Phase Probability Distribution Research Articles

Phase Properties of the Displaced Number State in a Kerr Medium

Abstract Influences of the interaction of the displaced-number-state field with a Kerr medium on phase properties of the field are investigated. The interaction brings about the symmetrical splitting of the phase probability distribution (PPD) sometimes. Collapses and revivals have also been found in the long-time behaviours of the Hermitian, cosine and sine phase operators at high intensities. In terms of the PPD, the origin for generating these revivals has been revealed.

On the measurability of the quantum phase distribution

We give a prescription for the measurement of the quantum phase distribution of a single-mode radiation field. The phase probability distribution is defined as the squared modulus of the photon wave function in the phase representation. The measurement involves all moments of the signal from the balanced homodyne detection.

New wigner function for number and phase

We present a new quasiprobability function defined on Fock space whose marginal distributions are the number and phase probability distributions of the single mode light field (or, equivalently, a harmonic oscillator). The new function is shown to have analogous properties to that of the Wigner function associated with the position and momentum observables. Examples are given of the new function for specific states.

Very small optimized phase uncertainties of two-photon coherent states.

Considering intense two-photon coherent states with minimum phase dispersion, the width of the phase probability distributions based on the Pegg-Barnett formalism, the Wigner function, and the Q function is discussed. Remarkable differences are found in certain regions depending on the mean photon number. These results are compared with the phase uncertainty of phase optimized states.

Phase properties of a field mode interacting with N two-level atoms.

We analyze the phase properties of a strong cavity field interacting with an ensemble of initially excited N two-level atoms. Using the Pegg-Barnett phase formalism [Phys. Rev. A 39, 1665 (1989)], we calculate the phase probability distribution as well as the phase variance. The phase probability density exhibits a (N+1)-peak structure at the initial stages of the evolution. The phase variance is used to illustrate the progressive randomization of the phase on the long-time evolution. The difference in the phase dynamics for the N even and the N odd case is pointed out.

A Random Wave Method for Detecting Phase Imbalance in a Coherent Radar Receiver

The question of monitoring the angle between the in-phase (I) and quadrature (Q) channels of a coherent radar receiver is considered in this paper. Random interference-type scattering (e.g., rain echo) is assumed so that the received signal is a random phasor sum. It is also assumed that I and Q voltages have a (90 + ϕ0) phase difference. The effects of nonzero phase imbalance ϕ0 on the I and Q statistics are examined. Joint I and Q as well as amplitude and phase probability distributions are derived. It is shown that the cross-correlation coefficient at zero lag between I and Q time series is proportional to ϕ0, which provides a simple algorithm to detect the phase imbalance. This is verified by Monte Carlo simulations.

Phase of the field in the interaction with two two-level atoms

The authors present phase properties of a field mode interacting with two two-level atoms using the Pegg and Barnett formalism. They derive analytical and approximate expressions for the phase probability distribution, and calculate the mean value of the phase and their fluctuations. A discussion with respect to the coupling constant of the atoms is given.

Phase properties of the radiation fields in Raman process

The general evolution of the interaction of two radiation fields with an effective two-level atom via the Raman-type transitions is presented. Using the Pegg-Barnett phase theory, the joint phase probability distribution of the two field modes, phase average values and phase fluctuations are studied in detail. Also, the effect of the presence of a field on the phase properties of the other mode is examined.

Phase properties of a field in the Jaynes-Cummings model for non-resonant behaviour

The phase properties of a coherent field non-resonant interacting with a two-level atom in a lossless cavity are studied using the new hermitian phase formalism of Pegg and Barnett. The phase probability distribution, the expectation value and the phase fluctuation of the hermitian phase operator are calculated. The results show that phase properties of the field in non-resonance JCM are strongly dependent on the intensity of the coherent field and the detuning parameter. The phase probability distribution splits into four separate asymmetry distributions as time goes on.

STATISTICAL PHASE PROPERTIES OF LIGHT FIELDS

Based on the definition of Pegg-Barnett phase state, the phase probability distribution functions of various light fields, such as Fock state, coherent state, squeezed state, pair coherent state, entangled state, and so forth and the time evolution of that of some single-mode light fields through the propagation in medium are analytically calculated, while the corresponding computational simulations are presented.

Phase properties of Schrödinger cat states of light decaying in phase-sensitive reservoirs

We study phase properties of quantum mechanical superposition states decaying into phase-sensitive reservoirs. We show that the Wigner phase quasiprobability distribution reflects the quantum interference effects very well while the Pegg–Barnett and the Husimi phase probability distributions are quite insensitive with respect to the character of the quantum interference between component states. We study in detail phase properties of the even coherent state which decays into the thermal and the squeezed reservoirs. In thermal reservoirs the phase of the superposition state becomes randomized under the influence of thermal fluctuations. The higher the number of thermal photons the faster the randomization process is. On the other hand we show that depending on the relative phase between the superposition state and the phase-sensitive reservoir the process of phase randomization can be either enhanced or completely suppressed.

