Kerr nonlinear coupler with varying linear coupling coefficient

Abstract

We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.     

Optical switching and normal mode splitting in hybrid semiconductor microcavity containing quantum well and Kerr medium driven by amplitude-modulated field

ABSTRACT

We theoretically investigate optical bistability/multistability for all optical switching signature in a hybrid semiconductor microcavity system comprising a quantum well and a Kerr nonlinear substrate. The system is essentially two optically coupled microcavities with one of the microcavity being driven by an external amplitude-modulated pump laser. We show that the switching between bistable and multistable behaviour is influenced by the modulated pump laser, Kerr nonlinearity and the optical coupling between the two microcavities. We further investigate the intracavity spectrum of quantum fluctuations which exhibit the well-known normal mode splitting (NMS). The NMS behaviour is also found to be influenced by the system parameters. These results demonstrate that the present hybrid nonlinear system can be used in designing sensitive optical devices.     

Quantum statistics and dynamics of nonlinear couplers with nonlinear exchange

Abstract

In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through non-degenerate optical parametric interaction. Main attention is paid to generation and transmission of non-classical light, based on a discussion of the squeezing phenomenon, the normalized second-order correlation function and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed with dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state |1〉 enters the first waveguide and the vacuume state |0〉 enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays a similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.     

Intensity-dependent Phase Shifts in Nonlinear Coupling Devices

Abstract

For nonlinear coupling devices, general solutions using Stokes parameters fail to give complete information of phase shifts, as they only provide the phase-shift difference between the two outputs of coupling waveguides (or two cores for fibre coupling devices). Thus the standard Stokes parameter formulation is not sufficient for some applications in which the nonlinear phase shifts through the devices are of great concern. The analysis given here presents complete and exact solutions for nonlinear phase shifts in optical coupling devices for the first time. This reveals unusual behaviour of the nonlinear phase shifts because, in a certain input power range, a small change of input power can bring about a large change in the nonlinear phase shift. Some basic characteristics of the nonlinear phase shifts and their potential influence on application of coupling devices to all-optic signal processing are discussed.     

A self‐tuning control approach of mechanical manipulators

Abstract

The dynamic model of a manipulator system is a time‐varying highly nonlinear coupling equation set. When the moving speed increases or the payload, compared to its own weight, is no longer small, the performance of the conventional control schemes is not satisfactory for precision industrial application. Here a new adaptive control approach is developed for the manipulators to solve these problems. This algorithm directly uses a nonlinear dynamic model in the controller design to account for the nonlinear effects of the system. The least‐square time‐varying parameter identification scheme has been used to identify the change in configuration and payload. The simulation results show that this new approach has a very good trajectory tracking performance.     

Special foundation lecture: A personal view

Abstract

I (try to) review some of my work in theoretical quantum optics done over some 45 years. Highlights include discovery of ?optical solitons‘ as solutions to the nonlinear Maxwell-Bloch (MB) systems of equations as reported at the 1st National QE Conference, also at Owens Park, Manchester, in 1973. Bose-Einstein condensation (BEC) in magnetic traps at temperatures T ～ 10^?9K achieved in 1995 is described by forms of the quantum nonlinear Schrödinger (NLS) equation closely related to the quantized MB equations. It may be possible to see quantum soliton solutions of the quantum attractive NLS equation in one-dimensional (d = 1) magnetic traps holding the Bose condensed metal vapour ⁷Li. More generally such d = 1 quantum solitons may be significant to modern long-distance optical fibre communication, and perhaps to ?quantum information‘.     

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.     

Quantum theory of two-mode nonlinear directional couplers

Abstract

The quantum two-mode nonlinear directional coupler exhibits intriguing variations on the self-trapping effect seen in the corresponding classical model. We study and compare the quantum counterparts of this phenomenon for number and coherent state inputs, and discuss their relation to the nature of the eigenvalues and eigenvectors of the Hamiltonian.     

