Coherent state expansion of squeezed states

1990 ◽  
Vol 149 (2-3) ◽  
pp. 67-70 ◽  
Author(s):  
P. Adam ◽  
J. Janszky
Keyword(s):  
Coherent State ◽  
Squeezed States ◽  
State Expansion

Gaussian coherent state expansion of the squeezed states

1990 ◽  
Vol 80 (2) ◽  
pp. 155-158 ◽  
Author(s):  
P. Adam ◽  
J. Janszky ◽  
An.V. Vinogradov
Keyword(s):  
Coherent State ◽  
Squeezed States ◽  
State Expansion

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.

QUANTUM OPTICS: GROUP AND NON-GROUP METHODS

1999 ◽  
Vol 13 (24n25) ◽  
pp. 3021-3038 ◽  
Author(s):  
ALLAN I. SOLOMON
Keyword(s):  
Quantum Optics ◽  
Coherent State ◽  
Quantum Group ◽  
Squeezed States ◽  
Theoretical Methods ◽  
Group Methods ◽  
Photon States

We give a brief review of some group and quantum group theoretical methods used for the construction of photon states, generalisations of coherent and squeezed states. We finally describe a more general approach, exemplified by a new generalized coherent state, a generalization of the Kerr state.

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.

scholarly journals Higher order properties and Bell inequality violation for the three-mode enhanced squeezed state

2010 ◽  
Vol 88 (5) ◽  
pp. 349-356
Author(s):  
Shuang-Xi Zhang ◽  
Hong-Chun Yuan ◽  
Hong-Yi Fan
Keyword(s):  
Coherent State ◽  
Bell Inequality ◽  
Higher Order ◽  
Photon Statistics ◽  
Squeezed States ◽  
Squeezed State ◽  
Squeezed Coherent State ◽  
Wigner Representation ◽  
Squeezing Operator

By extending the usual two-mode squeezing operator S2 = exp[iλ(Q1P2 + Q2P1)] to the three-mode squeezing operator S3 = exp{iλ[Q1(P2 + P3) + Q2(P1 + P3) + Q3(P1 + P2)]}, we obtain the corresponding three-mode squeezed coherent state. The higher order properties of this state, such as higher order squeezing and higher order sub-Possonian photon statistics, are investigated. It is found that the new squeezed state not only can be squeezed to all even orders but also exhibits squeezing enhancement compared with the usual cases. In addition, we examine the violation of the Bell inequality for the three-mode squeezed states by using the formalism of Wigner representation.

Analytical Solutions of the Two-Site Holstein Model by the Coherent State Expansion

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4252-4259 ◽  
Author(s):  
Zijing Lin ◽  
Rongsheng Han ◽  
Wang Kelin
Keyword(s):  
Coherent State ◽  
Analytical Solutions ◽  
Order Approximation ◽  
Nonlinear Dynamical System ◽  
Expansion Method ◽  
Third Order ◽  
State Expansion ◽  
The Third ◽  
Holstein Model ◽  
Highly Nonlinear

The polaron problem presents a highly nonlinear dynamical system in which the charge and lattice deformations are intricately coupled together. The coherent state expansion method was applied to the two-site Holstein model. Analytical solutions are found for the first, the second and the third order approximations. Comparison is made among the exact numerical results, based upon solving a recursive relation for the expansion coefficients, and the analytical solutions up to the third order approximation for various e-ph coupling strengths and electron hopping parameters.

scholarly journals SQUEEZED VACUA AND THE QUANTUM STATISTICS OF COSMOLOGICAL PARTICLE CREATION

1994 ◽  
Vol 09 (07) ◽  
pp. 991-1007 ◽  
Author(s):  
B. L. HU ◽  
G. KANG ◽  
A. MATACZ
Keyword(s):  
Coherent State ◽  
Particle Number ◽  
Particle Creation ◽  
Space Time ◽  
Quantum Statistics ◽  
Squeezed States ◽  
Quantum Fields ◽  
Squeezed State ◽  
Initial State ◽  
Systematic Description

We use the language of squeezed states to give a systematic description of two issues in cosmological particle creation: (a) Dependence of particle creation on the initial state specified; we consider in particular the number state, the coherent state and the squeezed state; (b) the relation of spontaneous and stimulated particle creation and their dependence on the initial state. We also present results for the fluctuations in particle number in anticipation of its relevance to defining noise in quantum fields and the vacuum susceptibility of space–time.

Effect of the oscillations in the photon distribution of a squeezed field on the fluorescence spectrum of the Jaynes–Cummings model

2020 ◽  
pp. 2050426
Author(s):  
L. Villanueva-Vergara ◽  
F. Soto-Eguibar ◽  
H. M. Moya-Cessa
Keyword(s):  
Electromagnetic Field ◽  
Coherent State ◽  
Fluorescence Spectrum ◽  
Squeezed States ◽  
Level System ◽  
Photon Distribution ◽  
Atomic Inversion ◽  
Squeezed Coherent State ◽  
Physical Spectrum

Following the scheme proposed by Eberly and Wodkiewicz for the physical spectrum, we calculate the fluorescence spectrum of the Jaynes–Cummings model when the two-level system interacts with an electromagnetic field that initially is in a squeezed coherent state. We show the appearing of “ringing lines” in the fluorescence spectrum that are echoes of the oscillations in the photon distribution of the compressed field. These ringing lines may be a similar effect as the ringing revivals of the atomic inversion that are a signature of squeezed states.

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