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arXiv:1910.02553 · Physical Review A

Nonlinear optical response of a two-dimensional quantum-dot supercrystal: Emerging multistability, periodic and aperiodic self-oscillations, chaos, and transient chaos

Igor Viktorovich Ryzhov, R. F. Malikov, A. V. Malyshev, Victor A Malyshev

Published Sep 16, 2019• 21 citations
arXivHTMLPDF

Abstract

We conduct a theoretical study of the nonlinear optical response of a two-dimensional semiconductor quantum-dot supercrystal subjected to a quasiresonant continuous-wave excitation. A constituent quantum dot is modeled as a three-level ladderlike system (comprising the ground, the one-exciton, and the biexction states). To study the stationary response of the supercrystal, we propose an exact linear parametric method of solving the nonlinear steady-state problem, while to address the supercrystal optical dynamics qualitatively, we put forward a method to calculate the bifurcation diagram of the system. Analyzing the dynamics, we demonstrate that the supercrystal can exhibit multistability, periodic and aperiodic self-oscillations, and chaotic behavior, depending on parameters of the supercrystal and excitation conditions. The effects originate from the interplay of the intrinsic nonlinearity of quantum dots and the retarded interdot dipole-dipole interaction. The latter provides a positive feedback which results in the exotic supercrystal optical dynamics. These peculiarities of the supercrystal optical response open up a possibility for all-optical applications and devices. In particular, an all-optical switch, a tunable generator of THz pulses (in self-oscillating regime), a noise generator (in chaotic regime), and a tunable bistable mirror can be designed.

DOI
10.1103/physreva.100.033820

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We conduct a theoretical study of the nonlinear optical response of a two-dimensional semiconductor quantum-dot supercrystal subjected to a quasiresonant continuous-wave excitation. A constituent quantum dot is modeled as a three-level ladderlike system (comprising the ground, the one-exciton, and the biexction states). To study the stationary response of the supercrystal, we propose an exact linear parametric method of solving the nonlinear steady-state problem, while to address the supercrystal optical dynamics qualitatively, we put forward a method to calculate the bifurcation diagram of the system. Analyzing the dynamics, we demonstrate that the supercrystal can exhibit multistability, periodic and aperiodic self-oscillations, and chaotic behavior, depending on parameters of the supercrystal and excitation conditions. The effects originate from the interplay of the intrinsic nonlinearity of quantum dots and the retarded interdot dipole-dipole interaction. The latter provides a positive feedback which results in the exotic supercrystal optical dynamics. These peculiarities of the supercrystal optical response open up a possibility for all-optical applications and devices. In particular, an all-optical switch, a tunable generator of THz pulses (in self-oscillating regime), a noise generator (in chaotic regime), and a tunable bistable mirror can be designed.
Abstract The optical response of a two-dimensional supercrystal (monolayer) of quantum emitters with a doublet in the excited state to the action of a continuous external field was theoretically studied, considering the dephasing of the electronic states of the system. The secondary field acting on the V-emitter from other V-emitters of the system forms their nonlinearity and provides internal positive feedback, which leads to bistability and periodic and aperiodic self-oscillations, including chaotic behavior. In the presence of dephasing, the multistability of the optical response is preserved. Phase relaxation leads to a change in the scenario of the system dynamics from chaos to periodic oscillations of the field amplitude, i.e., to a chaos–limit cycle bifurcation and to a decrease in the reflectivity of the monolayer in linear and nonlinear modes.
A theoretical study of the optical response of a two-dimensional supercrystal (monolayer) of quantum emitters with a doublet in the excited state to the action of a continuous external field has been carried out, considering the dephasing of the electronic states of the system. The secondary field acting on the V-emitter from other V-emitters of the system forms their nonlinearity and provides internal positive feedback, which leads to bistability, periodic and aperiodic auto-oscillations and including chaotic behavior. In the presence of dephasing, the multistability of the optical response is preserved. Phase relaxation leads to a change in the scenario of the system dynamics from chaos to periodic oscillations of the field amplitude, i. e., to a “chaos — limit cycle” bifurcation, a decrease in the reflectivity of the monolayer in linear and nonlinear modes.
Abstract We conduct a theoretical study of the nonlinear optical dynamics of a 2D super-crystal comprising regularly spaced identical semiconductor quantum dots (SQDs), subjected to a resonant continuous wave excitation. A single SQD is considered as three-level ladder-like systems involving the ground, one-exciton and bi-exction states. We show that the super - crystal reveals a rich nonlinear dynamics, exhibiting multistability, self-oscillations and chaos. The behaviour is driven by the retarded SQD-SQD interactions and bi-exciton binding energy.
We conduct a theoretical study of the nonlinear optical dynamics of a 2D super-crystal comprising regularly spaced identical semiconductor quantum dots (SQDs), subjected to a resonant continuous wave excitation. A single SQD is considered as three-level ladder-like systems involving the ground, one-exciton and bi-exction states. We show that the super-crystal reveals a rich nonlinear dynamics, exhibiting multistability, self-oscillations and chaos. The behaviour is driven by the retarded SQD-SQD interactions and bi-exciton binding energy.
Taking into account the foundations of the generalized two-level scheme, an analytical solution to the problem of the evolution of superradiance in a quasi-two-dimensional supercrystal formed by quantum dots is obtained under homogeneous lasing field assumption in the resonant medium of the quasicrystal.The calculation was performed for the physical parameters of a semiconductor structure with quantum-well effects in the presence of resonant nonlinearity and intraband relaxation.We use the generalized two-level scheme, which allows us to take into account the self-modulating spectral broadening of the light field due to the absorption of radiation in quasi-resonant transitions in the quantum mechanical material equations, which are solved together with the field coupling equations.A relation is formulated that is analogous to the law of conservation of the polar angle of the Bloch vector for the more general case of interaction under consideration, in which, along with the phase nonlinearity of the response, the spread rate of active dipoles within the spectral line width is taken into account (i.e., the finiteness of the phase relaxation time of elementary emitters).The use of the Bloch vector formalism in this case makes it possible to obtain an analytical solution of the original modification of the nonlinear system of equations for the semiconductor supercrystals response variables and to calculate the shape of the superradiance pulses.The calculations predict the pronounced asymmetry of the pulses emitted by the semiconductor supercrystals.The calculated estimates of the time dynamics of the superradiance process, taking into account the nonlinearities typical for the resonant response, can be used in the development of methods for obtaining and profiling optical pulses in the sub-picosecond range of durations in modern compact nanophotonics devices.