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Doklady of the National Academy of Sciences of Belarus

Bloch vector formalism in the problem of nonlinear resonant response of a quasi-two-dimensional supercrystal

E. V. Timoshchenko, V. A. Yurevich

Published Dec 31, 2020• 0 citations
Publisher

Abstract

Taking into account the ideas of the generalized two-level scheme, within the framework of the semiclassical approach to the consideration of the resonant interaction of the light field with matter, an analytical solution to the problem of the evolution of superradiance in a quasi-two-dimensional supercrystal formed by quantum dots is obtained. The calculation was carried out for the physical parameters of a semiconductor structure with quantum-well effects in the presence of resonant nonlinearity and intraband relaxation.

DOI
10.29235/1561-8323-2020-64-6-663-669

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Taking into account the ideas of the generalized two-level scheme, within the framework of the semiclassical approach to the consideration of the resonant interaction of the light field with matter, an analytical solution to the problem of the evolution of superradiance in a quasi-two-dimensional supercrystal formed by quantum dots is obtained. The calculation was carried out for the physical parameters of a semiconductor structure with quantum-well effects in the presence of resonant nonlinearity and intraband relaxation.
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.
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.
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.
Several modifications of the Maxwell–Bloch equations are presented for analyzing the emission characteristics of pulsed lasers. The analysis is performed under the condition of coherent interaction between light and a gain medium with resonant phase nonlinearity. For the first time, the interrelated factors of instability of the phase relationship of the light field and the response of the medium, caused by the dipole-dipole interaction and the contribution of quasi-resonant polarization, are taken into account. To describe the superradiance (SR) regime, semi-analytical expressions for the response variables in the Bloch vector formalism are refined. Various approximations of the original model are represented by systems of kinetic equations for the field and response variables of the medium, as well as a nonlinear oscillatory equation for the polar angle of the Bloch vector. Modeling of the coherent SR effect in a resonator showed that the temporal structure of SR is extremely sensitive to the resonant nonlinearity of the material response. It is shown that under nonlinear conditions, the typical nutational intensity structure of synchrotron radiation is transformed into a contrasting quasi-periodic modulation of the trailing edge of the main pulse in the subpicosecond range. A computational analysis of the synchrotron radiation process in a resonator is performed for the parameters of semiconductor quantum dot systems in nanoheterostructures. Such systems are considered promising for use in compact optical electronics and photonics devices.
The problem of the evolution in time of a system of two-level atoms that are coupled through their electromagnetic fields, is studied and solved in the framework of semiclassical radiation theory. The atoms may be in any initial states and the radiation reaction is fully taken into account. Both superradiance and time-dependent frequency shift or chirping effects are found. The assumption that all the atoms see the same field is shown to place severe constraints on the evolution of the system, in the form of constants of the motion. These constraints are most easily pictured in terms of the Bloch-vector representation of the atomic system, and they lead to explicit solutions for the time development of each atom. It is shown that the evolution of the complex system is describable by means of a collective super Bloch vector, whose behavior is similar to the behavior of the Bloch vector for a single isolated atom. The constraints on the motion also imply that the system cannot radiate all its energy coherently; some of it remains trapped, to be dissipated ultimately by incoherent processes. Some curves are presented to illustrate the behavior of the system in special cases.