Spatial and temporal dependence of single-pass parametric gain

Abstract

The use of focused Gaussian beams and short optical pulses to pump single-pass optical parametric amplifiers is examined. A simple model is introduced to mimic the experimental conditions used, and the expected intensity profile of the output signal for degenerate parametric amplification in LBO and MgO:LiNbO₃ is calculated. Experimental and theoretical results are compared for LBO. Second harmonic autocorrelation measurements were performed in order to determine the pulse duration of the output signal from the LBO parametric amplifier. These measurements showed that the amplified pulse was slightly shorter, and the deamplified pulse slightly longer, than the input signal—a result of the variation in the parametric gain over the 3 ps signal pulse. The implications of this spatial and temporal variation of the gain in squeezing are discussed.     

Squeezed Atomic Light Amplifiers

Abstract

Various authors have shown that for a particular type of atomic light amplifier, which can be identified as an unsqueezed amplifier, squeezing in the output is destroyed for gains greater than 2, and if the input is classical light then there are no non-classical effects (squeezing or sub-Poisson photon statistics) in the output for any value of the gain; however, these results are not necessarily true for a squeezed amplifier. Here we investigate single-stage and multi-stage squeezed atomic light amplifiers and show that the above non-classical effects can occur even with a coherent-state input. We find that the output of a multistage squeezed amplifier can be squeezed in principle for any desired gain, and that when this amplifier is used as an attenuator, output light can in principle be produced with any desired amount of squeezing for any input.     

Sub-Poissonian Photon Statistics and Higher-order Squeezing in the Light Amplifier with Input Binomial States

Abstract

We make a comparison between the necessary and sufficient conditions on the gain of the linear amplifier under which the light output exhibits sub-Poissonian photon statistics or squeezing and exact numerical results, obtained by solving the master equation by means of matrix procedures, and find good agreement. We find numerically that higher-order squeezing persists in a region in which sub-Poissonian statistics and second-order squeezing have already disappeared, for certain parameter ranges of input binomial states.     

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.     

Squeezing spectra from s -ordered quasiprobability distributions: application to dispersive optical bistability

It is well known that the squeezing spectrum of the field exiting a nonlinear cavity can be directly obtained from the fluctuation spectrum of normally ordered products of creation and annihilation operators of the cavity mode. In this article we show that the output field squeezing spectrum can be derived also by combining the fluctuation spectra of any pair of s -ordered products of creation and annihilation operators. The interesting result is that the spectrum obtained in this way from the linearized Langevin equations is exact, and this occurs in spite of the fact that no s -ordered quasiprobability distribution verifies a true Fokker–Planck equation; that is, the Langevin equations used for deriving the squeezing spectrum are not exact. The (linearized) intracavity squeezing obtained from any s -ordered distribution is also exact. These results are exemplified in the problem of dispersive optical bistability.     

Squeezing of Bound Solitary Waves in a Birefringent Optical Fibre

Abstract

The coupled nonlinear Schrödinger equations in a birefringent optical fibre are derived by means of the method of path integrals. The dependence of the squeezing effect on the coupled waves is obtained with a first-order perturbation approximation, considering zero-dispersion, normal and abnormal dispersion.     

Decoherence of nonclassical states of light can be very efficiently used in optical sensor technology

Abstract

In this article we demonstrate that decoherence of nonclassical states of light can be very efficiently used in optical sensor technology. As an example, we consider squeezing degradation of monomode or bipartite quantum states that are in contact with an environment serving as the measurand. The sensitivity of the measuring device will be greatly enhanced when using strongly squeezed states. Moreover, we show that sensitivity-used squeezing measurement is always larger than for absorption measurements. We present an idea for the important application of the measurement of concentration changes in gaseous flows.     

Perfect transmission of the sub-poissonian character of a field via continuous-variable teleportation

Abstract

We optimize the transmission of quantum features in light fields, such as squeezing and antibunching, using continuous variable teleportation and tuning the variable gain in Bob's output.     

Squeezing and Sub-poisson Statistics in Three-mode Interactions

Abstract

A unique approach to the photon statistics in nonlinear optical interactions is suggested based on the use of moment equations and generalized superposition of coherent fields and quantum noise. Non-classical features such as squeezing of fluctuations and sub-Poisson statistics are derived for finite interaction times in the three-mode interaction process and limits of the model are provided.     

Squeezed Light

Abstract

In this paper we review the current state of progress in research on squeezed light. We discuss the basic theory of squeezing and the nature of quantum noise in optical fields. We examine various atomic sources of squeezed light and discuss phase-sensitive detectors of quantum noise including homodyne and heterodyne detectors. Various successful nonlinear optical methods for generating squeezed light are reviewed. We conclude with a discussion of the possible applications of squeezed light.     

Quantum Statistical Properties of Mixed Degenerate and Non-degenerate Parametric Processes

Abstract

Quadrature and integrated intensity fluctuations are found for mixed degenerate and non-degenerate optical parametric processes in single and compound modes. Additionally to quantum statistical effects for single processes new phenomena can occur arising from the coupling of both the processes, which can support squeezing of vacuum fluctuations and sub-Poisson photon statistics in single and compound modes.     

