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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

New tests and clarification of some conceptual issues in the superposition of monochromatic light fields

Aditya Gilra, Vandna Gokhroo, C. S. Unnikrishnan

Published Aug 26, 2007• 1 citation
Publisher

Abstract

The linear mathematics of Fourier composition and decomposition of monochromatic electromagnetic fields is supposed to have a direct realization in the physical world in the sense that we assume complete equivalence of reality as well as of physical effects when an arbitrary electromagnetic field is substituted physically with its Fourier components, and vice versa, in the same spatial region. In the simplest cases, two superposed light fields at frequencies &ohgr;1 and &ohgr;2 are supposed to be identical in their physical effects to a single field at the average frequency, amplitude modulated at half the difference frequency, in spite of the significant differences in the experimental arrangements needed to produce the two cases. This equivalence has been questioned and recently Lee and Roychoudhury1 cited experimental results on atomic resonance and Fabry-Perot filters to assert that there is no such equivalence. Considering the importance of such assertions for the foundations of physics in general, we have conducted a detailed analysis of the issue, and have conducted tests in which amplitude modulated field at resonant frequency, corresponding mathematically to a superposition of two monochromatic fields detuned equally away from the resonance, is applied to Rb atomic vapor, and also passed through a Fabry-Perot cavity. We conclude from the results of these experiments that there is complete physical equivalence, corresponding to the mathematical equivalence. We clarify several conceptual issues that have been raised about the superposition of light in this context.

