The problem of the global stability of steady states in optical bistability is considered with emphasis toward the distinction between quantum switching (characterized by a classical diffusive process) and quantum tunneling (characterized by a nonclassical process with a singular and nonpositive Glauber-Sudarshan distribution). Relative to treatments of quantum switching in optical bistability for which nonpositive definite diffusion is excluded, we address the issue of global stability when the atom-field interaction is purely radiative and nonclassical processes (such as squeezing and antibunching) are involved. In the 1-D approximation, we point out certain anomalous features in the eigenvalue structure of the switching problem associated with a change in sign of the diffusion coefficient in the Glauber-Sudarshan representation. To substantiate the validity of the 1-D approximation, we explore the topology of the 2-D generalized potential. Finally, we compare our result with those previously obtained to emphasize in qualitative terms the distinction between switching and tunneling for bistable optical systems. Our analysis is motivated by an attempt to identify explicit experimental signatures of quantum tunneling.
The problem of the global stability of steady states in optical bistability is considered with emphasis toward the distinction between quantum switching (characterized by a classical diffusive process) and quantum tunneling (characterized by a nonclassical process with a singular and nonpositive Glauber-Sudarshan distribution). Relative to treatments of quantum switching in optical bistability for which nonpositive definite diffusion is excluded, we address the issue of global stability when the atom-field interaction is purely radiative and nonclassical processes (such as squeezing and antibunching) are involved. In the 1-D approximation, we point out certain anomalous features in the eigenvalue structure of the switching problem associated with a change in sign of the diffusion coefficient in the Glauber-Sudarshan representation. To substantiate the validity of the 1-D approximation, we explore the topology of the 2-D generalized potential. Finally, we compare our result with those previously obtained to emphasize in qualitative terms the distinction between switching and tunneling for bistable optical systems. Our analysis is motivated by an attempt to identify explicit experimental signatures of quantum tunneling.
We specialize the quantum-statistical theory of optical bistability developed in "Optical Bistability. II" to a low-Q cavity. From a linearized Fokker-Planck equation derived in the positive P representation, the steady-state correlation matrix and spectrum of fluctuations are calculated. Expressions which normally assume a positive-definite diffusion matrix are shown to be valid for nonpositive-definite diffusion. For absorptive bistability we find agreement with results derived previously by quite different methods. More generally we extend previously published results by including atomic and cavity detunings. We compare the transmitted spectrum for dispersive bistability with that for absorptive bistability, and photon antibunching in dispersive bistability is discussed.
The topic of this thesis is a theoretical study of nonequilibrium transitions and quantum statistical properties of nonlinear quantum optical systems driven by an external radiation source. In certain limiting cases, a comparison is made between these transitions and the phase transitions found in equilibrium physical systems. In chapters one and two, the mathematical tools are introduced. In operator terms, the time development is described by a Markovian master equation in the interaction picture. This is equivalent to a corresponding time development equation or Fokker-Planck equation in a vector space of c-numbers. In order to deal with the type of Fokker-Planck equation that results, we introduce a quantum classical correspondence resulting in a distribution function over a complex phase-space, which is a generalisation of the Glauber-Sudarshan P-function. In chapter three this is applied to a model of a coherently driven mode with nonlinear dispersion and absorption. We find in the limit of zero temperature, that the spectrum is symmetric relative to the input frequency, and an exact solution is obtained for the distribution function. For a detuned driving field and nonlinear dispersion, optical bistability can occur. In chapter four a model of sub/second harmonic generation is introduced. This has several non-equilibrium transitions, including dispersive optical bistability, and bistable behaviour with coherent phase-locked input to both modes. Exact solutions occur in the limit of zero temperature and adiabatic elimination of one mode. In both chapters three and four, steady-state photon anti-bunching occurs with an absorptive nonlinearity. In chapter five we include interactions between the radiation mode and a fluorescent atomic system. In this case different behaviour occurs depending on the relative decay rates of the individual atoms and of the radiation mode. In the case of a high-Q interferometer, the atomic variables can be adiabatically eliminated. Both dispersive and absorptive bistability can occur. We show by analytic and numerical calculations (in the case of inhomogeneous broadening) that dispersive operation has advantages in requiring a lower atomic density and input field to observe bistability. When the input field has Gaussian (rather than coherent) photon statistics, there is no bistability, but enhanced photon bunching occurs. Finally, there is a different type of behaviour when the field mode decays rapidly and can be adiabatically eliminated. Within the cooperation lifetime the system can be described by a J²-invariant Hamiltonian, giving the special case of only collective damping. The result is a new type of critical point transition in the thermodynamic limit, with the appearance of a family of solutions like Lotka-Volterra cycles for a coherent driving field above threshold.
While the problem of photon antibunching in optical bistability has been the subject of numerous theoretical investigations, there appears to be no general result in the literature that includes a complete specification of the dependence of antibunching on the system parameters. Motivated by the importance of such a result to experimental observation of this effect, we present a treatment that includes the parametric dependences on cavity and atomic detunings, cooperativity parameter, nonradiative (collisional) damping, and the ratio of cavity and atomic damping rates. We also attempt to analyze the contribution of fourth-order correlations of the fluctuating fields, which have been neglected in previous treatments. Although the antibunching initially increases with decreasing system size due to the approximate scaling of quantum fluctuations as the inverse of the saturation photon number ns, higher-order fluctuations begin playing an increasingly important role at values of ns ⪝ 1. We show that the linearized theory itself does not necessarily break down for arbitrarily small values of ns (as previously suggested), but that photon antibunching is lost in this limit, thus placing restrictions on the design of an experiment.
After a brief review of some known steady state properties of an absorptive bistable system, we discuss in some details new aspects of the transient response that follows a sudden perturbation from steady state. The evolution of the perturbed bistable system towards its new steady state consists of two generally distinct phases: one is the local relaxation within each well of the bimodal potential, the second is the tunneling through the local maximum that separates the metastable and stable steady states. We give an analytic description of both phases of the evolution, and give explicit formulas for the local and global relaxation rates.
In this paper, optical bistability in hybrid optomechanical systems consisting of two cavities (optomechanical and conventional) coupled to each other, which contain quantum dot molecules (QDMs), is investigated and compared. For this purpose, two different configurations are studied: in the first configuration, the quantum dot molecules (QDMs) are inside the optomechanical cavity, and in the second configuration, the quantum dot molecules are inside the conventional cavity. To calculate the dynamics of the system operators, the Heisenberg-Langevin approach is used under the mean field approximation. To achieve the phenomenon of optical bistability, which is used in optical switches and optical memories, the dynamic equations of the system are solved in a steady state. The effect of the system's physical parameters, including the detuning, the number of quantum dot molecules, and the tunneling intensity of the external field, on the phenomenon of optical bistability is studied. In addition, the switching threshold and the width of the optical bistability region in two different configurations are compared. Considering that the phenomenon of optical bistability can have potential applications in all-optical switches, optical transistors, quantum computing, and quantum communication, the obtained results can be useful for the mentioned applications and system optimization.