Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9308029 · Physical Review Letters

Squeezed states for general systems

Michael Martin Nieto, D. Rodney Truax

Published Nov 1, 1993• 112 citations
arXivHTMLPDF

Abstract

We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method with the minimum-uncertainty method for obtaining the squeezed and coherent states of general potential systems, and comment on the distinctions between these two methods and the displacement-order method.

DOI
10.1103/physrevlett.71.2843

Related papers

GENERALIZED SQUEEZED STATES FROM GENERALIZED COHERENT STATES

Michael Martin Nieto

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 squeezed states, give examples, and relate it to known concepts. I comment on the remaining concept, that of general displacement-operator squeezed states.

arXiv:hep-th/9311039•May 1, 1994•1 citation

Displacement operator squeezed states for general systems

Hong‐Chen Fu, Ryu Sasaki B

Among the three methods of defining the squeezed states of the harmonic oscillator, only two, i.e. the minimum uncertainty and ladder-operator methods were extended to investigate the squeezed states of the general symmetry systems. The only exception is the displacement-operator formalism. In this letter we propose a displacement-operator approach to the squeezed states for general systems. We show that the ladder-operator squeezed states for general symmetry systems can be obtained by applying an exponential displacement-operator on the ``vacuum'' state. The general formalism is presented and it is illustrated with su(1,1) as an explicit example. As a byproduct, the squeezed states of the q-deformed oscillator are obtained and, in particular, expressed in terms of the {\\it usual exponential} displacement-operator acting the ``vacuum'' state.

•Jan 1, 1995•0 citations

Coherent states for general potentials. I. Formalism

Michael Martin Nieto, L. M. Simmons

We first review the properties of the harmonic-oscillator coherent states which can be equivalently defined as (a) a specific subset of the $x\ensuremath{-}p$ minimum-uncertainty states, (b) eigenstates of the annihilation operator, or (c) states created by a certain unitary exponential displacement operator. Then we present a new method for finding coherent states for particles in general potentials. Its basis is the desire to find those states which most nearly follow the classical motion, but it is most nearly a generalization of the minimum-uncertainty method. The properties of these states are discussed in detail. Next we show that the annihilation operator and displacement operator methods, as heretofore defined, cannot be applied to general potentials (whose eigenvalues are not equally spaced). We define a generalization of these methods but show that the states so defined are not, in general, equivalent to the minimum-uncertainty coherent states. We discuss a number of properties of our coherent states and the procedures we have used.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Sep 15, 1979•210 citations

Ladder operators and coherent states for nonlinear potentials

R. Román-Ancheyta, O de los Santos-Sánchez, J. Récamier

In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.

arXiv:1503.01747•Journal of Physics A Mathematical and Theoretical•Oct 10, 2011•15 citations

Generalized coherent, squeezed and intelligent states for exactly solvable quantum systems and the analogue of the displacement and squeezing operators

A N F Aleixo, A. B. Balantekin

Using an algebraic approach, we construct purely coherent and squeezed states for a set of exactly solvable quantum confined systems assuming a generalization of both the ladder-operator and the displacement-operator methods, showing the equivalence between the two procedures. We obtain the analogue of the displacement and the squeeze operators and study their basic relations and their connections with the properties of the purely coherent and squeezed states that they produce. In a second approach, we construct generalized squeezed coherent and intelligent states for these systems considering the successive action of the displacement and the squeeze operators (in the first case) and the combined action of these operators (in the second case). We apply the generalized approach for shape-invariant systems with potential parameters related by a translation and by a scaling and show that the presence of the generalizing functionals of the potential parameters in the formalism opens a large number of possibilities in the construction of these special quantum states.