DOI
10.1117/12.731044

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The linear mathematics of Fourier composition and decomposition of monochromatic electromagnetic fields is supposed to have a direct realization in the physical world in the sense that we assume complete equivalence of reality as well as of physical effects when an arbitrary electromagnetic field is substituted physically with its Fourier components, and vice versa, in the same spatial region. In the simplest cases, two superposed light fields at frequencies &ohgr;1 and &ohgr;2 are supposed to be identical in their physical effects to a single field at the average frequency, amplitude modulated at half the difference frequency, in spite of the significant differences in the experimental arrangements needed to produce the two cases. This equivalence has been questioned and recently Lee and Roychoudhury1 cited experimental results on atomic resonance and Fabry-Perot filters to assert that there is no such equivalence. Considering the importance of such assertions for the foundations of physics in general, we have conducted a detailed analysis of the issue, and have conducted tests in which amplitude modulated field at resonant frequency, corresponding mathematically to a superposition of two monochromatic fields detuned equally away from the resonance, is applied to Rb atomic vapor, and also passed through a Fabry-Perot cavity. We conclude from the results of these experiments that there is complete physical equivalence, corresponding to the mathematical equivalence. We clarify several conceptual issues that have been raised about the superposition of light in this context.
When two electromagnetic fields of different frequencies are physically superposed, the linear superposition equation implies that the fields readjust themselves into a new mean frequency whose common amplitude undulates at half their difference frequency. Neither of these mathematical frequencies are measurable quantities. We present a set of experiments underscoring that optical fields do not interfere with each other or modify themselves into a new frequency even when they are physically superposed. The multi-frequency interference effects are manifest only in materials with broad absorption bands as their constituent diploes attempt to respond collectively and simultaneously to all the optical frequencies of the superposed fields. Interference is causal and real since the dipoles carry out the operation of summation dictated by their quantum mechanical properties.
The intention of this paper is to underscore that to understand fundamentally new properties of light beams, we must first find the limits of semi classical model to explain optical interference phenomena. We claim that we have not yet reached that limit. Careful analysis of the processes behind detecting fringes indicate that the effect of superposition of multiple optical beams can become manifest only through the mediation of the detecting dipoles. Since the detectors are quantum mechanical, (i) the observed effects are different for different detectors for the same superposed light beams, and further, (ii) they are only capable of registering discrete number of "clicks", whose rate will vary with the incident intensity. A reduced rate of "clicks" at very low intensity does not prove that light consists of indivisible packets of energy. We have also experimentally demonstrated that (i) neither Fourier synthesis, nor, (ii) Fourier decomposition actually model the behavior of EM fields under all possible circumstances. Superposed light beams of different frequencies do not synthesize a new average optical frequency. A pure amplitude modulated pulse does not contain any of the mathematical, Fourier analyzed frequencies. The QED definition of photon being a Fourier mode in the vacuum, it necessarily becomes non-local. Since we have demonstrated that the Fourier theorem has various limitations in classical physics, its indiscriminate use in quantum mechanics should also be critically reviewed.
Any superposition effect as measured (SEM) by us is the summation of simultaneous stimulations experienced by a detector due to the presence of multiple copies of a detectee each carrying different values of the same parameter. We discus the cases with light beams carrying same frequency for both diffraction and multiple beam Fabry-Perot interferometer and also a case where the two superposed light beams carry different frequencies. Our key argument is that if light really consists of indivisible elementary particle, photon, then it cannot by itself create superposition effect since the state vector of an elementary particle cannot carry more than one values of any parameter at the same time. Fortunately, semiclassical model explains all light induced interactions using quantized atoms and classical EM wave packet. Classical physics, with its deeper commitment to Reality Ontology, was better prepared to nurture the emergence of Quantum Mechanics and still can provide guidance to explore nature deeper if we pay careful attention to successful classical formulations like Huygens-Fresnel diffraction integral.
Pomeau et al.1 have shown that a two-level atom strongly driven by a single 100% amplitude modulated (AM) field can show broadband spectral behavior when the two-frequency components of the field are incommensurate. The equations describing the atomic response to a monochromatic field without making the rotating wave approximation (RWA) are identical to form to the equations describing a 100% amplitude modulated field within the RWA. This fact makes the observation of the predictions of Pomeau et al. experimentally realizable in an optical resonance experiment. We present theoretical and numerical results of a pair of 100% AM fields interacting with a single atomic resonance. The effects on the atomic response of commensurate and incommensurate modulation frequencies are discussed as are the experimental implications.
Any superposition effect as measured (SEM) by us is the summation of simultaneous stimulations experienced by a detector due to the presence of multiple copies of a detectee each carrying different values of the same parameter. We discus the cases with light beams carrying same frequency for both diffraction and multiple beam Fabry-Perot interferometer and also a case where the two superposed light beams carry different frequencies. Our key argument is that if light really consists of indivisible elementary particle, photon, then it cannot by itself create superposition effect since the state vector of an elementary particle cannot carry more than one values of any parameter at the same time. Fortunately, semiclassical model explains all light induced interactions using quantized atoms and classical EM wave packet. Classical physics, with its deeper commitment to Reality Ontology, was better prepared to nurture the emergence of Quantum Mechanics and still can provide guidance to explore nature deeper if we pay careful attention to successful classical formulations like Huygens-Fresnel diffraction integral.
A prototypical experiment in cavity quantum electrodynamics involves controlling the light-matter interaction by tuning the frequency of a cavity mode in- and out-of resonance with the frequency of a quantum emitter,1-3 while the field amplitude is generally unaltered. The opposite situation, where one perturbs the spatial pattern of a cavity mode without changing its frequency, has been considered only recently in a few works.4, 5 Changing the amplitude of the field at the emitter's position has important applications, at it allows a real-time control of the light-matter coupling rate, and therefore a direct control of processes such as spontaneous emission and Rabi oscillations. In view of this large potential, in this paper we discuss general design principles that allow obtaining large variations of the electromagnetic field, without change of the frequency, upon an external perturbation of the cavity. We showcase the application of these rules to two photonic structures, a single Fabry-Perot cavity and a coupled three-cavity system. As showed by our analysis and by the examples provided, a small frequency spacing between the modes of the unperturbed cavity is an important requirement to obtain large field variations upon small perturbations. In this regard, a coupled-cavity system, where the frequency spacing is controlled by the interaction rates between the single cavities, constitutes the most promising system to achieve large modulations of the field amplitude.