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.     

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.     

SU(2) and SU(1,1) Rotation Transformation and Pseudo-vector Model in Quantum Optics

Abstract

We construct a pseudo-vector model and realize the rotation transformation for the SU(2) and SU(1,1) dynamics. We introduce concepts of the pseudo-scalar and the scalar product in quantum optics. Several equivalents of the SU(2) and SU(1,1) unified rotation operator are given. By using this method, the two- and three-level Jaynes-Cummings model is discussed in the non-rotating wave approximation.     

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.     

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.     

Four-photon Coherent States

Abstract

We present a detailed discussion of a type of four-photon coherent state defined as right eigenstates of the operator â ⁴ where â is the usual annihilation operator. There are actually four sets of states that need to be considered, namely those containing as the lowest number states ¦0>, ¦1>, ¦2>, or ¦3>. These correspond to the possible unique superpositions of the ordinary coherent states ¦±α> and ¦±iα>. We discuss the nonclassical properties of these states such as photon antibunching and squeezing. The usual second order squeezing does not exist for these states but higher order squeezing and square field amplitude squeezing do exist. Also discussed are the quasiprobability distributions, namely the P-function, the Q-function and the Wigner function. Finally, a method of generating these states based on the competition between a four-photon parametric process and incoherent losses from four-photon absorption is presented.     

Collapse-revival Phenomenon in the Jaynes-Cummings Model Interacting with the Multiphoton Holstein-Primakoff SU(2) Coherent State

Abstract

We have analysed the behaviour of the atomic population inversion of the two-level atom interacting with a single-mode field initially prepared in the multiphoton Holstein-Primakoff SU(2) coherent state. It is shown that the behaviour of the atomic inversion depends on the parameters characterizing the initial state of the field. In particular, the atomic inversion can exhibit periodical oscillations as well as the collapse-revival phenomenon.     

Thermal Coherent States and Thermal Squeezed States

Abstract

Various definitions of thermal coherent states and thermal squeezed states are compared and interrelated. Different ordering of squeezing, displacement and thermalizing operators is discussed in order to establish a relation between all definitions. A one-to-one correspondence is exhibited between general Gaussian density matrices in coordinate space and thermal squeezed states.     

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.     

Phase Resolution and Coherent Phase States

Abstract

Various measures of phase resolution (including variance, entropy, confidence half-width, and reciprocal peak likelihood) are reviewed, and applied to the class of coherent phase states. These states arise naturally as eigenstates of the Susskind-Glogower phase operator, and are found to have near-optimal phase resolution properties for fixed mean photon number [nbar]. The mutual information for a communication channel based on coherent phase states is calculated as log ([nbar] + 1), within 1·5 bits of the theoretical maximum for single-mode channels.     

Entangled Coherent States with Variable Weighting

Abstract

Entangled coherent states, with arbitrary weighting of the two product coherent states in the superposition, might be produced by incorporating an optical bistable device in a coupled cavity configuration. This scheme is contrasted with the entangled coherent states that arise due to interaction in an optical Kerr medium and produce only equally weighted entanglements. The entanglement is shown to occur, not between coherent states, but between states which closely approximate coherent states. An interaction which does produce entanglement between true coherent states is introduced but is shown to be unphysical.     

Generalized Two-mode Squeezed States

Abstract

A new generalized two-mode squeezed state which has less fluctuation in one quadrature phase then the usual two-mode squeezed state at the expense of increased fluctuation in the other quadrature is proposed. The coordinate representations and normally ordered expansions of the generalized two-mode squeeze operators and are given. The wavefunction of the generalized two-mode squeezed coherent state is obtained. The non-classical properties of the state such as squeezing and sub-Poissionian statistics are discussed.     

Squeezing in Finite Superpositions of Photon-number States without the Vacuum

Abstract

We show that a finite superposition of photon-number states without the vacuum state can lead to squeezed fluctuations. The properties of these states are discussed.     

Multimode Coherent States and HeNe Laser Light

Abstract

Among the quantum optical states of a tremolant optical cavity are multimode coherent states. Such states are also possible in open cavities where the cavity stabilization time is greater than the multimode beat time. In open cavity resonator lasers they reduce the power limiting effects of spectral hole burning and therefore tend to grow at the expense of single mode coherent states.     

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.     

Strong Nonequilibrium Coherent States in Mesoscopic Superconductor-Semiconductor-Superconductor Junctions

A biased superconductor-normal metal-superconductor junction is known to be a strong nonequilibrium system, where Andreev scattering at the interfaces creates a quasiparticle distribution function far from equilibrium. A manifestation of this is the well-known subgap structure in the I/V characteristic, with peaks in the conductance at V = 2/ne. We study an SNS structure consisting of highly doped diffusive GaAs with superconducting electrodes of aluminum with one electrode configured as a flux-sensitive interferometer. This enables us to probe the coherent nature of the quasiparticle states at subgap bias voltage. Oscillations in the conductance as a function of flux are seen at zero bias voltage and disappear below experimental resolution as the bias voltage exceeds the Thouless energy E _t = D/L ², where L is the junction length. The oscillations reappear at higher bias in a region around the superconducting energy gap V = /e corresponding to the subgap conductance peak n = 2.     

灰色模型GM(1, 1)优化

分析了GM(1, 1)模型产生模拟误差的原因，经大量的数据模拟和GM(1, 1)模型比较，发现背景值的优化使GM(1, 1)模型在短期、中期及长期预测中扩大了适用范围，并且模拟及预测精度显著提高。     

Interaction of Superpositions of Coherent States of Light with Two-level Atoms

Abstract

We investigate some of the basic features of the interaction of superpositions of coherent states of light with two-level atoms in the framework of the Jaynes-Cummings model. We compare the behaviour of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. We investigate the collapses and revivals of the atomic inversion by studying the evolution of the Q function of the cavity field. We also establish the connection between the purity of the field and the collapses and revivals of the atomic inversion.