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QUANTUM TREATMENT OF SELF-ORGANIZATION PHENOMENA OF EXCITONS AND BIEXCITONS

Nellu Ciobanu, Anatol Rotaru, I. I. Gontia, Vasile Tronciu

Published Sep 18, 2019• 0 citations
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Abstract

We present in this paper the quantum treatment of self-organization phenomena of excitons and biexcitons in the geometry of a ring cavity. Applying the adiabatic elimination method of the exciton and biexciton variables, the Fokker-Planck equation for the transmitted field was obtained. The spectrum of transmission and second order correlation function were calculated. Thus, the spectrum of transmission describes a hysteresis cycle character, where a narrow spectral line in the end of cycle can be observed. The phenomena of optical bistability and switchings of excitons and biexcitons are investigated theoretically.

DOI
10.5281/zenodo.3443910

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We present in this paper the quantum treatment of self-organization phenomena of excitons and biexcitons in the geometry of a ring cavity. Applying the adiabatic elimination method of the exciton and biexciton variables, the Fokker-Planck equation for the transmitted field was obtained. The spectrum of transmission and second order correlation function were calculated. Thus, the spectrum of transmission describes a hysteresis cycle character, where a narrow spectral line in the end of cycle can be observed. The phenomena of optical bistability and switchings of excitons and biexcitons are investigated theoretically.
A system of nonlinear differential equations describing the dynamic evolution of coherent excitons, photons, and biexcitons is derived in the geometry of a ring cavity. Nonlinearity is caused by the direct binding of two excitons in a biexciton as a result of their Coulomb interaction, which was first predicted by Ivanov, Keldysh, and Panashchenko. The equation of state of the theory of optical bistability is obtained for the stationary case. The stability of stationary states is studied, and the switching times between the branches of the optical bistability curve are determined. It is shown that the appearance of nonlinear periodic and chaotic self-pulsations with the creation of a system of limit cycles and strange attractors in phase space is possible in the unstable portions of the equation of state. Dynamic optical bistability is studied, and the possibility of experimentally detecting the phenomena studied is discussed.
A quantum treatment of a coherently driven cavity with a medium of two-level atoms is given. The system displays both absorptive and dispersive bistability. Quantum fluctuations are included via a Fokker-Planck equation in a generalized PPP representation, after adiabatic elimination of the atomic variables. The transmitted spectrum and correlation function is calculated in a linearized (Gaussian) approximation. In the limit of large detuning and radiative damping, the quantum fluctuations are identical to those of a simple nonlinear polarizability theory. An analysis is given of the nonclassical statistical properties of the intensity-correlation spectrum.
The theory of dynamic optical bistability and self-pulsations in condensed media is elaborated. The nonlinearity is due to a process in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. A computer experiment is used to study the switching times between the optical bistability branches. The scenario for the transition to the dynamical chaos mode is found. The action of external periodical force upon the system is investigated and the range of amplitude values and frequencies of external harmonic pump were found at which the chaotic regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. Finally, we discuss the possibility of detecting these phenomena in experiments.
The theory of dynamic optical bistability and self-pulsations in condensed media is elaborated. The nonlinearity is due to a process in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. A computer experiment is used to study the switching times between the optical bistability branches. The scenario for the transition to the dynamical chaos mode is found. The action of external periodical force upon the system is investigated and the range of amplitude values and frequencies of external harmonic pump were found at which the chaotic regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. Finally, we discuss the possibility of detecting these phenomena in experiments.
We study a new class of nonlinear cooperative phenomena that occur when light propagates in direct-gap semiconductors. The nonlinearity here is due to a process, first discussed by A. L. Ivanov, L. V. Keldysh, and V. V. Panashchenko, in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. For the geometry of a ring cavity, we derive a system of nonlinear differential equations describing the dynamical evolution of coherent excitons, photons, and biexcitons. For the time-independent case we arrive at the equation of state of optical bistability theory, and this equation is found to differ considerably from the equations of state in the two-level atom model and in the exciton region of the spectrum. We examine the stability of the steady states and determine the switchover times between the optical bistability branches. We also show that in the unstable sections of the equation of state, nonlinear periodic and chaotic self-pulsations may arise, with limit cycles and strange attractors being created in the phase space of the system. The scenario for the transition to the dynamical chaos mode is found. A computer experiment is used to study the dynamic optical bistability. Finally, we discuss the possibility of detecting these phenomena in experiments.