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Physics-Uspekhi

Quantum nature of a nonlinear beam splitter

Aleksandr V. Belinsky, M Kh Shulman

Published Oct 10, 2014• 16 citations
Publisher

Abstract

This is a review of a very interesting (in the authors' view) phenomenon — the operation of a nonlinear light beam splitter. The beam splitter is a flat interface between two transparent dielectrics, at least one of which exhibits Kerr nonlinearity, i.e., its refractive index depends on the transmitted radiation intensity. Interestingly, quantum and classical theories make directly opposite predictions about the phase fluctuations of the output radiation of this device. In classical theory, the phases remain unchanged; in quantum theory, the phases fluctuate in accordance with the amplitude–phase uncertainty relation. The origin of this difference is established at the fundamental level. A further remarkable point about this quantum paradox is that not only is the source beam split in two but one can also create conditions where the two split parts are respectively dominated by amplitude noise and phase noise, thus allowing the selection of photon fluctuations. Results of original studies are summarized and further developed.

DOI
10.3367/ufne.0184.201410i.1135

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This is a review of a very interesting (in the authors' view) phenomenon — the operation of a nonlinear light beam splitter. The beam splitter is a flat interface between two transparent dielectrics, at least one of which exhibits Kerr nonlinearity, i.e., its refractive index depends on the transmitted radiation intensity. Interestingly, quantum and classical theories make directly opposite predictions about the phase fluctuations of the output radiation of this device. In classical theory, the phases remain unchanged; in quantum theory, the phases fluctuate in accordance with the amplitude–phase uncertainty relation. The origin of this difference is established at the fundamental level. A further remarkable point about this quantum paradox is that not only is the source beam split in two but one can also create conditions where the two split parts are respectively dominated by amplitude noise and phase noise, thus allowing the selection of photon fluctuations. Results of original studies are summarized and further developed.
A nonlinear beam splitter is shown to be an interesting object of investigation for the following reasons. First, the classical and quantum theories of its description give directly opposite behaviors of the phase fluctuations: according to the classical theory, the phase is unchanged; according to the quantum theory, the phase fluctuations increase or decrease, depending on the suppression or growth of amplitude fluctuations. The fundamental cause of these differences has been established. Second, the quantum fluctuations of the input mode can be separated into the amplitude and phase ones, so that the predominantly phase fluctuations are directed into one output mode, say, the reflected one, while the amplitude fluctuations are directed into the other (transmitted) mode.
It has been found that a nonlinear beam splitter is an interesting object for investigation for the following reasons. First, the classical and quantum descriptions of this object give opposite results for the behavior of phase fluctuations: according to the classical theory, the phase remains unchanged, whereas the quantum theory predicts that phase fluctuations increase or decrease in correlation with a decrease or increase in amplitude fluctuations. Second, quantum fluctuations of the input mode can be separated into amplitude and phase fluctuations, so that phase fluctuations are directed predominantly into one output mode, say the reflected mode, whereas amplitude fluctuations are directed predominantly into the other (transmitted) mode.
The transformation of light by a nonlinear beamsplitter is considered. The beamsplitter is formed by a plane interface between two transparent dielectrics, at least one of which has a Kerr nonlinearity; i.e., its refractive index depends on the intensity of the penetrating radiation. It is shown that the interpretation of the result of calculation of quantum fields at the outputs from such a beamsplitter indicates a violation of the principle of causality in the sense that a subsequent event affects the previous one.
A beam splitter is a key component used to direct and combine light paths in various optical and microwave systems. It plays a crucial role in devices like interferometers, such as the Mach–Zehnder and Hong–Ou–Mandel setups, where it splits light into different paths for interference measurements. These measurements are vital for precise phase and coherence testing in both classical and quantum optical experiments. In this work, we present a nonlinear beam splitter and beam combiner utilizing a frequency-tunable superconducting artificial atom in a one-dimensional open waveguide. Probed with coherent states at the single-photon level (average photon number ⟨N⟩ ≪1), this device demonstrates highly tunable transparency, ranging from near unity to complete reflection. Additionally, the beam combiner can merge two coherent beams, generating interference fringes as the relative phase between them varies.
Beam splitter Compared with other fundamental experiments in physics, optical tests of quantum mechanics are often distinguished by their simplicity. Most quantum optical experiments do not require a whole industry - an optical table of equipment and a few people are often sufficient. Good ideas, good research problems are more important. “Research is to see what everybody has seen and to think what nobody has thought” (Jammer, 1989). A simple optical beam splitter, for instance, is already a nice device to demonstrate the quantum nature of light. Quite a number of puzzling quantum effects have been seen by splitting or recombining photons at a small cube of glass. Additionally, the beam splitter serves as a theoretical paradigm for other linear optical devices. Interferometers, semitransparent mirrors, dielectric interfaces, wave guide couplers, and polarizers are all described sufficiently well by a simple beam splitter model. The quantum effects of almost all passive optical devices can be understood assuming appropriate beam splitter models. (It's all done with mirrors.) Heisenberg picture An ideal beam splitter is a reversible, lossless device in which two incident beams may interfere to produce two outgoing beams. For instance, a dielectric interface inside a cube or plate of glass splits a light beam into two, see Fig. 5.1. We may reverse this situation by sending the two beams back to the cube, where they interfere constructively to restore the original beam.
Quantum mechanical models of beam splitters1 predict interesting fourth-order interference effects when nonclassical light is used. If indistinguishable one-photon states are simultaneously input into each port of a 50/50 beam splitter, the theory predicts that each output will contain either two photons or none. A naive (particle) theory would predict a mixture of two’s and one’s. The required |1,1〉 photon state can be selected in nondegenerate parametric downconversion experiments by photon-counting coincidence detection. The disappearance of this coincidence after a beam splitter has recently been studied,1-2 and the range of path length differences over which the effect can be seen is related by Fourier transform to the photon bandwidth. In our work the bandwidth is not limited by external filters, and we have developed a theory which relates the measured photon length to the geometry of the apparatus and the detailed phase matching conditions at the parametric crystal. This theory of phase matching viewed through a beam splitter produces some unexpected results when the beam splitter is tilted and when large aperture detectors are considered.