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Quantum Description of Optical Devices Used in Interferometry

P. Kucera

Published Sep 1, 2007• 5 citations
OpenAlex

Abstract

A quantum-mechanical description of the phase shifters, retarders, mirrors and beam splitters is given in the paper. The description is then applied on two types of states. On a coherent state, a classical-like state, and on a number state, hence the strict quantum state. The quantum description of a beam splitter can be found in the literature. However the description does not treat with the polarization concept. The paper is aimed to introduce quantum description of an arbitrary oriented retarder and give a description of a beam splitter which treats with the polarization.

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A quantum-mechanical description of the phase shifters, retarders, mirrors and beam splitters is given in the paper. The description is then applied on two types of states. On a coherent state, a classical-like state, and on a number state, hence the strict quantum state. The quantum description of a beam splitter can be found in the literature. However the description does not treat with the polarization concept. The paper is aimed to introduce quantum description of an arbitrary oriented retarder and give a description of a beam splitter which treats with the polarization.
The photon is an attractive physical system for representing a quantum bit. Single photons can be detected with high quantum efficiency for a wide range of wavelengths, using a variety of technologies. Three of the most experimentally accessible devices for manipulating photon states are mirrors, phase shifters and beam splitters. Arbitrary unitary transforms can be applied to quantum information, encoded with single photons in the dual-rail representation, using phase shifters and beam splitters. We have gained some valuable insight into the nature of the architecture and system design of a quantum computer, from studying this optical quantum computer.
Using quantum theory, we study the propagation of an optical field in an inhomogeneous dielectric, and apply this scheme to traveling optical fields in a waveguide. We introduce a field-atom interaction Hamiltonian and derive the refractive index using quantum optics. We show that the transmission and reflection of optical fields at an interface between different materials can be described with normalized Fresnel coefficients and that this representation is related to the beam splitter operator. We then study the propagation properties of the optical fields for two types of slab waveguides: step-index and graded-index. The waveguides are divided into multiple layers to represent the spatial dependence of the optical field. We can evaluate the number of photons in an arbitrary volume in the waveguide using this procedure. Using the present method, the quantum properties of weak optical fields in a waveguide are revealed, while coherent states with higher amplitudes reduces to representation of classical waveguide optics.
The lossless beam splitter is classically well understood. The purpose of this work is to enable one to describe the action of a lossless plane-parallel beam splitter on an incident light beam in purely quantum-mechanical terms. Such a description may be obtained in terms of a unitary transformation that connects the incoming radiation-field operator to the outgoing one. This transformation, which we shall derive and discuss here, provides an elegant means to address issues and concepts that are intrinsically quantum-mechanical.
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.
The wide use of beam splitters in quantum interferometry, attosecond metrology, modern quantum information processing, foundations of quantum mechanics, has been based on coherence of beams emerging from a beam splitter.Here we further develop the approach in which a beam splitter is regarded as a transformer of an incident wave field (photon field or matter wave field) into a field which has narrow maxima at the points along and in close vicinity of two or more particular lines.This description was derived by considering a thin grating as a model of a beam splitter for photons, atoms and molecules.It is applied to answer some questions raised in the discussions on the interpretation of wave particle duality.
Abstract A beam splitter operator is a very important linear device in the field of quantum optics and quantum information. It can not only be used to prepare complete representations of quantum mechanics, entangled state representation, but it can also be used to simulate the dissipative environment of quantum systems. In this paper, by combining the transform relation of the beam splitter operator and the technique of integration within the product of the operator, we present the coherent state representation of the operator and the corresponding normal ordering form. Based on this, we consider the applications of the coherent state representation of the beam splitter operator, such as deriving some operator identities and entangled state representation preparation with continuous-discrete variables. Furthermore, we extend our investigation to two single and two-mode cascaded beam splitter operators, giving the corresponding coherent state representation and its normal ordering form. In addition, the application of a beam splitter to prepare entangled states in quantum teleportation is further investigated, and the fidelity is discussed. The above results provide good theoretical value in the fields of quantum optics and quantum information.