision, this being a consequence of the uncertainty relation satisfied by the two quadrature components of the field (Equation 5.32), which imposed a finite limit on the product of their variances. This limit is more than an abstract theoretical limit; it is often the overriding factor determining the resolution of high-precision optical measurements. In such situations measurements by photodetectors on the field exhibit uncontrollable fluctuations of quantum origin known as quantum noise . Fortunately, as we shall show in this complement, it is possible to overcome this by using non-classical states of the radiation field, namely the squeezed states , provided measurements are made of a single one of a pair of conjugate field variables. A field mode prepared in such a state exhibits reduced quantum noise in one of the variables at the expense of increased noise in the other, so that the uncertainty relation involving their variances is still satisfied. The potential of such states for increasing the obtainable precision of optical measurements is self-evident. However, the practical realization of the potential benefits requires delicate experimental techniques that we describe only briefly here.
Recent technological advances allow entire optical systems to be lithographically implanted on small silicon chips. These systems include tiny semiconductor lasers that function as light sources for digital optical signals. Future advances will rely on even smaller components. At the theoretical limit of this process, the smallest lasers will have an active medium consisting of a single atom (natural or artificial). Several suggestions for how this can be accomplished have already been published, such as nano-lasers based on photonic crystals and nano wires. In particular, the "dipole nanolaser" consists of a single quantum dot functioning as the active medium. It is optically coupled to a metal nanoparticles that form a resonant cavity. Laser light is generated from the near-field optical signal. The proposed work is a theoretical exploration of the nature of the resulting laser light.\nThe dynamics of the system will be studied and relevant time scales described. These will form the basis for a set of operator equations describing the quantum properties of the emitted light. The dynamics will be studied in both density matrix and quantum Langevin formulations, with attention directed to noise sources. The equations will be linearized and solved using standard techniques. The result of the study will be a set of predicted noise spectra describing the statistics of the emitted light. The goal will be to identify the major noise contributions and suggest methods for suppressing them. This will be done by studying the probability of getting squeezed light from the nanoparticle for the certain scheme of parameters.
The quantum correlation between junction voltage fluctuations1/frequency fluctuations2 and the intensity fluctuations of a semiconductor laser may be used to reduce the intensity noise. Here we address squeezed-state generation discussing both fundamental and practical limitations on noise reduction in conventional semiconductor lasers and microcavity lasers. In conventional semiconductor lasers, starting with intensity noise at the standard quantum limit, ideally a 3-dB amplitude squeezing is possible. This fundamental limit is set by spontaneous emission noise. Another fundamental limit is that noise reduction beyond the level set by optical losses and pump noise is not possible. It is also shown that the number-phase uncertainty in some conditions can reach the ultimate limit set by Heisenberg’s uncertainty principle. These conditions are clarified and a comparison made between junction voltage and frequency noise feedforward. Feedforward schemes realizing intensity noise reduction are discussed.