We consider the dynamics of a single-mode cavity field damped via its coupling to a broad-band squeezed heat bath. The density operator equation of motion is transformed to a Fokker-Planck equation (FPE) for the s-parametrized quasiprobability distributions. We show that the field amplitude, intensity, spectrum and quadrature variances can be evaluated easily using the differential equations derived directly from the FPE. The FPE is then solved subject to different initial conditions, and the solution is used to investigate squeezing and field state evolution. The time behaviour of the purity Tr ([pcirc] 2) is treated in detail both analytically and numerically. The general steady-state solution is found in the operator form. We also show that, when certain conditions are met, dissipation without change in fluctuation properties is possible. A comparison is made with the cases of single-atom damping and off-resonance field damping.
We consider the dynamics of a single-mode cavity field damped via its coupling to a broad-band squeezed heat bath. The density operator equation of motion is transformed to a Fokker-Planck equation (FPE) for the s-parametrized quasiprobability distributions. We show that the field amplitude, intensity, spectrum and quadrature variances can be evaluated easily using the differential equations derived directly from the FPE. The FPE is then solved subject to different initial conditions, and the solution is used to investigate squeezing and field state evolution. The time behaviour of the purity Tr ([pcirc] 2) is treated in detail both analytically and numerically. The general steady-state solution is found in the operator form. We also show that, when certain conditions are met, dissipation without change in fluctuation properties is possible. A comparison is made with the cases of single-atom damping and off-resonance field damping.
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.
A single two-level atom in a coherently driven cavity and damped by a broadband squeezed vacuum centered about the atomic transition frequency is studied. A second-order Fokker-Planck equation for this system is obtained without using system size expansion. Effects of detunings and cavity decays are also incorporated in the Fokker-Planck equation. This equation is used to study atomic inversion, fluorescent spectrum, and the intensity correlations of the transmitted and fluorescent photons in the bad-cavity limit. Several interesting effects in the atomic inversion, spectrum, and intensity correlations due to the squeezed vacuum are presented. These results are also compared with an atom that is damped by a thermal reservoir.
Abstract In this paper we consider a system consisting of a number of two-level atoms in a Bose–Einstein condensate (BEC) and a single-mode quantized field, which interact with each other in the presence of two different damping sources, i.e. cavity and atomic reservoirs. The reservoirs which we consider here are thermal and squeezed vacuum ones corresponding to field and atom modes. Strictly speaking, by considering both types of reservoirs for each of the atom and field modes, we investigate the quantum dynamics of the interacting bosons in the system. Then, via solving the quantum Langevin equations for such a dissipative BEC system, we obtain analytical expressions for the time dependence of atomic population inversion, mean atom as well as photon number and quadrature squeezing in the field and atom modes. Our investigations demonstrate that for modeling the real physical systems, considering the dissipation effects is essential. Also, numerical calculations which are presented show that the atomic population inversion, the mean number of atoms in the BEC and the photons in the cavity possess damped oscillatory behavior due to the presence of reservoirs. In addition, non-classical squeezing effects in the field quadrature can be observed especially when squeezed vacuum reservoirs are taken into account. As an outstanding property of this model, we may refer to the fact that one can extract the atom–field coupling constant from the frequency of oscillations in the mentioned quantities such as atomic population inversion.
We consider a single-mode radiation field initially in a displaced squeezed thermal state. The weak interaction of such a field with a heat bath of arbitrary temperature is shown to preserve the Gaussian form of the characteristic function. Accordingly, the study of the time development of the density operator reduces to our previous description [P. Marian and T. A. Marian, preceding paper, Phys. Rev. A 47, 4474 (1993)] of the initial quantum state. As examples, photon statistics and squeezing properties of the damped field are analyzed. Based on the close relation between field dissipation and photon detection, we derive simple analytic formulas for the counting distribution and its factorial moments. Nonclassical features of a displaced squeezed thermal state, such as oscillations of the photon-number distribution, survive in the counting process, provided that the quantum efficiency of the detector is high enough.