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

Communications in Theoretical Physics

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

Xubing Tang, Xuefen Xu, Fan Hong‐Yi

Published Jul 1, 2010• 2 citations
Publisher

Abstract

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique of integration within an ordered product of operators. The normally ordered time evolution operator is thus obtained. We then derive the Wigner function of u(t)|n⟩, where |n⟩ is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.

DOI
10.1088/0253-6102/54/1/13

Related papers

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

唐绪兵, 许雪芬, 范洪义

理论物理通讯：英文版•Jan 1, 2010•0 citations

Design of squeezing

Hong-Yi Fan, Alfred Wünsche

The design of squeezing by a time-dependent harmonic oscillator is considered. The predetermined general time-dependent squeezing transformations are taken as the starting point from which the time evolution operator U(t,0) and then the corresponding time-dependent Hamiltonian are derived. The technique of integration within an ordered product of operators and the coherent-state representation are used in the intermediate derivations, where U(t,0) is obtained as an operator image of the classical symplectic transformation in phase space by a phase-space integral over coherent states.

Journal of Optics B Quantum and Semiclassical Optics•Jun 21, 2000•24 citations

Squeezing in the Schrodinger picture: normal ordering technique to solve the mass-varying oscillator

A. L. De Brito, B. Baseia

Recent papers by Cheng and Fung (1988) and Lo (1990) have studied the generation of squeezed states out of coherent states in systems described by some time-dependent Hamiltonians. They have employed the evolution operator method for the Schrodinger equation with a Hamiltonian expressible as H(t)=a l (t)J + +a 2 (t)J 0 + +a 3 (t)J - , where J +- ,J 0 are the SU(2) group generators. Here, for the sake of comparison of methods and results, the present authors employ the normal ordered Hamiltonian H(t)= Sigma h l,m (t)(a) l a m and investigate squeezing through an alternative approach using the normal ordering technique to solve the evolution operator for the same system.

Quantum Optics Journal of the European Optical Society Part B•Aug 1, 1992•3 citations

SQUEEZING AND SOME OTHER CHARACTERISTICS OF TIME-DEPENDENT HARMONIC OSCILLATOR WITH VARIABLE MASS

Amitabh Joshi, S. V. Lawande

In this paper we investigate the time evolution of a general time-dependent harmonic oscillator (TDHO) with variable mass using Feynman path integral approach. We explicitly evaluate the squeezing in the quadrature components of a general quantum TDHO with variable mass. This calculation is further elaborated for three particular cases of variable mass whose propagator can be written in a closed form. We also obtain an exact form of the time-evolution operator, the wave function, and the time-dependent coherent state for the TDHO. Our results clearly indicate that the time-dependent coherent state is equivalent to the squeezed coherent state.

Modern Physics Letters B•Jun 30, 1994•2 citations

FRESNEL OPERATOR, SQUEEZED STATE AND WIGNER FUNCTION FOR CALDIROLA–KANAI HAMILTONIAN

Shuai Wang, Hong‐Chun Yuan, Hong-Yi Fan

Based on the technique of integration within an ordered product (IWOP) of operators, we introduce the Fresnel operator for converting a kind of time-dependent Hamiltonian into the standard harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A, B, C, D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of coupled partial differential equations set up in the above-mentioned converting process. In this way, the Caldirola–Kanai Hamiltonian has been easily converted into the standard harmonic oscillator Hamiltonian. And then the exact wave function solution of the Schrödinger equation governed by the Caldirola–Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations.

arXiv:1012.0741•Modern Physics Letters A•Jun 8, 2011•9 citations

New approach for Damping in a squeezed bath and its time evolution through Complete Class of Gaussian Quasi-distributions

M. R. Bazrafkan, Seyed Mahmoud Ashrafi, Fahimeh Naghdi

By virtue of the thermal entangled states representation of density operator and using dissipative interaction picture we solve the master equation of a driven damped harmonic oscillator in a squeezed bath. We show that the essential part of the dynamics can be expressed by the convolution of initial Wigner function with a special kind of normalized Gaussian in phase space and relate the dynamics with the change of Gaussian ordering of density operator.

arXiv:1402.2545•Feb 11, 2014•0 citations
For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique of integration within an ordered product of operators. The normally ordered time evolution operator is thus obtained. We then derive the Wigner function of u(t)|n⟩, where |n⟩ is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.
The design of squeezing by a time-dependent harmonic oscillator is considered. The predetermined general time-dependent squeezing transformations are taken as the starting point from which the time evolution operator U(t,0) and then the corresponding time-dependent Hamiltonian are derived. The technique of integration within an ordered product of operators and the coherent-state representation are used in the intermediate derivations, where U(t,0) is obtained as an operator image of the classical symplectic transformation in phase space by a phase-space integral over coherent states.
Recent papers by Cheng and Fung (1988) and Lo (1990) have studied the generation of squeezed states out of coherent states in systems described by some time-dependent Hamiltonians. They have employed the evolution operator method for the Schrodinger equation with a Hamiltonian expressible as H(t)=a l (t)J + +a 2 (t)J 0 + +a 3 (t)J - , where J +- ,J 0 are the SU(2) group generators. Here, for the sake of comparison of methods and results, the present authors employ the normal ordered Hamiltonian H(t)= Sigma h l,m (t)(a) l a m and investigate squeezing through an alternative approach using the normal ordering technique to solve the evolution operator for the same system.
In this paper we investigate the time evolution of a general time-dependent harmonic oscillator (TDHO) with variable mass using Feynman path integral approach. We explicitly evaluate the squeezing in the quadrature components of a general quantum TDHO with variable mass. This calculation is further elaborated for three particular cases of variable mass whose propagator can be written in a closed form. We also obtain an exact form of the time-evolution operator, the wave function, and the time-dependent coherent state for the TDHO. Our results clearly indicate that the time-dependent coherent state is equivalent to the squeezed coherent state.
Based on the technique of integration within an ordered product (IWOP) of operators, we introduce the Fresnel operator for converting a kind of time-dependent Hamiltonian into the standard harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A, B, C, D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of coupled partial differential equations set up in the above-mentioned converting process. In this way, the Caldirola–Kanai Hamiltonian has been easily converted into the standard harmonic oscillator Hamiltonian. And then the exact wave function solution of the Schrödinger equation governed by the Caldirola–Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations.