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.     

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.     

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.     

Quantum Theory of Hyper-Raman Scattering

Abstract

We develop the quantum theory of stimulated hyper-Raman scattering (HRS) and discuss the quantum statistics of pump and Stokes fields. We show that the initially coherent pump field acquires a strong squeezing that exceeds the similar squeezing in other nonlinear processes also involving two-photon absorption. Stokes field statistics are analysed in detail as a function of the initial statistics of both modes. Bunching effects are shown to be amplified in the short-time region, while in asymptotics the antibunching of Stokes photons becomes dominant, which in many cases results in sub-Poissonian statistics of Stokes mode. We also find a number of correlation effects between the photons of the two modes.     

Quantum Statistics of Single-mode Processes Preserving Generalized Superposition of Coherent and Chaotic Fields

Abstract

A unified approach to the quantum statistics of single-mode linear processes described by the general Fokker-Planck equation and the generalized initial superposition of coherent and chaotic fields is developed to reveal the common traits in the mathematical models of several quantum optical systems. Processes such as the degenerate parametric amplification and the harmonic oscillator eventually coupled to the thermal or rigged reservoir are involved as special cases. A sufficient condition for the validity of the master equation is formulated as its being formally independent of possible reservoirs. The dependence of non-classical phenomena such as the sub-Poisson photon statistics and squeezing on the drift and diffusion coefficients is discussed.     

The role of squeezing in quantum key distribution based on homodyne detection and post-selection

Abstract

The role of squeezing in quantum key distribution with continuous variables based on homodyne detection and post-selection is investigated for several specific eavesdropping attacks. It is shown that amplitude squeezing creates strong correlations between the signals of the legitimate receiver and a potential eavesdropper. Post-selection of the received pulses can therefore be used to reduce the eavesdropper's knowledge of the raw key, which increases the secret key rate by orders of magnitude over large distances even for modest amounts of squeezing.     

Non-classical Features in the Three-level Jaynes-Cummings Model

Abstract

The eigenfunctions and eigenenergies of the system composed of a cascade three-level atom and bichromatic or monochromatic field with arbitrary detunings are presented. The development of the state vector of the system with arbitrary initial conditions is obtained. The development of the quantum fluctuations and the second-order coherence degree for the field is calculated. The dependence of the squeezing and antibunching on the detunings, initial intensities and initial squeezing is studied. The contribution of single-photon and two-photon transitions to, and the influence of, the a.c. Stark effect on the squeezing are discussed.     

RISQ-reduced instruction set quantum computers

Abstract

Candidates for quantum computing which offer only restricted control, e.g. due to lack of access to individual qubits, are not useful for general purpose quantum computing. We present concrete proposals for the use of systems with such limitations as RISQ-reduced instruction set quantum computers and devices-for simulation of quantum dynamics, for multi-particle entanglement and squeezing of collective spin variables. These tasks are useful in their own right, and they also provide experimental probes for the functioning of quantum gates in premature prototypes of quantum computers.     

Effective Dipole Squeezing in the Non-degenerate Two-photon Jaynes-Cummings Model with Superposition State Preparation

Abstract

Effective dipole squeezing in the non-degenerate two-photon Jaynes-Cummings model for atom and fields initially prepared in superposition of states is investigated. It is shown that the squeezing can be exhibited in certain periods of time but it cannot be achieved for atomic spontaneous radiation processes.     

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.     

Dynamics of a Q-analogue of the Quantum Harmonic Oscillator

Abstract

We analyse the dynamics of the q-deformed quantum harmonic oscillator initially prepared in the q-analogue of the coherent state. Non-trivial behaviour of the mean values of the q-position operator is observed. The squeezing of the second-order moments of this operator is studied.     

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.     

Stimulated Raman Scattering of Squeezed Light with Pump Depletion

Abstract

Using the approximation of small fluctuations around a stationary point, photon statistics and squeezing of vacuum fluctuations are derived in stimulated Raman scattering including the coupling of photon-photon and photon-phonon modes. The depletion of pump light is described and it is shown that a regime of inversion of the process is related to an increase in quantum fluctuations, which are finally reduced again, more in the anti-Stokes mode than in the Stokes mode. If the anti-Stokes coupling is stronger than the Stokes coupling, then an oscillating behaviour of the statistical characteristics occurs and substantial squeezing can be found in photon-phonon modes.     

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 Coupled Nonlinear Oscillators with Losses

Abstract

The statistical properties of two coupled nonlinear oscillators including losses are discussed using the statistics for the generalized superposition of coherent fields and quantum noise. Exact and approximate formulae for squeezing of vacuum fluctuations are derived. The photon statistics are shown to be Poissonian from the nonlinear dynamics of the lossless case. Non-classical behaviour is degraded by noise.     

SU(1, 1) and SU(2) Squeezing in Trilinear Optical Processes

Abstract

The squeezing properties in terms of SU(1, 1) and SU(2) operators for the case of trilinear processes are studied. The initial state of the system is supposed to be a coherent state in one of the modes and number states in the remaining modes. It is pointed out that in several cases a considerable amount of squeezing can be achieved. Due to the common mathematical structure the case of a two-mode coupler with intensity dependent coupling is also analysed.     

Non-classical Properties of Even and Odd Coherent States

Abstract

We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a ². We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.     

Multiphoton Jaynes-Cummings Model without the Rotating-wave Approximation

Abstract

The general time evolution of operators in the multiphoton Jaynes-Cummings model without the rotating-wave approximation is obtained. The contributions of the counter-rotating terms to atomic dynamics and field squeezing are examined in multiphoton processes.     

Squeezed States for Interferometric Gravitational-wave Detectors

Abstract

The possibility of using squeezed states for improving the shot-noise limit of the strain sensitivity of Michelson interferometers is discussed. We find that the spectrum of squeezing required depends on the method of stabilization used in the experiment. Details are given for the widely used phase-modulation technique (which also allows for recycling of the field), where we find an important application for broadband (‘two-mode’) squeezing.     

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.