Optomechanical effect on the Dicke quantum phase transition and quasi-particle damping in a Bose–Einstein condensate: a new tool to measure weak force

Abstract

We make a semi-classical steady state analysis of the influence of mirror motion on the quantum phase transition for an optomechanical Dicke model in the thermodynamic limit. An additional external mechanical pump is shown to modify the critical value of atom–photon coupling needed to observe the quantum phase transition. We further show how to choose the mechanical pump frequency and cavity–laser detuning to produce extremely cold condensates. The present system can be used as a quantum device to measure weak forces.     

Quantum amplifiers at microwave frequencies using Josephson junctions

Abstract

Josephson junctions are quantum mechanical devices with sinusoidal nonlinearity and their use as amplifiers of non-classical microwaves in cavities at low temperatures, is discussed. Self-pumped amplifiers as well as externally pumped three- and four-photon amplifiers are considered, and a quantum theory that describes their operation is developed. It is shown that the sinusoidal nonlinearity can be expanded into a series of terms, the first few of which are familiar from quantum optical amplifiers that use nonlinear optical materials, while the others are higher order corrections.     

Nonlinear quantum optical computing via measurement

Abstract

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel (2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM (2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.     

Valence Band Structure of Coupled Diluted Magnetic Quantum Dots

The valence band structure of double InAs/GaAs diluted magnetic vertical quantum dots has been studied in the frame of multiband k⋅p calculation. We find that due to anisotropic effective mass, the ground state can be tuned from the characteristic of heavy- to light-hole state through just changing the parameter of quantum coupling between two QDs. We also show how this crossover manifests itself in the p–d exchange interaction between hole and Mn spins.     

Interference and the lossless lossy beam splitter

Abstract

By directing the input into a particular mode it is possible to obtain as output all of the input light for a beam splitter which is 50% absorbing. This effect is also responsible for nonlinear quantum interference when two photons are incident on the beam splitter.     

How events come into being: EEQT,particle tracks,quantum chaos and tunnelling time

Abstract

We review Event Enhanced Quantum Theory (EEQT), discuss applications of EEQT to tunnelling time, and compare its quantitative predictions with other approaches, in particular with phase time and the Büttiker-Larmor approach. We discuss quantum chaos and quantum fractals resulting from simultaneous continuous monitoring of several non-commuting observables. In particular we show self-similar, nonlinear, iterated function system type, patterns arising from quantum jumps and from the associated Markov operator.     

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.     

Back-action-induced Squeezed Light in a Detuned Quantum Non-demolition Scheme

Abstract

We describe the experimental observation and theoretical interpretation of a squeezing effect which occurs through the coupling of two light beams in a three-level atomic system. The origin of this effect can be attributed to the transfer of the intensity fluctuations of one beam to the phase fluctuations of the other one, followed by an optical feedback onto the intensity of the initial beam. The first step of the information transfer is similar to the one which occurs in a quantum non-demolition (QND) measurement of the intensity. The feedback effect is obtained through mixing of the phase and intensity quadratures, due to the detuning of the optical cavity which contains the nonlinear medium. Therefore the information obtained by the QND measurement is used to correct the intensity fluctuations of the signal beam by a build-in mechanism, which does not require any use of external electronics.     

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.     

The standard model in cavity quantum electrodynamics. I. General features of mode functions for a Fabry-Perot cavity

Abstract

In the present and the accompanying paper a justification of the standard model of cavity quantum electrodynamics is given in terms of a quasi-mode theory of macroscopic canonical quantization. The coupling of the cavity quasi-mode to external quasi-modes is treated for the representative case of the three-dimensional Fabry-Perot cavity. The general form of the travelling and trapped mode functions for this cavity are derived in this paper and the mode-mode coupling constants are calculated in the accompanying paper. The slow dependence of the coupling constants with the mode frequency difference demonstrates that the conditions for Markovian damping of the cavity quasimode are satisfied. As also discussed in the accompanying paper, the interaction of radiative atoms with cavity quasi-modes is associated with reversible energy exchanges between atom and cavity and represented by Rabi coupling constants. The interaction of radiative atoms located within the cavity with sideways travelling external quasi-modes involves slowly varying coupling constants and is associated with irreversible spontaneous emission dampling. The basic processes represented in the standard cavity quantum electrodynamics model and the associated coupling constant and decay rates thereby follow from the quasi-mode theory.     

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.