Theory of the excitation of a quantum oscillator by resonant electromagnetic radiation

B. A. Veklenko

Quantum electrodynamics is a very cumbersome theory, and one tries to avoid it in applied problems. Experience shows that the semiclassical theory of radiation, which operates with a nonquantized elec� tromagnetic field, provides, as a rule, required accu� racy of calculations. The authority of the semiclassical theory of radiation has grown greatly, because it describes adequately the operation of quantum devices such as lasers. In this work we present an example that demon� strates the inadequacy of the semiclassical theory of radiation. It is shown that, upon resonance scattering of an electromagnetic field by excited systems, quanti� zation of the electromagnetic field is necessary and the consequences of this operation manifest themselves at the macroscopic level. Suppose that resonance radiation is scattered by a certain system, the initial state of which is described in the interaction representation by the wave function . The total wave function of the electromagnetic field and scattering system after the scattering is denoted by . Expansion of the function in terms of the basis of the wave functions of the scatterer has the form

Volodymyr M. Kuklin, В.Т. Лазурик, Eugen V. Poklonskiy

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.

Valery V. Pavlovskiy, Vladimir N. Gubankov, I. Gundareva

Josephson oscillators attract a considerable interest as parts of superconducting electronic devices. Numerical simulation of Josephson oscillator in resonator was performed at arbitrary coupling. Parametric excitation is indicated by voltage break at dc IV-curve of Josephson oscillator. A numerical procedure was developed for calculation of static characteristics of the oscillator at any coupling with resonator. The influence of thermal fluctuations of normal electron current on parametric excitation was analyzed. The results obtained can be used in development of electronic devices, based on Josephson oscillators in mm- and sub-mm wavelength spectral range of electromagnetic radiation.