Semiclassic Models of the Dissipative Regime of Instability and Superradiation of a Quantum Radiator System

Abstract

The paper discusses the similarity between dissipative generation and superradiance regimes for systems of excited quantum emitters placed in an open cavity. In the case of the existence of a resonator field due to reflections from the ends of the system, a dissipative generation regime is usually realized. In this case, the decrement of oscillations in the waveguide in the absence of radiators turns out to be greater than the increment of the arising instability of the system of radiators placed in the resonator. When describing this mode, the influence of the emitters on each other and the sum of their own fields is neglected. The resonator field forces the oscillators to emit or absorb quanta synchronously with it, depending on the local value of the population inversion. Lasing takes on a weakly oscillatory character due to an asynchronous change in the population inversion of the system of emitting dipoles (nutations), which have a ground and excited energy levels. To describe the process, the equations of the semiclassical theory based on the use of the density matrix are quite sufficient. In the case when there is no resonator or waveguide field, taking into account the eigenfields of the oscillators becomes essential. To simulate the superradiance process, large emitting particles are used, to describe which one should use the equations for the density matrix. It is shown that the interaction of quantum emitters in this case is due to electromagnetic fields under conditions when the overlap of their wave functions is insignificant. Equations are obtained that allow considering the process of interaction of emitters. When the emitters interact, an integral field is formed in the resonator, an increase in the intensity of which leads to synchronization of the emitters. It is shown that the characteristic times of the development of the process, as well as the attainable amplitudes of the excited fields for dissipative regimes of generation and regimes of superradiance of emitters filling an open resonator, are comparable.

Superradiation of Mobile Oscillators

“…It is important to note that at a relatively low density of oscillators, their wave functions do not overlap [15]; therefore, they can affect each other only by their own radiation fields. And here the increments of the processes and the maximum achievable amplitudes of the field of these two regimes practically coincide [16].…”

Including the Own Fields of Quantum Emitters in Describing Generation Regimes

“…Let us show that, on the one hand, it is necessary to take into account the intrinsic field of the emitters, because it qualitatively affects all the characteristics of the mode of oscillation generation. On the other hand, a comparison of the achievable amplitudes of the resonator field and the superradiance field for one system of emitters showed that they are of the same order [6]. This is an additional argument for the need to take into account the eigenfields of the emitters in the resonator.…”

Superradiation of Classical Oscillators at Constant Pumping

“…If this resonator is filled with an active medium, a dissipative waveguide excitation regime is also possible, in which quantum oscillators interact only with the resonator field, and there is no direct interaction between them [10].…”

“…It is important to note that at a relatively low density of oscillators, their wave functions do not overlap. Quantum oscillators at their low density can affect each other only by electromagnetic fields of their own radiation [10].…”

“…A comparison was made of the dissipative mode of field generation in an open system, a resonator, with the superradiance mode in the same resonator uniformly filled with immobile excited classical and quantum oscillators. The analysis showed that the process increments and the maximum achievable field amplitudes of these two regimes practically coincide [10,13]. The behavior of a system of oscillators similar to the case studied earlier [13] was considered, taking into account the possibility of longitudinal motion of oscillators along the resonator due to the action of the Lorentz force [18].…”