Quantum Fluctuations in the Stokes Parameters of Light Propagating in a Kerr Medium

Abstract

The quantum theory of light propagation in a nonlinear Kerr medium is applied to calculate the Stokes parameters and their variances in the process of light propagation. Exact quantum formulae are derived for the expectation values of the Stokes operators and thus for the azimuth θ and ellipticity η of the beam. The role of quantum fluctuations in light polarization characteristics is discussed. The periodic behaviour of quantum evolution of the light polarization is revealed explicitly. It is shown that the degree of polarization is diminished at early stages of each period of the evolution but then reverts to its initial state of complete polarization at the end of the period. The variances of the Stokes parameters are also periodic and intensity-dependent; however, they never fall below their coherent state values.     

Squeezing in Correlated Quantum Systems

Abstract

We discuss the connection between quantum correlations and squeezing in simple quantum optical systems. We illustrate this connection by a study of two-mode states of light produced by parametric down-conversion and similar two-photon processes. The intermode correlations in these systems are shown to be responsible for modifications in photon-number sum and difference operators, and for squeezing in the superpositions of the two modes. The disappearance of the diagonal coherent-state quasiprobability function P(α) when non-classical light properties are important is noted, and alternative and better-behaved Wigner functions and coherent-state expectation Q-functions for the two-mode system are developed.     

Fiber-based single-channel polarization-sensitive spectral interferometry

We present a novel, to our knowledge, fiber-based single-channel polarization-sensitive spectral interferometry system that provides depth-resolved measurement of polarization transformations of light reflected from a sample. Algebraic expressions for the Stokes parameters at the output of the interferometer are derived for light reflected from a birefringent sample by using the cross-spectral density function. By insertion of a fiber-optic spectral polarimetry instrument into the detection path of a common-path spectral interferometer, the full set of Stokes parameters of light reflected from a sample can be obtained with a single optical frequency scan. The methodology requires neither polarization-control components nor prior knowledge of the polarization state of light incident on the sample. The fiber-based single-channel polarization-sensitive spectral interferometer and analysis are demonstrated by measurement of phase retardation and fast-axis angle of a birefringent mica plate.     

On the quantumness of correlations in nuclear magnetic resonance

Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.     

Population trapping with quantized fields in two-channel models of atomic excitation

Abstract

In this paper, we study several models of two-channel atomic excitation involving quantized fields and search for field states that result in the trapping of the atomic population in a single bare state. This trapping is a result of quantum interference between the two channels. We study the following models: a two-level atom resonantly interacting with two quantized field modes, a two-level atom with competing one and three photon transitions, and a Raman coupled model containing both Stokes and anti-Stokes fields. We find a great variety of trapping states of the field, some of the states being highly non-classical. The effects of dissipation on the stability of the trapping states are discussed and a method for generating some of the states is presented.     

Superposition of displaced number states and interference effects

Abstract

We introduce a new state of light field by superposing two displaced number states having a phase difference between them in the phase space. The influence of this phase upon its various non-classical properties is investigated, including a discussion on the generation of this state, which contains as particular cases important states studied in the literature.     

Principles of calculating the dynamical response of misaligned complex resonant optical interferometers

In the long-baseline laser interferometers for measuring gravitational waves that are now under construction, understanding the dynamical response to small distortions such as angular alignment fluctuations presents a unique challenge. These interferometers comprise multiple coupled optical resonators with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular alignment and longitudinal displacement of the resonator mirrors. The electromagnetic field is decomposed into a superposition of higher-order spatial modes, Fourier frequency components, and polarization states. Alignment fluctuations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field.     

Phase auto-compensating high-dimensional quantum cryptography in elliptical-core few-mode fibres

High-dimensional quantum cryptography through optical fibres with several spatial modes requires an efficient quantum key distribution (QKD). However, optical modes acquire different phases and lags due to modal dispersion and random fluctuations, and a modal crosstalk appears under propagation. At present, special optical fibres for spatial multiplexing are being proposed in order to reduce notably the modal crosstalk, however, arbitrary relative phases and lags between modes are always present, which prevents getting an efficient phase encoding QKD. In this work, we take advantage of elliptical-core few-mode optical fibres presenting a very low modal crosstalk and propose an exact phase auto-compensating method by making photons travel several times the path between Alice and Bob (rounds) and by using appropriate modal inversions in each round trip. In order to make clear the proposed phase auto-compensating method, we study in detail a four-dimensional BB84 QKD case with single photon states excited in both polarization and spatial LP modes.     

