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Annual Meeting Optical Society of America

Quantum noise in the classical limit

J. D. Franson

Published Jan 1, 1993• 0 citations
Publisher

Abstract

Spontaneous emission noise can be thought of as being due to vacuum fluctuations and may appear to be inherently quantum-mechanical in nature. The same can be said of the loss of coherence in which-path experiments, which is due to the entanglement of a photon with some other system in one path through an interferometer. Both of these processes have been considered in the limit of high field intensities in order to determine whether or not they have a classical analogy. It was found that the same phenomena occur classically as well due to chaos. The extent to which these phenomena can or cannot be considered to be inherently quantum-mechanical will be discussed.

DOI
10.1364/oam.1993.wxx.5

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Spontaneous emission noise can be thought of as being due to vacuum fluctuations and may appear to be inherently quantum-mechanical in nature. The same can be said of the loss of coherence in which-path experiments, which is due to the entanglement of a photon with some other system in one path through an interferometer. Both of these processes have been considered in the limit of high field intensities in order to determine whether or not they have a classical analogy. It was found that the same phenomena occur classically as well due to chaos. The extent to which these phenomena can or cannot be considered to be inherently quantum-mechanical will be discussed.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]
An account is given of noise in electrical circuits and its relation to quantum noise connected with Heisenberg’s uncertainty principle. A phase-insensitive amplifier must introduce noise (most commonly the spontaneous emission noise) in order to satisfy the constraint imposed by quantum mechanics on the simultaneous measurement of two observables represented by noncommuting operators. Nonstationary, phase-sensitive amplifiers can employ squeezed radiation and reduce the noise below that of phase-insensitive amplifiers. Experiments on squeezing in optical fibers and the attendant noise reduction are presented. The squeezing apparatus can also be employed as a quantum nondemolition measurement of photon number. A thought experiment of a two-slit interferometer is described, in which the fringes are washed out progressively with the accuracy of the photon number determination in one of its arms. Implications of measurements of this kind for the resolution of the Einstein–Podolsky–Rosen paradox are discussed.
An examination is made of the relationship between the uncertainty principle and minimum amplifier noise. First, the concept of coherence is discussed, and an incoherence parameter is defined in terms of the uncertainty that enters into the uncertainty principle. Harmonic oscillator states are examined for coherence. The concept of noise is then discussed and contrasted with incoherence, noise referring to behavior in time of a single system while incoherence involving comparison among members of an ensemble. It is shown, with illustrations, that the two concepts are different, and that an incoherent field of a cavity mode need not exhibit noise. In particular, the zero-point field in a lossless cavity is not noise. The superposition of many incoherent effects, however, usually leads to noise. Spontaneous emission is examined both for coherence and noise. It is shown that the spontaneous emission field of a single molecule is incoherent but does not exhibit noise; the (low order) spontaneous emission from a molecular beam, however, does constitute noise. Spontaneous emission from complex systems is also discussed. The origin of fundamental noise in an amplifier is investigated and is shown to come from spontaneous emission by the amplification mechanism. It is concluded that fundamental noise cannot be determined by a consideration of quantum fluctuations of---or by the application of the uncertainty principle to---the electromagnetic field only, as has been done in several recent articles. The physical significance of the zero-point field is analyzed, and is shown to lie in a formal contribution to spontaneous emission by the mechanism coupled to the field, provided this mechanism is treated quantum mechanically.
The interaction of light and matter can be described by a set of coupled nonlinear evolution equations for the material and electromagnetic fields. In order to account for the effects of vacuum fluctuations, noise forces which cause spontaneous transitions have to be included. In these macroscopic systems various sources of noise besides fundamental quantum fluctuations exist which are of macroscopic origin. These cause fluctuations of the cavity dissipation as well as of the external pumping power. In the course of an adiabatic elimination procedure, these fluctuations appear as multiplicative noise in the equations of motion (e.g. for the field intensity, due to the nonlinearity of the interaction). While fluctuations of the cavity damping create noise linear in the field intensity, randomness in the pump strength causes fluctuations that depend nonlinearly on the light intensity. In this respect, the noise terms enter the equations of motion quite differently and have to be distinguished from spontaneous emission noise which is independent of the field strength, and is the basis of all traditional laser models.
The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.