Effects of Even and Odd Coherent States on the Evolution of the Two-photon Jaynes-Cummings model

We discuss the two-photon Jaynes-Cummings model prepared in even or odd coherent states in terms of its dynamical evolution and the statistical aspects of field, such as intensity-intensity correlation and squeezing. Time evolution of the quasiprobability function has also been investigated. This study reveals how the quantum interference present in the even and odd coherent states affects the nonlinear process of the two-photon transition.     

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.     

奇偶层交错对瓦楞纸板缓冲性能的影响

目的研究在奇偶层交错方式下,交错角度对瓦楞纸板缓冲性能的影响。方法将单瓦楞纸板按奇偶层交错的方式进行多层粘合以制备试样,交错角度分别为0°,30°,45°,60°和90°,采用共面静压、侧向静压和共面冲击的试验方法,对各试样共面和侧向的缓冲性能进行研究。结果与奇偶层不交错的样品相比,在共面静压下,奇偶交错使瓦楞纸板的初始峰应力、平台应力、密实化单位体积变形能和密实化比吸能分别提高了4.15%~9.38%,6.49%~10.39%,5.00%~7.94%和7.43%~10.81%;在沿瓦楞方向侧向静压下,抗压强度和平台应力分别减少了1.18%~14.34%和0.89%~20.66%,密实化比吸能和密实化单位体积变形能与交错角度近似呈二次函数关系。在共面冲击载荷下,当交错角度一定时,总能量吸收与冲击能近似呈一次函数关系。结论奇偶层交错一定角度能改善瓦楞纸板的共面缓冲性能,降低其沿瓦楞方向的侧向缓冲性能。     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Statistical Properties of the Even Binomial State

Abstract

In this paper we introduce the even binomal state, which interpolates between the even number state and the even coherent state. We consider the effect of this state on the Glauber second order correlation function. Both squeezing phenomena are discussed, i.e., normal squeezing and amplitude squared squeezing. The quasiprobability distribution functions (Wigner function and Q function) for such a state are also examined.     

Some Statistical Properties of Random Speckle Patterns in Coherent and Partially Coherent Illumination

The power spectrum of the intensity fluctuations in a random speckle pattern is derived in a simplified manner for coherent illumination. The effect of the power spectrum on the measured signal-to-noise ratio is discussed, and some preliminary measurements of the power spectrum are presented. The power spectrum of the intensity fluctuations for partially coherent illumination is derived for the special case of an aberration-free system, using quadratic filter theory.     

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.     

Mutual Coupling and Its Effect on Steady-State Performance and Position Estimation of Even and Odd Number Phase Switched Reluctance Motor Drive

In this paper, we analyze mutual coupling of switched reluctance (SR) motors with even and odd numbers of phases. We illustrate that SR motors with an even number of phases produce asymmetric mutual flux in different phases. On the other hand, an SR motor with an odd number of phases produces symmetric mutual coupling in all the phases. Then, we explain a practical way of measuring the mutual flux in SR motors and present the test results for an 8/6 pole, four-phase 4 kW motor. We simulated the performance of the SR motor with and without mutual flux, thereby demonstrating the effect of mutual flux on phase current, flux, and average torque. We verified the effect of mutual flux on position estimation by simulation and experiment. We show that appropriate correction for mutual flux may improve the accuracy of estimated position by 3deg, which will give better performance of the drive while driven without any shaft sensors. We also show that an SR motor with an odd number of phases is a better choice than one with an even number of phases because of its symmetric mutual coupling, its ability to utilize short flux paths, and the fact that it does not require costly bipolar excitation.     

Wigner Functions for Coherent and Squeezed States with Thermal Noise

Abstract

A generalized Wigner function W _T(α, ) including the thermal degrees of freedom is presented to calculate the ‘reduced’ Wigner functions for all kinds of coherent and squeezed states with thermal noise by the formalism of thermofield dynamics. The results show that the different definitions of coherent and squeezed state with the same corresponding density matrix give rise to the same reduced Wigner function. By our method, the reduced Wigner function can be calculated for an arbitrary vector in the thermal Fock space, of which the density matrix is too complicated to use.     

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.     

Evolution of Coherent States in a Dispersionless Fibre with Saturable Nonlinearity and the Generation of Macroscopic Quantum-superposition States

Abstract

We study the evolution of a initially coherent state of an electromagnetic field propagating in a Kerr medium with saturable nonlinearity. By using the quantum phase distribution formalism, we analyse the dependence of the output signal phase configuration upon input field amplitude. We observe that the saturation of the nonlinear contribution of the refractive index of the propagation medium introduces interference effects that compromise the observation of macroscopically well distinguishable components of the output state. For input amplitudes much larger than a characteristic saturation amplitude the final state differs from the input state only by an overall phase shift. Possible relevance of the present results in the experimental search of Schrödinger cat-like states using semiconductor-doped glass optical fibres is discussed.