Properties of Squeezed Superposition States

Abstract

We study the properties of quantum states of the electromagnetic field obtained from the application of the squeeze operator to superpositions of the ordinary coherent states ¦α> and ¦?α>.     

Phase Properties of Squeezed Number States

Abstract

We have studied the phase properties of the squeezed number states by evaluating the expression for the phase probability distribution and the phase variance. In addition, the expression for the photon number distribution of the squeezed phase states has been evaluated.     

Approximating the Negative Binomial

This paper presents the results of a numerical investigation of six approximations to the cumulative negative binomial distribution. The approximations studied include two Poissons, Poisson Gram-Charlier, Normal, Normal Gram-Charlier and the Camp-Paulson. Two approximations were found to be extremely good: the Poisson Gram-Charlier when the probability p is large, and the Camp-Paulson almost everywhere.     

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.     

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.     

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.     

Tables of the Negative Binomial Probability Distribution

An age replacement policy requires that a unit be replaced when it attains a specified age, or at failure, whichever occurs first. The mathematical solution to the problem of what is the optimal age for replacement is well known. This paper adapts this general mathematical solution to the cases when a truncated normal, Gamma, or Weibull distribution can be assumed. Graphs are presented from which one can readily ascertain the optimal solutions for these models.     

Time Evolution of Stable Squeezed States

Abstract

It is shown using a straightforward approach that, for a single mode of an electromagnetic field, only quadratic Hamiltonians can preserve squeezed states for all time. The time-evolution equations for the parameters of a stable squeezed state are given for arbitrary quadratic Hamiltonians. It is also pointed out that there is no single Hamiltonian that preserves minimum uncertainty for all squeezed minimum-uncertainty states.     

Squeezed States for Interferometric Gravitational-wave Detectors

Abstract

The possibility of using squeezed states for improving the shot-noise limit of the strain sensitivity of Michelson interferometers is discussed. We find that the spectrum of squeezing required depends on the method of stabilization used in the experiment. Details are given for the widely used phase-modulation technique (which also allows for recycling of the field), where we find an important application for broadband (‘two-mode’) squeezing.     

A Note on the Negative Binomial Distribution

In this paper, the technique known as “elemental analysis”, developed by Newton and Surrell (1967) is extended to the multivariate case. It is shown that the use of elements aids in the selection of variables in multivariate multiple regression or in multiple discriminant analysis.     

On the Quantum Mechanics of Squeezed States

Abstract

We show that the squeezed states of quantum optics are physically and mathematically equivalent to Gaussian wave packets. In the framework of wave mechanics it is possible to formulate and investigate in a very simple way all the properties of reduced or squeezed fluctuations of the position and momentum operators. We study squeezed quantum fluctuations of a minimum-uncertainty Gaussian wave function under two different dynamical conditions of free evolution and harmonic oscillation.     

CUSUM and EWMA Control Charts for Negative Binomial Distribution

In public health surveillance, control charts based on the daily number of hospitalizations may be monitored to detect outbreaks and/or to plan the offer of health assistance. A generalized linear model with negative binomial distribution is proposed to the number of hospitalizations, and it depends on the exposed population and covariates, as the day of week and sines and cosines to describe the seasonality. The objective of this study is to compare (in terms of ARL₁) the exponentially weighted moving average and the cumulative sum control charts for monitoring daily counts based on simulations of the daily number of hospitalizations due to respiratory diseases for people over 65 years old in São Paulo city (Brazil). Copyright © 2016 John Wiley & Sons, Ltd.     

Quantum Superpositions of Binomial States of Light

We introduce new kinds of states of electromagnetic field, which are quantum superpositions of binomial states. They not only exhibit remarkable non-classical properties but can also interpolate between the ‘Schrödinger cat’ type of states and the number states in a particularly interesting way. We basically discuss some of their main statistical properties, as well as schemes for their generation. We also employ quasiprobability distributions in phase space.     

Squeezed States Generated by Boson Creation Operator

Using the normal ordering techniques of an operator, we show that a general squeezed state may be expressed in the form N exp [1/2 ξ â σ² m nâ σ] S 0 ¢, where S 0 ¢ is the vacuum state. We obtain the normalization constant N and various other representations. We also discuss conditions for squeezing and photon antibunching.     

Revival Hamiltonians,Phase Operators and Non-Gaussian Squeezed States

Abstract

The phase operators P ^± of the electromagnetic field, whose classical analogues are exp (? iθ), θ being the classical phase, and the number operator N associated with a harmonic oscillator mode are used to construct a class of operators T _m = N(P ^?)^m and T ⁺ _m = (P ⁺)^m N, m = 1, 2,…. It is shown that T _m, T ⁺ _m and N satisfy a simple algebra. T _m and T ⁺ _m are used to construct model Hamiltonians H _m describing the coupling of a two-level atom to a field that leads to decay and exact revivals in the atomic dynamics. In the second part of the paper, a family of unitary operators U _m is constructed in terms of T _m and T ⁺ _m. For m = 1 and m = 2 the states generated by U _m from the vacuum are non-Gaussian squeezed states. The variance properties of the squeezed states so constructed are analysed and compared with those of the Gaussian squeezed states. It is shown that the non-Gaussian squeezed states constructed in this paper have small values for the variance product that rise only logarithmically with for large values of , the mean number of quanta.     

负二项分布可靠度的经验Bayes估计

本文在平方损失下,给出了负二项分布可靠度θ的Bayes估计、Bayes置信下限,同时构造了θ的渐近最优的经验Bayes（EB）估计,并证明了该EB估计的收敛速度为O（n^-1）.     

On the Evaluation of the Negative Binomial Distribution with Examples

The Negative Binomial Distribution is a frequently encountered standard dis-crete distribution function. By the use of the available Binomial or Incomplete Beta Function tables it can be evaluated easily through the use of certain identities.     

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.     

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.