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Annual Meeting Optical Society of America

Generation of squeezing by polarizable media?

Roy J. Glauber, Maciej Lewenstein

Published Jan 1, 1987• 1 citation
Publisher

Abstract

Photons created in free space change in nature when interacting with even the simplest of linearly polarizable media. There is a sense in which this transformation characteristically involves the effects of squeezing as well as scattering. The field fluctuations present in the media or their vicinity may, as a result, differ dramatically from zero-point fluctuations in free space. Such altered fluctuation properties are observable, for example, through the inhibition or enhancement of the spontaneous emission rates of excited probe atoms. Not all the effects that have been discussed in connection with squeezing are observable, however. Because interactions with polarizable media can be described by means of mode expansions for which the photon occupation numbers are conserved, they do not lead to qualitative changes in the counting statistics of photoabsorption processes. The field of a dielectric illuminated by a coherent laser beam, for example, yields Poisson photon counting statistics everywhere. We shall discuss other experiments bearing on field fluctuations in dynamic models of polarizable media as well as passive ones.

DOI
10.1364/oam.1987.mq2

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Photons created in free space change in nature when interacting with even the simplest of linearly polarizable media. There is a sense in which this transformation characteristically involves the effects of squeezing as well as scattering. The field fluctuations present in the media or their vicinity may, as a result, differ dramatically from zero-point fluctuations in free space. Such altered fluctuation properties are observable, for example, through the inhibition or enhancement of the spontaneous emission rates of excited probe atoms. Not all the effects that have been discussed in connection with squeezing are observable, however. Because interactions with polarizable media can be described by means of mode expansions for which the photon occupation numbers are conserved, they do not lead to qualitative changes in the counting statistics of photoabsorption processes. The field of a dielectric illuminated by a coherent laser beam, for example, yields Poisson photon counting statistics everywhere. We shall discuss other experiments bearing on field fluctuations in dynamic models of polarizable media as well as passive ones.
The interaction of light with atomic media, i.e., media describable as an ensemble of free particles, can be used to alter the quantum statistics of the interacting light field. Nonlinear effects present in such an interaction are rather weak unless the light is tuned dose to resonance with a transition between two atomic energy eigenstates. Although semiclassical optical effects are now enhanced, the desired changes to the quantum statistics are normally washed out by atomic noise from absorption and spontaneous emission. Tuning away from resonance turns off nonlinearities faster than it turns off absorption.
We examine the coherence properties of stationary light obtained by the superposition of nonstationary independent emissions occurring at random space–time points. The positions of the points are independent and uniformly distributed over the volume of the source. The emission times fluctuate in accordance with a stationary renewal point process. This process admits of super-Poisson, sub-Poisson, or Poisson behavior. The individual emissions are assumed to be in a coherent, chaotic, or n state. The statistical nature of the random-emission space–time points plays an important role in determining the coherence properties and photon statistics of the total field. This is manifested in the normalized second-order correlation function, which turns out to have the usual form for chaotic light with two additional terms. The first of these is determined by the statistical nature of the individual emissions (it is positive for coherent or chaotic, but zero for single-photon, emissions). The second term is governed by the statistics of the primary excitations (it is positive for super-Poisson, zero for Poisson, and negative for sub-Poisson excitations). Both additional terms become small for light with a high degeneracy parameter (many total photons per emission lifetime). The behavior of the light is then asymptotically chaotic. In the opposite limit, when the degeneracy parameter is small (or the emissions are instantaneous), the correlation properties of the primary excitations are directly transferred to the correlation properties of the photons. The first-order spatial-coherence properties of the field turn out to be identical with those of chaotic light (i.e., the van Cittert–Zernike theorem is obeyed), although the second-order properties differ. The photon-counting distribution reflects the character of the correlation function. Thus sub-Poisson primary excitations, together with n-state emissions, can lead to sub-Poisson photon counts under certain conditions. Such nonclassical light may be made arbitrarily intense if interference effects are eliminated by detecting many spatial modes. As an example of our theory, we cite a Franck–Hertz experiment excited by a space-charge-limited electron beam. If the electron excitations are represented as a sub-Poisson renewal point process, and the photon emissions as one-photon states, the light generated should be antibunched and sub-Poisson.
In Chapter 1 we consider the question of squeezing in a two-photon laser. A two-photon laser is modelled as N two-level atoms interacting via a two-photon transition with a single resonant cavity field mode. A Fokker-Planck equation containing all leading noise terms is derived. A linearised fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing is present in two-photon optical bistability. In Chapter 2 a microscopic model of degenerate four wave mixing including the quantisation of the medium is presented. Time-dependent solutions show ideal squeezing to be obtained in the limits of large detuning, low saturation and zero loss. The effect of nonideal atomic parameters is analysed. Equations describing the spatial propagation of the field through the medium are also derived. In Chapters 3 and 4 we are concerned with quantum effects, in particular violation of Bell's Inequalities, present in optical systems. An optical field produced by an intracavity four wave mixing is shown to exhibit the nonclassical features of photon antibunching, squeezing and violation of Cauchy-Schwarz and Bell's Inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P-function.
We discuss the quantum fluctuations of the fields associated with a broad class of optical scattering and transmission problems by developing the quantum electrodynamics of an idealized linear, but nonuniform, dielectric medium. We present and compare two quantization schemes for this purpose. The first is based on the expansion of the field in terms of a set of single-frequency solutions of the Maxwell equations. The second involves expanding the field in the set of plane-wave solutions of the Maxwell equations in the vacuum. The relation between the two quantization schemes is discussed in the framework of the scattering theory that connects them. The methods presented are used to show that various field components within a dielectric medium may be either superfluctuant or subfluctuant relative to their fundamental uncertainties in the vacuum. These alterations of the fluctuation properties of the fields are shown to lead to changes in the spontaneous emission rates for both electric and magnetic dipole transitions of excited atoms within or near dielectric media. We also analyze the quantum properties of the transition radiation emitted by a fast charged particle in passing from one dielectric medium to another.