Intracavity Optical Bistability Driven by Squeezed Light from a Parametric Amplifier

Abstract

We describe the theory of optical bistability when atoms are collectively excited within the cavity of a parametric oscillator. Both optical bistability and parametric amplification can squeeze significantly the cavity-field quantum noise. When they are coupled together we find significant changes both on the mean value bistability and on the spectrum of squeezing as the parametric coupling increases. These are calculated directly from the appropriate master equation for the density matrix using a quantum distribution function (positive P) to develop Fokker—Planck and Ito equations.     

On the Squeezing of Coherent States by the Multiphoton Jaynes-Cummings Hamiltonian with an Intensity-dependent Coupling

Abstract

The squeezing properties of the multiphoton Hamiltonian with intensity-dependent coupling are evaluated for the [xcirc] and [pcirc] _x quadratures, for the initial state of a coherent electromagnetic field and an atom in the ground state. Two measures of squeezing: the percentage of total squeezing and the squeezing time-period percentage, are introduced. Interesting squeezing properties with respect to [xcirc] are observed for real coherent states when the time evolution of the above measures and of the time-averaged squeezing are analysed. The multiphoton intensity-dependent coupling Hamiltonian is found to be almost independent of the specific powers of the annihilation and creation operators, as long as the sum of the powers is kept constant.     

Nonlinear Dissipative Oscillator with Displaced Number States

Abstract

We study the interaction of a Kerr-like medium with light initially prepared in a displaced number state. We analyse squeezing properties and photon statistics at the output of a Kerr-like medium. We show that under certain conditions the superposition of two displaced number states can be created. We study the influence of dissipation on the formation of the superposition state.     

Graphical Representation of Self-phase Modulation Noise

Abstract

We develop graphical representations of the noise characteristics imposed on initially coherent light by the process of self-phase modulation in an optical fibre. The graphical methods provide physical understanding of the squeezing that sets in at the shorter propagation distances, and the subsequent desqueezing that occurs as the distance of propagation is increased. They also provide quantitative agreement with the results of the quite complicated analytical theory of self-phase modulation.     

Parametric oscillation with squeezed vacuum reservoirs

Employing the quantum Hamiltonian describing the interaction of a two-mode light (signal–idler modes) generated by a non-degenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master and the Fokker–Planck equations. The corresponding Fokker–Planck equation for the Q-function is then solved employing a propagator method developed by K. Fesseha [J. Math. Phys. 33 2179 (1992)]. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal–idler modes are in squeezed states. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in one of the quadratures can be achieved.     

Squeezing of Spectral Components in the Jaynes-Cummings Model

Abstract

Squeezing of spectral components of a fluorescence field in the framework of the Jaynes-Cummings model has been studied. It has been shown that squeezing is observed only in sidebands of the fluorescence field. The degree of squeezing increases as the intensity of the cavity mode is increased. Contrary to squeezing in the cavity mode (see Kuklinski and Madajczyk [14] a large degree of squeezing in sidebands of the fluorescence field is observed in the short-time limit.     

Entropy squeezing for a two-level atom

Abstract

The usual definition of squeezing, based on the Heisenberg uncertainty principle, measures uncertainty in terms of the standard deviation. It can run into difficulties when applied to squeezing in the two-level atom. An alternative definition of squeezing is presented for this system, based on information entropy theory, which overcomes the disadvantages of the definition based on the Heisenberg uncertainty relation. The utility of this definition is illustrated by examining squeezing in the information entropy of a two-level atom in the Jaynes-Cummings model, and in resonance fluorescence.     

Signal-to-noise Ratio of Optical System Consisting of Squeezer and Optical Kerr Medium

Abstract

In this paper, we analyse the properties of a quantum state transformation system consisting of a squeezer and an optical Kerr medium. An average, a variance, and a signal-to-noise ratio (SNR) of a quadrature-phase amplitude are calculated analytically. We show that the SNR is increased by this system; in particular the use of a squeezer with a large squeezing gain gives a drastic improvement in the SNR. Furthermore, the reason for the improvement in SNR and the usefulness of the squeezed state are discussed.     

Coherent States of a Harmonic Oscillator in a Finite-dimensional Hilbert Space and Their Squeezing Properties

Abstract

New coherent states of a harmonic oscillator in a finite-dimensional Fock space are introduced. Some properties of these coherent states are discussed. The second-order squeezing of these coherent states with respect to the quadrature operators is studied in detail. In particular, for a two-state system the arbitrary higher-order squeezing of these states is investigated. It is shown that these coherent states exhibit much richer squeezing properties than the coherent states of a usual harmonic oscillator in an infinite-dimensional Fock space. It is found that these coherent states have not only second-order squeezing but also higher-order squeezing with respect to the quadrature operators of the field under consideration.