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SUPERRADIATION OF CLASSICAL OSCILLATORS AT CONSTANT PUMPING

Eugen V. Poklonskiy, Stanislav Totkal

Published Nov 10, 2022• 0 citations
Publisher

Abstract

The dependence of the generation efficiency in the superradiance regime of an ensemble of oscillators on the pump energy input rate, as well as on the characteristics of the change in the pump phase, is studied. It is assumed that the pumping phase can vary both in time and in space. The most efficient pumping method remains the mode with slow energy input into the system, in comparison with the characteristic generation time, and the nature of the distribution of the field phase along the system can be either random or with a certain spatial period, but slightly changing with time.

DOI
10.46813/2022-141-136

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The influence of noise on field generation in the superradiant regime, when all oscillators interact with each other, is discussed. The process of phase synchronization of excited oscillators is considered and it is noted that its efficiency is affected by the spread of their amplitudes. External noise leads to phase mismatch and can suppress generation. The behavior of a system of oscillators near the generation threshold is considered. It has been shown that even below the threshold, a small external field can provoke generation up to amplitudes characteristic of processes in the absence of noise.

•Jun 10, 2024•1 citation
The dependence of the generation efficiency in the superradiance regime of an ensemble of oscillators on the pump energy input rate, as well as on the characteristics of the change in the pump phase, is studied. It is assumed that the pumping phase can vary both in time and in space. The most efficient pumping method remains the mode with slow energy input into the system, in comparison with the characteristic generation time, and the nature of the distribution of the field phase along the system can be either random or with a certain spatial period, but slightly changing with time.
The problems of phase synchronization in an ensemble of oscillators or dipoles, and the mechanisms of coherent field generation in superradiance mode, are discussed. It is shown that an increase in the spread of the initial amplitudes of an ensemble of oscillators suppresses their phase synchronization and reduces the efficiency of field generation. The influence of noise is discussed; it is shown that, below the generation threshold, even an external initiating field cannot synchronize the phases of an ensemble of particles. When the generation threshold is exceeded, the initiating field may not be required. It is shown that the convergence of the oscillator phases with the field phases at the locations of moving oscillators is noticeable only near their exit from the system. At the same time, a complete coincidence of the phases of synchronized oscillators and the field phases in the region of their localization is not observed. Nevertheless, the intensity of the generation field in the superradiance mode significantly exceeds the spontaneous level, which allows us to speak about the signs of induced radiation. The features of the development of the quantum process of superradiance of an ensemble of dipoles are discussed, and a system of equations for its description is given. The features of the quantum analog of superradiance are qualitatively modeled, and the role of the Rabi frequency determining the dynamics of the population inversion is noted. The nutation of the population inversion in the region occupied by the field affect the field intensity not only in this local zone, but also in subsequent regions of the active zone. This explains the unusual nature of the generation development: the field growth in a certain region of the active zone first stabilizes and then decreases significantly. This decrease in intensity also occurs in the direction of radiation in the peripheral regions of the active zone, despite the large energy reserve in them in the form of unperturbed population inversion.
The paper discusses three different modes of electromagnetic field generation by an ensemble of oscillators placed at the radiation wavelength in the one-dimensional case. The excitation of the resonator field is considered, which, as a rule, is determined by the geometry of the system, with and without taking into account the eigenfields of the emitters. The superradiance regime of the same ensemble of oscillators is also analyzed. In fact, superradiance is formed due to the emitters' own fields even in the absence of a resonator. It is noted that the maximum achievable amplitudes of induced fields both in the superradiance regime and in the regime of excitation of the resonator field are comparable. This makes us think about the role of the self-fields of emitters in electronic devices. It is shown that in describing the resonator excitation mode, in addition to the resonator field, it is also necessary to take into account the sum of the natural fields of the emitters in the active zone. Synchronization of emitters leads not only to an increase in the resonator field, but also, as in the superradiance regime, it significantly increases the amplitude of the sum of the oscillator fields. It is shown that in the practically interesting case of open systems (dissipative generation modes), taking into account the eigenfields of the emitters significantly reduces the characteristic time for the development of the generation process and increases the maximum achievable oscillation amplitude. This account also changes the conditions for achieving the maximum energy flow from the system. This can change the operating point of the generation process, which is determined by the requirement for the maximum rate of energy output from the system.
The superradiant response of a collection of three-level atoms to a train of pump pulses has been investigated numerically. It is assumed that the size of the system is small enough that propagation may be neglected and that the pump is resonant. The atoms are considered to be homogeneously broadened, and all relaxation rates are taken to be equal. The period of the pump pulse train is of the order of the atomic relaxation time, and the width of individual pulses is <4% of the period. Coherence remaining from previous pulses results in qualitative changes in the superradiant pulse train as the pump intensity is increased. Three cases of increasing complexity have been studied: square pump pulses, nondegenerate energy levels; mode-locked pulses, non-degenerate levels; and mode-locked pulses, degenerate levels. The sequence of behavior patterns is somewhat different for different cases. Features of the superradiant output common to the three cases are inversion of the electric field, alternation of positive and negative pulses, and recovery of pulses of one sign after more complicated behavior such as period-doubling, chaos, or intermittency. The effects of varying pump period or pulse shape are found to be less straightforward than that of varying pump intensity. The feasibility of experimental observation is discussed.
Abstract In this work we consider the dynamics of an ensemble of two-level atoms that interact with finite-width resonator mode. The superradiant burst occurs under a wide range of parameters in such a system. However, if the initial phase distribution of dipole moments of N two-level atoms is random, not all atoms take part in the superradiant process, but only the part of them that results in the intensity of supperradiance I ∼ N α , where α < 2 . In this paper we investigate the dependence of the parameter α on the resonator mode decay rate. It is shown that there is a critical value of resonator mode decay rate that divides two different regimes of superradiance. If the decay rate is lower than the critical rate, superradiance demonstrates a multi-peak character and the number of dipoles forming superradiant burst increases while α grows from 1 to 2. When the decay rate is larger than the critical value there is a single-peak superradiant regime. The delay time dependence on N changes from power to logarithmic law at the critical decay rate. The existence of the optimal value of resonator decay rate can be used for superradiance enhancement by a resonator with finite losses.
The paper presents the transition to the regime of induced radiation of a system of oscillators in the classical and the quantum cases. This transition occurs due to synchronization by the integral field of the phases of a small part of oscillator-emitters. In the quantum analogue of this model, it is shown that the formation of an induced (and, therefore, coherent, as noted by Ch. Towns) pulse of the field is due to the interference of nutation of population inversion in different regions of the system of oscillators. The law of spatial variation of the field intensity is deter-mined by the dispersion characteristics of the system and the level of absorption or output of the radiation energy. Only a small fraction of oscillators provide induced radiation: 8% in the classical case and half as much in the case of a quantum system, where a change in the sign of population inversion in the regions of the highest field values significantly affects the limitation of the radiation intensity.
The influence of noise on field generation in the superradiant regime, when all oscillators interact with each other, is discussed. The process of phase synchronization of excited oscillators is considered and it is noted that its efficiency is affected by the spread of their amplitudes. External noise leads to phase mismatch and can suppress generation. The behavior of a system of oscillators near the generation threshold is considered. It has been shown that even below the threshold, a small external field can provoke generation up to amplitudes characteristic of processes in the absence of noise.