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LOCALIZATION OF MULTIPOLE PHOTONS

A.S. Shumovsky

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

multipole radiation, the local properties of the radiation field can be rigorously described in spite of the fact that photons are defined in whole space-time. In particular, the local intensity operators for the field components with different polarization can be introduced. The intensities associated with two different space-time points along the same direction can be measured together. A method of quantum measurement of correlation of polarizations at different distances based on the use of Aharonov-Bohm effect is proposed.

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multipole radiation, the local properties of the radiation field can be rigorously described in spite of the fact that photons are defined in whole space-time. In particular, the local intensity operators for the field components with different polarization can be introduced. The intensities associated with two different space-time points along the same direction can be measured together. A method of quantum measurement of correlation of polarizations at different distances based on the use of Aharonov-Bohm effect is proposed.
We discuss the spatial properties of quantum radiation emitted by a multipole transition in a single atom. The qualitative difference between the representations of plane and spherical waves of photons is examined. In particular, the spatial inhomogeneity of the zero-point oscillations of multipole field is shown. We show that the vacuum noise of polarization is concentrated in a certain vicinity of atoms where it strongly exceeds the level predicted by the representation of the plane waves. A new general polarization matrix is proposed. It is shown that the polarization and its vacuum noise strongly depend on the distance from the source. 1 I.
The author reviews investigations of the photon localization and quantum phase problems based on the use of the representation of multipole photons. Section II presents a general consideration of the field quantization, including a comparison of zero-point oscillations of the plane and multipole waves of photons. Section III discusses the atom-field interaction leading to the multipole radiation. The SU(2) quantum phase representation of atomic variables is considered, as is a connection between the SU(2) quantum phase states and entanglement phenomenon. In Section IV the author describes the quantum phase of multipole radiation caused by the angular momentum conservation in the process of radiation. This approach is compared with the Pegg–Barnett formalism and with Mandel's operational approach. Section V covers the quantum polarization properties of multipole radiation. Photon localization, quantum measurements, and causality are considered in Section VI.
Quantum features of correlated optical modes define a major aspect of the nonclassicality in quantized radiation fields. However, the phase-sensitive detection of a two-mode light field is restricted to interferometric setups and local intensity measurements. Even the full reconstruction of the quantum state of a single radiation mode relies on such detection layouts and the preparation of a well-defined reference light field. In this work, we establish the notion of the essential quantum correlations of two-mode light fields. It refers to those quantum correlations which are measurable by a given device, i.e., the accessible part of a nonclassical Glauber-Sudarshan phase-space distribution, which does not depend on a global phase. Assuming a simple four-port interferometer and photon-number-resolving detectors, we derive the reconstruction method and nonclassicality criteria based on the Laplace-transformed moment-generating function of the essential quasiprobability. With this technique, we demonstrate that the essential quantum correlations of a polarization tomography scheme are observable even if the detectors are imperfect and cannot truly resolve the photon statistics.
Quantum features of correlated optical modes define a major aspect of the nonclassicality in quantized radiation fields. However, the phase-sensitive detection of a two-mode light field is restricted to interferometric setups and local intensity measurements. Even the full reconstruction of the quantum state of a single radiation mode relies on such detection layouts and the preparation of a well-defined reference light field. In this work, we establish the notion of the essential quantum correlations of two-mode light fields. It refers to those quantum correlations which are measurable by a given device, i.e., the accessible part of a nonclassical Glauber-Sudarshan phase-space distribution, which does not depend on a global phase. Assuming a simple four-port interferometer and photon-number-resolving detectors, we derive the reconstruction method and nonclassicality criteria based on the Laplace-transformed moment-generating function of the essential quasiprobability. With this technique, we demonstrate that the essential quantum correlations of a polarization tomography scheme are observable even if the detectors are imperfect and cannot truly resolve the photon statistics.
So far no mechanism is known, which could connect the two measurements in an Aspect-type experiment. Here, we suggest such a mechanism, based on the phase of a photon’s field during propagation. We show that two polarization measurements are correlated, even if no signal passes from one point of measurement to the other. The non-local connection of a photon pair is the result of its origin at a common source, where the two fields acquire a well defined phase difference. Therefore, it is not actually a non-local effect in any conventional sense. We expect that the model and the detailed analysis it allows will have a major impact on quantum cryptography and quantum computation.
For light fields, the manifestation of correlations between fluctuating electric field components at different space–time points is referred to as coherence, whereas these correlations appearing between orthogonal electric field components at a single space–time point are referred to as polarization. In this context, a natural question is as follows: how are coherence and polarization interconnected? Very recently, a tight equality P2=V2+D2, namely, the “polarization coherence theorem” (PCT) connecting polarization P with interference visibility V (measure of coherence) and distinguishability D (measure of which-path information) has been proposed [Optica4, 1113 (2017)OPTIC82334-253610.1364/OPTICA.4.001113]. We here report a direct observation of the PCT for classical light fields using a Mach–Zehnder interferometer along with a synthesized source producing a complete gamut of degrees of polarizations. Our experimental demonstration could motivate ongoing experimental efforts toward probing the hidden coherences and complementarity features.