Phase state and phase probability distribution

The properties of the phase state and phase probability distribution of photons are investigated in terms of the phase operator formalism based on the relative-number state representation. The calculation method of phase dynamics is also presented. The results are compared with those obtained by using the Pegg-Barnett phase operator formalism. The phase properties of a nonlinear oscillator and a damped harmonic oscillator are calculated explicitly.

How to realize phase optimized quantum states

We analyze the problem of identifying a nonlinear optical process which changes a coherent state in such a way that the resulting state comes close to a phase optimized state. Due to the uncertainty relation this state must possess a specially broadened photon distribution what points to degenerate parametric amplification to provide such a broadening. Detailed numerical calculations show the feasibility of experimentally realizing approximate phase optimized states by optimized parametric amplification. Investigating also the photon and the phase probability distributions reveals the reasons why such optima exist.

Number and phase quantum fluctuations in the down-conversion with a quantum pump

The photon number and phase quantum fluctuations in the field produced by the down-conversion process with a quantum pump are studied. The fully quantum approach using the method of numerical diagonalization of the interaction Hamiltonian is applied to find the evolution of the system. The evolution of the photon number fluctuations, the joint number of photons probability distribution, the quadrature variances, the joint phase probability distribution, the marginal number and phase distributions for the signal mode, the number and phase uncertainty products and squeezing parameters are calculated and illustrated graphically. The results for the signal mode are compared to the corresponding results for the ideal squeezed vacuum to show the range of validity of the parametric approximation.

Fluctuation of Phase in the Displaced Number States

Using Pegg-Barnett formalism the author has studied the phase properties of displaced number states. It has been found that the phase probability distribution exhibits the same oscillations as the photon number distribution. Using the Hermitian phase operator the fluctuations of the phase of the displaced number states have been studied. The dependence of the fluctuations on the value of the reference phase have been analysed in detail. It has been found that phase of displaced number states exhibit squeezing in the high-intensity limit of the driving field. These states are approximately equivalent to phase states with precisely defined phase. It has been shown that displaced number states are not minimum uncertainty states with respect to the phase and the number operators.

Phase properties of a coherent field interacting with two two-level atoms in a cavity

Abstract We use the Hermitian phase formalism of Pegg and Barnett to study phase properties of a coherent field interacting with a cooperative system. We show that if the number of eigenvalues in a subspace with fixed photon number n is large, as the evolution proceeds, the phase probability distribution exhibits a multi-peaked structure, each of them is associated with one eigenvalue or corresponding eigenstate. We consider in detail the field phase in the system consisting of two two-level atoms and show that its time behaviour reflects the collapses and revivals of the level occupation probabilities.

Phase properties of elliptically polarized light propagating in a Kerr medium with dissipation

The phase properties of two modes of elliptically polarized light propagating in a nonlinear Kerr medium with dissipation are studied. Exact analytical formulas for the joint phase probability distribution, the marginal phase distributions, and the individual mode phase operators, as well as the phase-difference operator expectation values and variances, the phase correlation function, and the expectation value and the variance of the phase-difference cosine, are obtained. Some of the results are illustrated graphically to show explicitly the effect of dissipation on the evolution of the phase properties of the field.

Squeezing and bifurcation in the phase probability distribution in a two-photon micromaser

We derive a master equation for the two-photon micromaser with atomic coherence. We find that the presence of the atomic coherence modifies the threshold condition in the two-photon micromaser, and also produces squeezing and bifurcation in the phase probability distribution. The maximum squeezing is of 36% and it happens below threshold.

Quasi-probability distribution Q(α, α*) versus phase distribution P(θ) in a description of superpositions of coherent states

The generation of discrete superpositions of coherent states in the anharmonic oscillator model is discussed from the point of view of their quasi-probability distribution Q(α, α*) and phase probability distribution P(θ). It is shown that for the superposition with well-distinguishable states both distributions show the same rotational symmetry. The maximum number of well-distinguishable states is estimated. The two functions are illustrated graphically to show explicitly their symmetry and the influence of the interference terms. The similarity between the Q function integrated over the amplitude and the phase distribution P(θ) is shown to exist for the anharmonic oscillator states.

Phase Properties of Elliptically Polarized Light Propagating in a Kerr Medium

Abstract Phase properties of elliptically polarized light propagating through a nonlinear Kerr medium are considered within the framework of the Pegg-Barnett Hermitian phase formalism. The joint phase probability distribution function for the phases of two orthogonal modes describing elliptical polarization of the field is calculated and its evolution discussed and illustrated graphically. The marginal phase probability distribution for the individual phases are also calculated and discussed. Analytical formulae for phase expectation values and variances are derived for the individual phases as well as for the phase difference. It is shown that in the course of propagation the correlation between the phases of the two modes builds up. This correlation is responsible for lowering phase difference variance. The expressions for the sine and cosine functions and their variances of the individual phases as well as the phase difference are obtained and discussed. The effect of randomization of individual phases and the phase difference, which is a purely quantum effect, is shown to appear during propagation. The relation between phase randomization and degradation of the degree of polarization of the light is established.