Displaced and Squeezed Number States

A short review of the main properties of coherent and squeezed states is given in introductory form. The efforts are addressed to clarify concepts and notions, including some passages of the history of science, with the aim of facilitating the subject for nonspecialists. In this sense, the present work is intended to be complementary to other papers of the same nature and subject in current circulation.

We propose a displacement-operator approach to some aspects of squeezed states for general multiphoton systems. The explicit displacement-operators of the squeezed vacuum and the coherent states are achieved and expresses as the ordinary exponential form. As a byproduct the coherent states of the $q$-oscillator are obtained by the {\it usual exponential} displacement-operator.

The fundamental properties of recently introduced stretched coherent states are investigated. It has been shown that stretched coherent states retain the fundamental properties of standard coherent states and generalize the resolution of unity, or completeness condition, and the probability distribution that $n$ photons are in a stretched coherent state. The stretched displacement and stretched squeezing operators are introduced and the multiplication law for stretched displa...

The time evolution of even and odd squeezed states, as well as that of squeezed number states, has been given in simple, analytic form. This follows experimental work on trapped ions which has demonstrated even and odd coherent states, number states, and squeezed (but not displaced) ground states. We review this situation and consider the extension to even and odd squeezed number states. Questions of uncertainty relations are also discussed.

Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the 1) displacement operator, 2) annihilation- (or ladder-) operator, and minimum-uncertainty methods. For general systems, there is the same understanding except for ladder-operator and displacement-operator squeezed states. After reviewing the known concepts, I propose a method for obtaining generalized minimum-uncertainty squee...

This review is intended for readers who want to have a quick understanding on the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the prototype harmonic oscillator but not always restricting to it. Noting that the treatments of building up such states have a long history, we collected the important ingredients and reproduced them from a fresh perspective but refrained from delving into detailed derivation of each topic....

We establish some of the properties of the states interpolating between number and coherent states denoted by $| n >_{\lambda}$; among them are the reproducing of these states by the action of an operator-valued function on $| n>$ (the standard Fock space) and the fact that they can be regarded as $f$-deformed coherent bound states. In this paper we use them, as the basis of our new Fock space which in this case are not orthogonal but normalized. Then by some special superpos...

In this article, results from the previous paper (I) are applied to calculations of squeezed states for such well-known systems as the harmonic oscillator, free particle, linear potential, oscillator with a uniform driving force, and repulsive oscillator. For each example, expressions for the expectation values of position and momentum are derived in terms of the initial position and momentum, as well as in the $(\alpha,z)$- and in the $(z,\alpha)$-representations described i...

We investigate a broad class of non-classical states, composed of superposed squeezed and displaced number states. The phase space structure is analysed, keeping in mind, Heisenberg limited sensitivity in parameter estimation. Appropriate squeezing and displacement parameters are identified, wherein state fidelity in comparison to metrologically sensitive compass state, is more than 99$\%$. Also, the variance in small shifts measurements, is found equal for both proposed and ...

We generalize the wave functions of the displaced and squeezed number states, found by Nieto, to a time-dependent harmonic oscillator with variable mass and frequency. These time-dependent displaced and squeezed number states are obtained by first squeezing and then displacing the exact number states and are exact solutions of the Schr\"{o}dinger equation. Further, these wave functions are the time-dependent squeezed harmonic-oscillator wave functions centered at classical tr...