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European Quantum Electronics Conference (EQEC)

Quasi-Probability Distribution for Photon Number Operator and Quadrature Operator in Coherent State

Vlasta Peřinová, A. Lukš

Published Jan 1, 1996• 0 citations
Publisher
DOI
10.1109/eqec.1996.561847

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Quasiprobability distributions of the photon number and the momentum-like quadrature appropriate to partial symmetrizations of products of the photon-number and quadrature operators allowing these operators to alternate at most (2r-2) times are good approximations to the Wigner function for these simultaneously considered noncommuting quantities related to the fully symmetric ordering. It is shown that the r-parametrized quasiprobability distributions must take on values at multiples of 1/r. A scheme for simultaneous measurement of the photon number and the momentum-like quadrature is proposed. The r-parametrized quasidistributions can be compared with a joint distribution of the photon number and the momentum-like quadrature measured simultaneously.
In this thesis, we investigate the quantum optical properties of a single cavity mode interacting with an external classical coherent driving field inside a closed cavity, which is coupled to a thermal reservoir via a single-port mirror. We establish a mathematically comprehensive framework utilizing both the Master Equation under the density operator formalism and the Quantum Langevin Equation under the Heisenberg picture. By analyzing the system with an arbitrary ordering of reservoir noise operators, we derive the steady-state P-representation of the quasi-probability distribution. Employing this quasi-probability distribution, we analytically compute the mean photon number, photon number variance, photon number distribution, and the second-order intensity correlation function. Our findings establish that the interaction of the cavity mode with the coherent drive in the presence of thermal fluctuations exhibits strictly super-Poissonian statistics. The mean photon number and photon number variance scale monotonically with both the strength of the external coherent drive and the average thermal photon occupation of the reservoir. Furthermore, we prove that the produced cavity field does not exhibit quadrature squeezing, confirming that the presence of thermal noise effectively destroys quantum squeezing in this configuration. Finally, the input-output is evaluated to verify the preservation of the commutation relations of the formalism output field. Keywords: Quantum Optics, Master Equation, Fokker-Planck, Quantum Langevin Equation, P- function, Photon Statistics, Super-Poissonian, Squeezing.
In this thesis, we investigate the quantum optical properties of a single cavity mode interacting with an external classical coherent driving field inside a closed cavity, which is coupled to a thermal reservoir via a single-port mirror. We establish a mathematically comprehensive framework utilizing both the Master Equation under the density operator formalism and the Quantum Langevin Equation under the Heisenberg picture. By analyzing the system with an arbitrary ordering of reservoir noise operators, we derive the steady-state P-representation of the quasi-probability distribution. Employing this quasi-probability distribution, we analytically compute the mean photon number, photon number variance, photon number distribution, and the second-order intensity correlation function. Our findings establish that the interaction of the cavity mode with the coherent drive in the presence of thermal fluctuations exhibits strictly super-Poissonian statistics. The mean photon number and photon number variance scale monotonically with both the strength of the external coherent drive and the average thermal photon occupation of the reservoir. Furthermore, we prove that the produced cavity field does not exhibit quadrature squeezing, confirming that the presence of thermal noise effectively destroys quantum squeezing in this configuration. Finally, the input-output is evaluated to verify the preservation of the commutation relations of the formalism output field. Keywords: Quantum Optics, Master Equation, Fokker-Planck, Quantum Langevin Equation, P- function, Photon Statistics, Super-Poissonian, Squeezing.