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.     

Two-point Resolution in Partially Coherent Light

This paper is an extension of an earlier paper to cover the study of the effects of the annular source of illumination in ordinary microscopy on the resolution of general two-point targets. The limit of resolvable separation has been obtained, = (K _s + j)u/sin f, where K _s + 0·446 + 0·32 o gives the Sparrow limit when the illumination is such as to yield a degree of coherence, o, between the two particles at the limit of resolution. It is also seen that this resolution does not change significantly with the width of the annular source having a fixed mean radius.     

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.     

Resolution of Phase Particles in Phase Microscopy

This paper deals with the question of two-point resolution for pure phase particles in a phase contrast microscope (no amplitude contrast is considered) illuminated with partially coherent light. It is seen that the phase particles in phase microscopy behaves in a manner equivalent to that of amplitude particles in ordinary microscopy. The limit of resolution as estimated on the basis of Sparrow criterion is seen to be independent of Δ, i.e. the magnitude of phase particles. In other words, the limit of resolvable separation with any finite contrast may be expressed as K = K _s+δK, where K _s, the limit obtainable on the basis of Sparrow criterion, is independent of the magnitude of Δ and δK is an incremental term that depends on the magnitude of Δ and the final required image contrast. Both terms, however, depend on the degree of coherence between the object particles. Results are given for the phase particles both leading or lagging in phase with respect to the background. The question of low contrast or small phase approximation is also discussed.     

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.     

Quasi-photon Phase States

Abstract

We introduce quasi-photon phase states of radiation in the single mode, and study the fluctuations in the measured phase operators. We also show that these states exhibit bunching, unlike coherent states which show no bunching.     

Influence of Partially Coherent Illumination and Spherical Aberration on Microscopic Resolution

Starting from linearity considerations and the Huygens-Fresnel principle, the use of ‘matched’ illumination in image formation with coherent light is described. As typical examples, the influence of a longitudinal mismatch of illumination on the images of small circular apertures is numerically studied. For comparison, the results on the defocused images of the same objects under ‘matched’ coherent illumination are also given.     

Phase Contrast Imagery of Circular Phase Objects in Partially Coherent Light

A general solution of the problem of imagery of phase discs in partially coherent phase contrast microscopy is given. The solution has been obtained in a form very much amenable to analysis of optimum phase plate characteristics.     

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.     

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.     

Berry's Phase in the Coherent Excitation of Atoms

Abstract

The adiabatic variation of a Hamiltonian can cause the wavefunction, governed by the Hamiltonian, to acquire an unexpected phase. The existence of this phase (Berry's phase) is an additional element in the well-known quantum adiabatic theorem. Berry's phase is observable in the interference between two identically prepared systems only one of which is adiabatically varied. We show that a single quantum system prepared in a superposition of the eigenstates of its Hamiltonian leads to observable Berry phase effects at all times. We examine this principle within the context of two-level optical resonance.     

Phase States and Their Statistical Properties

Abstract

We study the statistical properties of radiation in the single-mode phase states by evaluating the expression for the photon-counting distribution and its factorial moments. A detailed comparison has been made of the properties of phase states with those of coherent and chaotic states.     

动态波前相位的高分辨率测量

动态波前相位信息测量是大气光学，气动光学和激光技术等领域的重要实验手段。提出了一种具有高的时间和空间分辨率以及长的测量持续时间的动态波前相位测量方法。应用Ｈａｒｔｍａｎｎ－Ｓｈａｃｋ波前传感器获得高空间分辨率的相位信息，采用高帧频ＣＣＤ摄象机获得高时间分辨率图象数据。     

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.