Journal of Physics A Mathematical and Theoretical•Jul 12, 2013•8 citations

Holstein-Primakoff/Bogoliubov Transformations and the Multiboson System

Michael Martin Nieto, D. Rodney Truax

As an aid to understanding the displacement operator definition of squeezed states for arbitrary systems, we investigate the properties of systems where there is a Holstein-Primakoff or Bogoliubov transformation. In these cases the ladder-operator or minimum-uncertainty definitions of squeezed states are equivalent to an extent displacement-operator definition. We exemplify this in a setting where there are operators satisfying [A, Aå] = 1, but the A's are not necessarily the Fock space a's; the multiboson system. It has been previously observed that the ground state of a system often can be shown to to be a coherent state. We demonstrate why this must be so. We close with a discussion of an alternative, effective definition of displacement-operator squeezed states.

arXiv:quant-ph/9506025•Fortschritte der Physik/Progress of Physics•Jan 1, 1997•37 citations
We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method with the minimum-uncertainty method for obtaining the squeezed and coherent states of general potential systems, and comment on the distinctions between these two methods and the displacement-order method.
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 squeezed states, give examples, and relate it to known concepts. I comment on the remaining concept, that of general displacement-operator squeezed states.
Among the three methods of defining the squeezed states of the harmonic oscillator, only two, i.e. the minimum uncertainty and ladder-operator methods were extended to investigate the squeezed states of the general symmetry systems. The only exception is the displacement-operator formalism. In this letter we propose a displacement-operator approach to the squeezed states for general systems. We show that the ladder-operator squeezed states for general symmetry systems can be obtained by applying an exponential displacement-operator on the ``vacuum'' state. The general formalism is presented and it is illustrated with su(1,1) as an explicit example. As a byproduct, the squeezed states of the q-deformed oscillator are obtained and, in particular, expressed in terms of the {\\it usual exponential} displacement-operator acting the ``vacuum'' state.
We first review the properties of the harmonic-oscillator coherent states which can be equivalently defined as (a) a specific subset of the $x\ensuremath{-}p$ minimum-uncertainty states, (b) eigenstates of the annihilation operator, or (c) states created by a certain unitary exponential displacement operator. Then we present a new method for finding coherent states for particles in general potentials. Its basis is the desire to find those states which most nearly follow the classical motion, but it is most nearly a generalization of the minimum-uncertainty method. The properties of these states are discussed in detail. Next we show that the annihilation operator and displacement operator methods, as heretofore defined, cannot be applied to general potentials (whose eigenvalues are not equally spaced). We define a generalization of these methods but show that the states so defined are not, in general, equivalent to the minimum-uncertainty coherent states. We discuss a number of properties of our coherent states and the procedures we have used.
In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schrödinger equation. We show that both methods yield coherent states with identical algebraic structure.
Using an algebraic approach, we construct purely coherent and squeezed states for a set of exactly solvable quantum confined systems assuming a generalization of both the ladder-operator and the displacement-operator methods, showing the equivalence between the two procedures. We obtain the analogue of the displacement and the squeeze operators and study their basic relations and their connections with the properties of the purely coherent and squeezed states that they produce. In a second approach, we construct generalized squeezed coherent and intelligent states for these systems considering the successive action of the displacement and the squeeze operators (in the first case) and the combined action of these operators (in the second case). We apply the generalized approach for shape-invariant systems with potential parameters related by a translation and by a scaling and show that the presence of the generalizing functionals of the potential parameters in the formalism opens a large number of possibilities in the construction of these special quantum states.
As an aid to understanding the displacement operator definition of squeezed states for arbitrary systems, we investigate the properties of systems where there is a Holstein-Primakoff or Bogoliubov transformation. In these cases the ladder-operator or minimum-uncertainty definitions of squeezed states are equivalent to an extent displacement-operator definition. We exemplify this in a setting where there are operators satisfying [A, Aå] = 1, but the A's are not necessarily the Fock space a's; the multiboson system. It has been previously observed that the ground state of a system often can be shown to to be a coherent state. We demonstrate why this must be so. We close with a discussion of an alternative, effective definition of displacement-operator squeezed states.