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

Evolution and Generation of Dynamics of Two-Mode Squeezed States of Time-Dependent Coupled Boson System

Xue Zhang, Zheng Tai-Yu, Zheng Li

Published Oct 1, 2008• 0 citations
Publisher

Abstract

The system of the Hamiltonian involving a driving part, a single mode part, and a two-mode squeezed one and a two-mode coupled one is discussed using the Lewis–Riesenfeld invariant theory. The time evolution operator is obtained. When the initial state is a coherent state, the quantum fluctuation of the system is calculated, and it is dependent on the squeezed part and the two-mode coupled part, but not dependent on the driving one.

DOI
10.1088/0253-6102/50/4/33

Related papers

The evolution and two-mode squeezed states of the time-dependent two coupled harmonic oscillators

Jiangfan Li, Huang Chun-Jia, Jiang Zong-Fu +2 more

A closed solution of the Schrdinger equation for a timedependent two coupled harmonic oscillators including a driving part and a twomode coupled part is derived by adopting the LewisRiesenfeld invariant theory and properly chosen Hermitian invariant operators. The evolution operator of the system and the condition for generating twomode squeezed states are obtained. It is shown that the quantum fluctuation of squeezed states of the system is independent of the driving part, but depends on the initial states of the system.

Acta Physica Sinica•Jan 1, 2005•3 citations

The time evolution and the quantum fluctuation for two forced quantum oscillators with mixing of two modes

Jiangfan Li, Fuliang Xiao, Zongfu Jiang +1 more

By using the Lewis–Riesenfeld quantum invariant theory and properly choosing Hermitian invariant operator, a closed solution of the Schrödinger equation is derived for two forced quantum oscillators with mixing of two modes, and the quantum fluctuations in the output fields are evaluated. For the initial two-mode squeezed number or squeezed coherent state, in some particular conditions, the time evolution of the oscillators can not only preserve the initial two-mode squeezing, but also produce squeezing in the individual modes; and exhibit a periodical squeezing behaviour. For the initial two-mode number state or coherent state, there is no squeezing in the individual and mutual quadrature phases of the two-mode fields. Furthermore, regardless of which state above being initially considered, the quantum fluctuations of all the quadrature phases in the output fields are all independent of the driving parameters. In particular, for the initial two-mode coherent state, the variances of the output fields are also independent of other parameters in the Hamiltonian, and always preserve their initial values 1/4.

Journal of Physics A Mathematical and General•Oct 5, 2005•1 citation

Time Evolution and Squeezing of Degenerate and Non-degenerate Coupled Parametric Down-Conversion with Driving Term

Jiangfan Li, Fang Jia-Yuan, Xiao Fu-Liang +2 more

By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the degenerate and non-degenerate coupled parametric down-conversion system with driving term. By means of this invariant and the Lewis–Riesenfeld quantum invariant theory, we obtain closed formulae of the quantum state and the evolution operator of the system. We show that the time evolution of the quantum system directly leads to production of various generalized one- and two-mode combination squeezed states, and the squeezed effect is independent of the driving term of the Hamiltonian. In some special cases, the current solution can reduce to the results of the previous works.

Communications in Theoretical Physics•Mar 1, 2009•4 citations

A general solution for the dynamics of a generalized non-degenerate optical parametric down-conversion interaction by virtue of the Lewis–Riesenfeld invariant theory

Jiangfan Li, Zongfu Jiang, Fuliang Xiao +1 more

The dynamics of a generalized non-degenerate optical parametric down-conversion interaction whose Hamiltonian includes an arbitrary time-dependent driving part and a two-mode coupled part is studied by adopting the Lewis–Riesenfeld invariant theory. The closed formulae for the evolution of the quantum states and the evolution operators of the system are obtained. It is shown that various generalized squeezed states arise naturally in the process, and the two-mode squeezed effect is independent of the driving part. An explicitly analytical solution of the Schrödinger equation is further derived as the classical generalized force acting on each mode and the coupling of the two modes both have harmonic time dependences. This solution is found to be in agreement with previous research in special cases.

