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Physics World

Photons below the Poisson barrier

ARTUR K. EKERT

Published Oct 1, 1989• 1 citation
Publisher

Abstract

Quantisation of the electromagnetic field leads us simplistically to think of the field as fluctuating around some average value that could be predicted by a classical theory, whereas all statistical properties of the fluctuations must be derived from a quantum theory. The character of the fluctuations depends on the quantum state of the field. Even in a vacuum, where the average value of the field is zero, its mean square value due to fluctuations is positive. This quantum noise associated with these fluctuations is inherent and cannot be removed no matter how carefully we get rid of various environmental disturbances and fluctuations. But even though the quantum noise is here to stay, we can still control and manipulate it.

DOI
10.1088/2058-7058/2/10/18

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Quantisation of the electromagnetic field leads us simplistically to think of the field as fluctuating around some average value that could be predicted by a classical theory, whereas all statistical properties of the fluctuations must be derived from a quantum theory. The character of the fluctuations depends on the quantum state of the field. Even in a vacuum, where the average value of the field is zero, its mean square value due to fluctuations is positive. This quantum noise associated with these fluctuations is inherent and cannot be removed no matter how carefully we get rid of various environmental disturbances and fluctuations. But even though the quantum noise is here to stay, we can still control and manipulate it.
The electromagnetic field commutation relations are defined in terms of geometric factors that are double averages over two finite four-dimensional space-time regions. The square root of any of the uncertainty relations derived from the aforementioned commutators is taken as a critical field, in the sense that any electromagnetic field much larger than it can be treated as classical. Another critical electromagnetic field associated with the quantum information control of vacuum fluctuations can be chosen as the square root of the mean quadratic fluctuation of each quantity of electromagnetic field, when the number of photons is defined and is equal to zero. Any electromagnetic field expectation value could be measured if it is much greater than the last critical field. This article covers a magnitude order comparison between the critical fields and its consequences for measuring the electromagnetic field information.
We show by means of a quantum electrodynamic calculation that excess noise is inherent in the process of optical phase conjugation, both in that the state of the field leaving a phase-conjugate mirror can always be described classically (i.e., its phase-space density is positive semidefinite) and in that the fluctuations in the generated field are always greater than those predicted by Poisson statistics. Except in special cases, quantum noise imposes a limitation on the ability of phase conjugation to remove the effects of aberrations.
The strong resonance interaction of a two-level atom with the continuum of quantized electromagnetic modes falling within the contour of a resonance mode of a dielectric microsphere is considered within the framework of quantum electrodynamics. Analytical solutions are derived. As an initial condition, we consider the case when, at time t = 0, the atom is excited and the resonance modes of the microsphere contain a single-photon wavepacket. It is shown that the properties of the emitted photon pair depend crucially on space-time properties of the photon wavepacket contained in the resonator. When the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is close to the vacuum value, the radiation of an atom is similar to a spontaneous one and the emitted photon pair has no correlations. On the contrary, if the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is substantially greater than the vacuum value, the radiation of an atom has a stimulated nature and the emitted photon pair has very complicated strong correlations. The relationship between the results obtained and the predictions of the dressed states theory are briefly discussed. The results obtained are of a general character and can be applied to the description of the resonant interaction of an excited atom and an excited resonator of an arbitrary shape.