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arXiv:quant-ph/0311089

Microscopic Origin of Spatial Coherence and Wolf Shifts

G. S. Agarwal

Published Nov 13, 2003• 0 citations
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Abstract

We show that the vacuum of electromagnetic field has intrinsic partial spatial coherence in frequency domain which effectively extends over regions of the order of wavelength $λ$. This spatial coherence leads to a dynamical coupling between atoms and is the cause of source correlations and Wolf shifts. We show how the source spatial correlations can lead to tailor made coherent emissions. We discuss the universality of source correlation effects and presents several application.

DOI
10.48550/arxiv.quant-ph/0311089

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We show that the vacuum of electromagnetic field has intrinsic partial spatial coherence in frequency domain which effectively extends over regions of the order of wavelength λλλ. This spatial coherence leads to a dynamical coupling between atoms and is the cause of source correlations and Wolf shifts. We show how the source spatial correlations can lead to tailor made coherent emissions. We discuss the universality of source correlation effects and presents several application.
Wolf discovered how the spatial coherence characteristics of the source affect the spectrum of the radiation in the far zone. In particular the spatial coherence of the source can result either in red or blue shifts in the measured spectrum.His predictions have been verified in a large number of different classes of systems. Wolf and coworkers usually assume a given form of source correlations and study its consequence. In this paper we consider microscopic origin of spatial coherence and radiation from a system of atoms. We discuss how the radiation is different from that produced from an independent system of atoms. We show that the process of radiation itself is responsible for the creation of spatial correlations within the source. We present different features of the spectrum and other statistical properties of the radiation, which show strong dependence on the spatial correlations. We show the existence of a new type of two-photon resonance that arises as a result of such spatial correlations. We further show how the spatial coherence of the field can be used in the context of radiation generated by nonlinear optical processes. We conclude by demonstrating the universality of Wolf shifts and its application in the context of pulse propagation in a dispersive medium.
A microscopic model for the origin of the source correlations responsible for Wolf shifts is proposed. To illustrate the main features of the phenomenon of these correlation-induced frequency shifts, a simple atomic system consisting of a pair of identical two-level atoms interacting with each other via the dipole-dipole interaction is considered. Effects of the finite temperature of the source are also included. For this microscopic model, the far-zone spectrum for two different experimental situations is calculated. The red and blue frequency shifts of the spectrum can be understood in terms of the dipole-dipole interaction. The magnitude of the shifts depends on the strength of the dipole-dipole interaction. The dependence of the frequency shifts on the temperature of the radiating source is also given.
Not long ago Wolf discovered a modification of the spectrum of radiation due to the spatial coherence of the source.1 His analysis used a model correlation function that demonstrated the effect, without discussing any physical mechanism by which the correlations may arise. This paper presents an analysis of one such physical mechanism, namely, the radiation reaction. Following earlier work by Varada and Agarwal,2 an explicit calculation, performed in the harmonic oscillator approximation, for two radiating atoms in equilibrium with a thermal field reveals a relationship between this effect and the well-known shift of atomic oscillator frequencies due to Lamb.
It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.
A model radiating system consisting of two atoms in close proximity is analyzed. This system demonstrates the influence of spatial coherence on the spectrum of the radiation field. Explicit expressions for the degree of coherence, the source spectrum, and the spectrum of the radiation field are derived. The results are discussed in terms of Wolf's work [Phys. Rev. Lett. 56, 1370 (1986)] on this effect, which can be considered in terms of a multiple-atom analog of the effects of radiation reaction on a single atom, i.e., spontaneous decay and the Lamb shift.