Optical noise induced by Gaussian sources in stokes parameter measurements

A novel formalism for determining the source-induced noise in Stokes parameter measurements is derived for sources with Gaussian statistics. The formalism is based on a concise expression for the autocovariance functions of the Stokes parameters in terms of the second-order correlation properties of the optical field. At the output of an optical system, source-induced noise can result not only from the intensity fluctuations of the source but also from phase or polarization fluctuations. To describe the effect of the system, another formalism for the propagation of the second-order correlation properties of the optical field is derived. We apply the formalisms to analyze source-induced noise at the output of a birefringent medium, and in coherence-multiplexing networks.     

Two-photon interferometry for high-resolution imaging

This paper discusses the advantages of using non-classical states of light for two aspects of optical imaging: the creation of microscopic images on photosensitive substrates, which constitutes the foundation for optical lithography, and the imaging of microscopic objects. In both cases, the classical resolution limit given by the Rayleigh criterion is approximately half of the optical wavelength. It has been shown, however, that by using multi-photon quantum states of the light field, and a multi-photon sensitive material or detector, this limit can be surpassed. A rigorous quantum mechanical treatment of this problem is given, some particularly widespread misconceptions are addressed, and turning quantum imaging into a practical technology is discussed.     

Non-classical Properties of Two-mode SU(1, 1) Coherent States

Abstract

We examine the non-classical properties of two-mode coherent states based on different unitary irreducible representations of SU(1, 1). Such states are generated by the action of the two-mode squeezing operator on initial states of the field containing arbitrary numbers of photons in each of the two modes. If the initial state of the field is a two-mode vacuum state, the final state is of course the two-mode squeezed vacuum. An initial occupation generalizes the idea of a squeezed vacuum to the SU(1, 1) coherent states. We show that fields in such states have remarkable quantum properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, strong correlations in the photon number fluctuations and squeezing. Using information theory formalism, we show that these coherent states are less correlated than the usual two-mode squeezed vacuum. Moreover, we show that an initial coherent amplitude contribution, in a large amplitude limit, can result in the reduction of correlations between modes.     

Quantum Dynamics of a Nonlinear Birefringent Model with Anticorrelated Field States

Abstract

In this paper, anticorrelated field states with a binomial distribution over orthogonal polarizations, interacting with a nonlinear birefringent medium, are discussed. The field states are the SU(2) coherent states, where the angular momentum operators are realized as bilinear products of the boson operators associated with the two polarizations. The system discussed here provides an optical realization of a nonlinear rotator. We study the quantum dynamics of the statistical properties of the field and the evolution of the degree of polarization.     

Fast,common-path,switchable, achromatic phase-shifter for polarization interferometry

Abstract

A fast switchable phase-shifter using a pair of liquid-crystal devices with a switching angle of 60° is described. This phase-shifter can be placed in the common path traversed by the two orthogonally polarized beams emerging from a polarization interference microscope and used for digital phase measurements over a wide range of wavelengths. It can also be used in a stellar interferometer with orthogonally polarized beams for measurements of fringe visibility with white light.     

Simulations of continuum coherent states and its use in quantum cryptographic systems

Abstract

The continuum states formalism is suitable for field quantization in optical fibre; however, they are harder to use than discrete states. On the other hand, a Hermitian phase operator can be defined only in a finite dimensional space. We approximated a coherent continuum state by a finite tensor product of coherent states, each one defined in a finite dimensional space. Using this, in the correct limit, we were able to obtain some statistical properties of the photon number and phase of the continuum coherent states from the probability density functions of the individual, finite dimensional, coherent states. Then, we performed a simulation of the BB84 protocol, using the continuum coherent states, in a fibre interferometer commonly used in quantum cryptography. We observed the fluctuations of the mean photon number in the pulses that arrive at Bob, which occurs in the practical system, introduced by the statistical property of the simulation.     

