Time-dependent invariant for the quadratic Hamiltonian and the stable squeezed states

1987 ◽  
Vol 65 (5) ◽  
pp. 525-526 ◽  
Author(s):  
Fan Hong-Yi ◽  
H. R. Zaidi
Keyword(s):  
General Expression ◽  
Time Dependent ◽  
Squeezed States ◽  
Quadratic Hamiltonian

The conditions for the existence of a time-dependent invariant for the general quadratic Hamiltonian are investigated. A general expression for such an invariant is obtained, and it is shown that the stable squeezed states are eigenstates of this invariant.

On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency

2003 ◽  
Vol 17 (18) ◽  
pp. 983-990 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Present Solution ◽  
Quadratic Hamiltonian ◽  
Dependent Mass ◽  
Quantization Problem

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation

1997 ◽  
Author(s):  
Eric A. Butcher ◽  
S. C. Sinha
Keyword(s):  
Perturbation Theory ◽  
Classical Method ◽  
Time Dependent ◽  
Fast Time ◽  
Quadratic Part ◽  
Canonical Perturbation ◽  
Internal Excitation ◽  
Quadratic Hamiltonian ◽  
Unperturbed Part ◽  
Time Periodic

Abstract In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.

Time-dependent mode coupling and generation of two-mode squeezed states

1991 ◽  
Vol 157 (4-5) ◽  
pp. 226-228 ◽  
Author(s):  
Y.S. Kim ◽  
V.I. Man'ko
Keyword(s):  
Mode Coupling ◽  
Time Dependent ◽  
Squeezed States

Berry phase for the SU(1,1) coherent state

1988 ◽  
Vol 66 (11) ◽  
pp. 978-980 ◽  
Author(s):  
Fan Hong-Yi ◽  
H. R. Zaidi
Keyword(s):  
Coherent State ◽  
General Expression ◽  
Berry Phase ◽  
Squeezed States

We derive a general expression for the Berry phase for the case of the SU(1,1) coherent state. The results are also applicable to one- and two-mode squeezed states.

Exact quantum theory of a time-dependent bound quadratic Hamiltonian system

1993 ◽  
Vol 48 (4) ◽  
pp. 2716-2720 ◽  
Author(s):  
Kyu Hwang Yeon ◽  
Kang Ku Lee ◽  
Chung In Um ◽  
Thomas F. George ◽  
Lakshmi N. Pandey
Keyword(s):  
Quantum Theory ◽  
Hamiltonian System ◽  
Time Dependent ◽  
Exact Quantum ◽  
Quadratic Hamiltonian

TIME-DEPENDENT WIGNER DISTRIBUTION FUNCTION EMPLOYED IN SQUEEZED SCHRÖDINGER CAT STATES: |Ψ(t)〉 = N-1/2(|β〉+eiϕ|-β〉)

2009 ◽  
Vol 23 (25) ◽  
pp. 5049-5066
Author(s):  
JEONG RYEOL CHOI ◽  
KYU HWANG YEON
Keyword(s):  
Distribution Function ◽  
Harmonic Oscillator ◽  
Wigner Distribution ◽  
Time Dependent ◽  
Squeezed States ◽  
Wigner Distribution Function ◽  
Practical Applications ◽  
Schrödinger Cat ◽  
Cat States ◽  
Theory Of Invariants

The Wigner distribution function (WDF) for the time-dependent quadratic Hamiltonian system is investigated in the squeezed Schrödinger cat states with the use of Lewis–Riesenfeld theory of invariants. The nonclassical aspects of the system produced by superposition of two distinct squeezed states are analyzed with emphasis on their application into special systems beyond simple harmonic oscillator. An application of our development to the measurement of quantum state by reconstructing the WDF via Autler–Townes spectroscopy is addressed. In addition, we considered particular models such as Cadirola–Kanai oscillator, frequency stable damped harmonic oscillator, and harmonic oscillator with time-variable frequency as practical applications with the object of promoting the understanding of nonclassical effects associated with the WDF.

THE DEPENDENCY ON THE SQUEEZING PARAMETER FOR THE UNCERTAINTY RELATION IN THE SQUEEZED STATES OF THE TIME-DEPENDENT OSCILLATOR

2004 ◽  
Vol 18 (16) ◽  
pp. 2307-2324 ◽  
Author(s):  
JEONG RYEOL CHOI
Keyword(s):  
Quantum Mechanics ◽  
Coherent State ◽  
Coherent States ◽  
Uncertainty Relation ◽  
Time Dependent ◽  
Squeezed States ◽  
Time Dependency ◽  
Minimum Value ◽  
Number State

We obtained the uncertainty relation in squeezed states for a time-dependent oscillator. The uncertainty relation in coherent states is same as that of the number states with n=0. However, the uncertainty relation in squeezed states does not satisfy this property and depends on squeezing parameter c. For instance, the uncertainty relation is ℏ/2 which is the minimum value as far as quantum mechanics permits for c=1, same as that in coherent state for c=±∞, and infinity for c=-1. If the time-dependency of the Hamiltonian for the system vanishes, the uncertainty relation in squeezed states will no longer depend on c and becomes the same as that in number state with n=0, like the uncertainty relation in coherent states.

Sign in / Sign up

Export Citation Format

Share Document