Non-classical Light in Nonlinear Symmetric and Asymmetric Couplers

Abstract

We derive the quantum-statistical properties of light beams in nonlinear symmetric and asymmetric couplers composed of linear waveguides and a nonlinear waveguide operating by the second-harmonic generation. This device can exhibit non-classical behaviour in single and compound modes and produce squeezed and/or sub-Poissonian light. Power solutions are obtained up to the twelfth order adopting a symbolic computer method. In addition, new higher-order results for the asymmetric coupler are presented.     

Quantum statistics and dynamics of nonlinear couplers

Abstract

We investigate both codirectional and contradirectional nonlinear couplers composed of two nonlinear waveguides operating by second-harmonic generation. We take into account possible mismatches inside the waveguides and between them. We calculate the photon number distribution, its factorial moments, quadrature and integrated intensity variances and quadrature uncertainty product taking into account the effects of transmission of light between waveguides. Incident beams are assumed to be coherent, squeezed and mixed with external noise. Second-harmonic modes are assumed to be pumped with strong coherent beams. We show that non-classical behaviour of beams generated by the nonlinear waveguides can be transferred between them and controlled by linear and nonlinear mismatches. In the contradirectional regime of propagation, asymptotic non-classical states can be generated.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

Quantum Statistics of the Optical Parametric Process for Arbitrary Initial States

Abstract

Photon statistics and non-classical behaviour of light produced in the optical parametric process are studied in the approximation of small fluctuations around a stationary point. The depletion of the pump mode is included. An initial generalized superposition of a coherent state and noise as well as the influence of reservoir noise and internal losses are considered.     

Two-mode Squeezed Gaussons

Abstract

Two-mode squeezed Gaussons are non-classical states of light which are intermediate between single-mode and two-mode squeezed states. They may be prepared by coherently mixing two single-mode squeezed states at a beam-splitter or via a frequency converter. When equally squeezed single-mode squeezed states are incident on a 50/50 beam-splitter the output will range between a two-mode squeezed state and two single-mode squeezed states as the phase of the input squeezed light is varied. This behaviour is reflected when the properties of such states are investigated.     

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.     

Two-mode Squeezed Pair Coherent States

Abstract

The properties of states generated by the application of the two-mode squeeze operator to the pair coherent states are studied. These states are the two-mode analogues of the single-mode squeezed states generated by the application of the single-mode squeeze operator to an ordinary coherent state. In the present case there are correlations between the modes and strong non-classical properties are to be expected. We study the statistical properties of the photon number distributions, squeezing, violations of the Cauchy-Schwartz inequality, quasiprobability distributions and the phase distributions.     

Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model

Abstract

We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.     

Photon Number Distribution in a Linear Directional Coupler

Abstract

The photon counting distribution of two modes in a directional coupler is studied, looking in particular at the behaviour of photon number states when losses are taken into account.     

Entanglement of a two-mode squeezed state in a phase-sensitive gaussian environment

Abstract

Some non-classical properties such as squeezing, sub-Poissonian photon statistics or oscillations in photon-number distributions may survive longer in a phase-sensitive environment than in a phase-insensitive environment. We examine if entanglement, which is an inter-mode non-classical feature, can also survive longer in a phase-sensitive environment. Differently from the single-mode case, we find that making the environment phase-sensitive does not aid in prolonging the inter-mode non-classical nature, i.e. entanglement.     

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.     

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.     

Can the kicked top be realized?

Abstract

Collections of identical two-level atoms can give rise to (quantum) chaotic behaviour if non-resonantly coupled to a resonator mode and periodically driven. Observation of such chaos would require a new generation of experiments on microwave superradiance, or optical variants thereof which would exploit the strong coupling characteristic of very small cavities. Similarly, collections of identical three-level atoms non-resonantly coupled to two cavity modes could provide ‘SU(3) laboratories’, capable of realizing the semiclassical and classical limits of SU(3) dynamics, both integrable and chaotic. Some of the more interesting modes of behaviour of such systems are discussed.     

Macroscopic jumps of the axial angular momentum variance of a bidimensionally trapped ion

Abstract

The time evolution of the axial angular momentum [Lcirc] _z of an ion confined in a bidimensional trap is investigated. We find that, under suitable initial conditions, the interaction of the ion with two properly configured classical laser beams induces a peculiar dynamical behaviour of the axial angular momentum fluctuations. We show, in fact, that there exists an instant of time at which the variance of [Lcirc] _z undergoes variations proportional to N ² further to a change of one quantum only in the initial total number N ? 1 of vibrational quanta. The non-classical origin of these macroscopic jumps is brought to the light and carefully discussed.     

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.     

A Multi-oscillator Ring Laser with Zeeman Bias

Abstract

A laboratory multi-oscillator ring laser of monoblock construction employing a non-planar cavity and the Zeeman effect on the helium-neon discharge is used to bias oppositely travelling modes from lock-in. A theoretical model of the laser is used to explain the behaviour with respect to gain, tuning and magnetic field. Methods for stabilizing the gyro operating point and correcting for ambient magnetic fields are presented.     

Optical Measurement Accuracy in the Case of Non-classical Light

Abstract

The influence of optical elements on the statistical properties of the input radiation is analysed by quantum-theoretical means for a representative optical arrangement consisting of beam splitters as well as for various types of grating spectrometers. In particular non-classical light states are studied. Optimum conditions for the maintenance of the signal-to-noise ratio of sub-Poissonian input radiation are derived.     

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.     

Scaling of decoherence effects in quantum computers

Abstract

The scaling of decoherence rates with qubit number N is studied for a simple model of a quantum computer in the situation where N is large. The two state qubits are localized around well-separated positions via trapping potentials and vibrational centre of mass motion of the qubits occurs. Coherent one and two qubit gating processes are controlled by external classical fields and facilitated by a cavity mode ancilla. Decoherence due to qubit coupling to a bath of spontaneous modes, cavity decay modes and to the vibrational modes is treated. A non-Markovian treatment of the short time behaviour of the fidelity is presented, and expressions for the characteristic decoherence time scales obtained for the case where the qubit/cavity mode ancilla is in a pure state and the baths are in thermal states. Specific results are given for the case where the cavity mode is in the vacuum state and gating processes are absent and the qubits are in (a) the Hadamard state (b) the GHZ state.     

Detector efficiency limits on quantum improvement

Abstract

Although the National Institute of Standards and Technology has measured the intrinsic quantum efficiency of Si and InGaAs avalanche photo diode (APD) materials to be above 98% by building an efficient compound detector, commercially available devices have efficiencies ranging between 15 and 75%. This means bandwidth, dark current, cost, and other factors are more important than quantum efficiency for existing applications. For non-classical correlated photon applications, the system's correlated signal-to-noise ratio is proportional to (ηN)^½ /(1 ? η)^½, rather than the classical signal-to-noise (ηN)^½. Consequently, the detector design trade space must be re-evaluated. This paper systematically examines the generic detection process, lays out the considerations needed for designing detectors for non-classical applications, and identifies the ultimate physical limits on quantum efficiency.