Invariant polarimetric contrast parameters of coherent light

Many applications use an active coherent illumination and analyze the variation of the polarization state of optical signals. However, as a result of the use of coherent light, these signals are generally strongly perturbed with speckle noise. This is the case, for example, for active polarimetric imaging systems that are useful for enhancing contrast between different elements in a scene. We propose a rigorous definition of the minimal set of parameters that characterize the difference between two coherent and partially polarized states. Indeed, two states of partially polarized light are a priori defined by eight parameters, for example, their two Stokes vectors. We demonstrate that the processing performance for such signal processing tasks as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by two scalar functions of these eight parameters. These two scalar functions are the invariant parameters that define the polarimetric contrast between two polarized states of coherent light. Different polarization configurations with the same invariant contrast parameters will necessarily lead to the same performance for a given task, which is a desirable quality for a rigorous contrast measure. The definition of these polarimetric contrast parameters simplifies the analysis and the specification of processing techniques for coherent polarimetric signals.     

Quantum Superpositions of Binomial States of Light

We introduce new kinds of states of electromagnetic field, which are quantum superpositions of binomial states. They not only exhibit remarkable non-classical properties but can also interpolate between the ‘Schrödinger cat’ type of states and the number states in a particularly interesting way. We basically discuss some of their main statistical properties, as well as schemes for their generation. We also employ quasiprobability distributions in phase space.     

Polarization characterization of a Mach-Zehnder interferometer

Polarization characterization of a Mach-Zehnder interferometer, based on the state of polarization (SOP) and power measurement at the interferometer output, is presented. We study the SOP and degree of polarization (DOP) of the output light, first as a function of the light power in each arm of the interferometer for a fixed input SOP and DOP, and second as a function of the SOP's in each arm of the interferometer for a fixed input power. Stokes formalism and the Poincaré sphere are used for simultaneous representation of the SOP and DOP, as well as their evolution. It is shown that the SOP and DOP stability and also the output light power are highly dependent on the light source coherence. Knowledge of these different parameters leads to configurations that allow simultaneous control of the SOP and DOP. We can hence realize a quasi-monochromatic nonpolarized light source, which is useful for the polarization-independent characterization of optical components.     

Phase Properties of Elliptically Polarized Light Propagating in a Kerr Medium

Abstract

Phase properties of elliptically polarized light propagating through a nonlinear Kerr medium are considered within the framework of the Pegg-Barnett Hermitian phase formalism. The joint phase probability distribution function for the phases of two orthogonal modes describing elliptical polarization of the field is calculated and its evolution discussed and illustrated graphically. The marginal phase probability distribution for the individual phases are also calculated and discussed. Analytical formulae for phase expectation values and variances are derived for the individual phases as well as for the phase difference. It is shown that in the course of propagation the correlation between the phases of the two modes builds up. This correlation is responsible for lowering phase difference variance. The expressions for the sine and cosine functions and their variances of the individual phases as well as the phase difference are obtained and discussed. The effect of randomization of individual phases and the phase difference, which is a purely quantum effect, is shown to appear during propagation. The relation between phase randomization and degradation of the degree of polarization of the light is established.     

Light polarization states of a cholesteric liquid crystal probed with optical ellipsometry

Herein a useful methodology to study optical properties of cholesteric liquid crystals (Ch-LC) is proposed by using the Fourier decomposition ellipsometry technique to calculate the Stokes parameters of transmitted and reflected light in the UV–Vis spectral range. Combining Bragg reflection and optical activity we were able to obtain ∼100% of linear or circular light polarization from the Ch-LC sample using achromatic and non-polarized light source. The photonic bandgap and the polarization components can be controlled with the temperature as a result of alterations in the helix pitch of the cholesteric phase. Finally, it is demonstrated the correlation between the dissymmetry factor (g) calculated via the Stokes parameter S₃ and the reflection spectrum. The data revealed that the maximum value of S₃ is not coincident with the peak of maximum reflection. The reflected or transmitted light analysis via Stokes parameters obtained by ellipsometry showed an alternative and low cost method for optical characterization in Ch-LC.     

Ray picture of polarization and coherence in a Young interferometer

We apply a polarization Wigner formalism to the propagation of polarization in a Young interferometer within paraxial approximation. With a very simple ray picture, we obtain complete and rigorous information about polarization evolution via the superposition of the spatial-angular Stokes parameters associated with three light rays. We compare the degree of polarization in the interference region with several measures of the degree of coherence for vectorial fields.