scholarly journals A New Expansion of the Heisenberg Equation of Motion with Projection Operator

2000 ◽  
Vol 104 (3) ◽  
pp. 575-594 ◽  
Author(s):  
T. Koide ◽  
M. Maruyama
Keyword(s):  
Projection Operator ◽  
Equation Of Motion ◽  
Heisenberg Equation

Wigner Representation for Investigation of Entangled Photon Evolution in Four-Wave Mixing Process within a Fiber Ring Resonator

2015 ◽  
Vol 804 ◽  
pp. 316-320
Author(s):  
Chatchawal Sripakdee
Keyword(s):  
Ring Resonator ◽  
Equations Of Motion ◽  
Numerical Approach ◽  
Equation Of Motion ◽  
Nonlinear Susceptibility ◽  
Heisenberg Equation ◽  
Fiber Ring ◽  
Wigner Representation ◽  
Fiber Ring Resonator ◽  
Photon States

The aim of this study is to analyze the quantum correlation of entangled photons for four-wavemixing process within Kerr nonlinear susceptibility χ(3) of an optical fiber ring resonator. The main system Hamiltonian composes of two types of coupling photon modes, including pumping and parametric-down conversion. Wigner representation is applied to the Heisenberg equation of motion derived from the system Hamiltonian in order to obtain the corresponding stochastic equations of motion in a c-number. Quantum trajectories obtained from the stochastic equation of motion of photon states are then derived. Finally, the entanglement inseparability criteria for a pair of entangled photonfrom a numerical approach is also satisfied.

WEHRL ENTROPY AND ENTANGLEMENT OF A TIME-DEPENDENT TWO-LEVEL TRAPPED ION INTERACTING WITH A LASER FIELD

2008 ◽  
Vol 06 (02) ◽  
pp. 331-339
Author(s):  
MAHMOUD ABDEL-ATY ◽  
SAYED ABDEL-KHALEK ◽  
ABDEL-SHAFY F. OBADA
Keyword(s):  
Exact Solution ◽  
Time Evolution ◽  
Laser Field ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Heisenberg Equation ◽  
Wehrl Entropy ◽  
Entanglement Generation ◽  
Trapped Ion ◽  
Cat States

The time evolution of the atomic Wehrl entropy and long-lived entanglement generation using a single trapped ion interacting with a laser field are analyzed. Starting from the Heisenberg equation of motion, an exact solution of the system is obtained by indicating that there are some interesting features when a time-dependent modulating function is considered. We demonstrate that the long-living quantum entanglement can be obtained using the time-independent interaction when the field is initially in a pair cat states.

nTH-ORDER SQUEEZING OF THE FIELD AMPLITUDE IN RAMAN PROCESS AS A GENERALIZATION OF THE HIGHER-ORDER SQUEEZING

2005 ◽  
Vol 19 (11) ◽  
pp. 1943-1953 ◽  
Author(s):  
DILIP KUMAR GIRI ◽  
P. S. GUPTA
Keyword(s):  
Photon Number ◽  
Equation Of Motion ◽  
Higher Order ◽  
Field Amplitude ◽  
Quantum Mechanical ◽  
Heisenberg Equation ◽  
Raman Process ◽  
Mechanical Approach ◽  
Quantum Mechanical Approach ◽  
Short Time

The concept of nth-order amplitude squeezing is introduced in the fundamental mode in Raman process as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing up to n = 5 are studied. The coupled Heisenberg equation of motion involving real and imaginary parts of the quadrature operators is established. Dependence of squeezing on photon number is also established.

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