Journal of Physics A Mathematical and General•May 3, 2005•3 citations

Coherent and squeezed states of light in linear media with time-dependent parameters by Lewis–Riesenfeld invariant operator method

Jeong Ryeol Choi

We investigated coherent and squeezed states of light in linear media whose parameters are explicitly dependent on time by making use of the Lewis–Riesenfeld invariant operator method. Not only the field strengths but also the fluctuations of the fields both in coherent and in squeezed states are decayed with time. The relative noise of the field strengths are calculated in coherent state. Quantum statistical properties of the chaotic field are investigated. We applied our theory to a phenomenological model of the biophoton system and compared the corresponding result of the uncertainty product with that obtained from a previous report.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 9, 2006•25 citations

WAVE FUNCTIONS OF TIME-DEPENDENT TWO COUPLED OSCILLATORS BY LEWIS–RIESENFELD METHOD

Hong-Yi Fan, Zhonghua Jiang

For the two time-dependent coupled oscillators model we derive its time-dependent invariant in the context of Lewis–Riesenfeld invariant operator theory. It is based on the general solutions to the Schrödinger equation which is obtained and turns out to be the superposition of the generalized atomic coherent states in the Schwinger bosonic realization. The energy eigenvectors and eigenvalues of the corresponding time-independent Hamiltonian are also obtained as a by-product.

International Journal of Modern Physics B•Apr 4, 2006•2 citations
The system of the Hamiltonian involving a driving part, a single mode part, and a two-mode squeezed one and a two-mode coupled one is discussed using the Lewis–Riesenfeld invariant theory. The time evolution operator is obtained. When the initial state is a coherent state, the quantum fluctuation of the system is calculated, and it is dependent on the squeezed part and the two-mode coupled part, but not dependent on the driving one.
A closed solution of the Schrdinger equation for a timedependent two coupled harmonic oscillators including a driving part and a twomode coupled part is derived by adopting the LewisRiesenfeld invariant theory and properly chosen Hermitian invariant operators. The evolution operator of the system and the condition for generating twomode squeezed states are obtained. It is shown that the quantum fluctuation of squeezed states of the system is independent of the driving part, but depends on the initial states of the system.
By using the Lewis–Riesenfeld quantum invariant theory and properly choosing Hermitian invariant operator, a closed solution of the Schrödinger equation is derived for two forced quantum oscillators with mixing of two modes, and the quantum fluctuations in the output fields are evaluated. For the initial two-mode squeezed number or squeezed coherent state, in some particular conditions, the time evolution of the oscillators can not only preserve the initial two-mode squeezing, but also produce squeezing in the individual modes; and exhibit a periodical squeezing behaviour. For the initial two-mode number state or coherent state, there is no squeezing in the individual and mutual quadrature phases of the two-mode fields. Furthermore, regardless of which state above being initially considered, the quantum fluctuations of all the quadrature phases in the output fields are all independent of the driving parameters. In particular, for the initial two-mode coherent state, the variances of the output fields are also independent of other parameters in the Hamiltonian, and always preserve their initial values 1/4.
By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the degenerate and non-degenerate coupled parametric down-conversion system with driving term. By means of this invariant and the Lewis–Riesenfeld quantum invariant theory, we obtain closed formulae of the quantum state and the evolution operator of the system. We show that the time evolution of the quantum system directly leads to production of various generalized one- and two-mode combination squeezed states, and the squeezed effect is independent of the driving term of the Hamiltonian. In some special cases, the current solution can reduce to the results of the previous works.
The dynamics of a generalized non-degenerate optical parametric down-conversion interaction whose Hamiltonian includes an arbitrary time-dependent driving part and a two-mode coupled part is studied by adopting the Lewis–Riesenfeld invariant theory. The closed formulae for the evolution of the quantum states and the evolution operators of the system are obtained. It is shown that various generalized squeezed states arise naturally in the process, and the two-mode squeezed effect is independent of the driving part. An explicitly analytical solution of the Schrödinger equation is further derived as the classical generalized force acting on each mode and the coupling of the two modes both have harmonic time dependences. This solution is found to be in agreement with previous research in special cases.
We investigated coherent and squeezed states of light in linear media whose parameters are explicitly dependent on time by making use of the Lewis–Riesenfeld invariant operator method. Not only the field strengths but also the fluctuations of the fields both in coherent and in squeezed states are decayed with time. The relative noise of the field strengths are calculated in coherent state. Quantum statistical properties of the chaotic field are investigated. We applied our theory to a phenomenological model of the biophoton system and compared the corresponding result of the uncertainty product with that obtained from a previous report.