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Journal of Experimental and Theoretical Physics

Classical analog of superradiance in a system of interacting nonlinear oscillators

Iu. A. Il'Inskii, N. S. Maslova

Published Jan 1, 1988• 4 citations
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Journal of the Physical Society of Japan•Feb 7, 2022•1 citation
We suggest a mechanism by which a superradiant burst emerges from a subwavelength array of nonlinear classical emitters that are not initially synchronized. The emitters interact via the field of their common radiative response. We show that only if the distribution of initial phases is not uniform does a non-zero field of radiative response arise, leading to a superradiant burst. Although this field cannot synchronize the emitters, it engenders long period envelopes for their fast oscillations. Constructive interference in the envelopes of several emitters creates a large fluctuation in dipole moments that results in a superradiant pulse. The intensity of this pulse is proportional to the square of the number of emitters participating in the fluctuation.
The two-level quantum model proposed by Preparata, according to which the interaction of a material system with a electromagnetic field can cause the loss of stability of the lower level, is examined. As a result of this instability, the role of the ground state is played by a periodic process generating superradiance (in contrast to laser radiation induced by overpopulation of the upper level). A classical analogue of a super-radiant quantum transition, a system of van der Pol-Duffing oscillators (generators) weakly coupled via a linear oscillator, is for the first time described. Such an analogue is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. It is shown that a necessary condition for the transition to intense energy exchange in the classical system is the instability of one of the nonlinear normal modes, similar to how the condition for a superradiant transition to occur is the instability of the ground state of a two-level quantum system coupled with a resonant electromagnetic field.
Synchronization phenomena in multiple polarizations through quantum effects of photon fields have been observed as superradiance. These phenomena are often observed in macroscopic and classical systems. In contrast, superradiance is cooperative spontaneous emission, that is, a synchronization phenomenon in microscopic and quantum systems. In this study, we consider two emitters in a free photon field and investigate their exact phase dynamics. By analogy with the Kuramoto model, we illustrate clearly that the interaction of synchronization in superradiance originates from spontaneous emission owing to the quantum effects of photon fields. In contrast to superradiance in-phase, subradiance in antiphase is also possible. We illustrate the parameter diagram that determines whether in-phase or antiphase oscillation occurs. In addition, we find that a temporal transition occurs from the in-phase to antiphase synchronization owing to the energy dissipation. The results of this study will stimulate further research on synchronization phenomena in microscopic and quantum systems.