Nonlinear Dynamics of the Phonon Stimulated Emission in Microwave Solid-State Resonator of the Nonautonomous Phaser Generator

Abstract

The microwave phonon stimulated emission (SE) has been investigated in a solidstate resonator of a non-autonomous acoustic quantum generator (phaser). Branching and long-time refractority (absence of the reaction on the external pulses) for deterministic chaotic and regular processes of SE were observed in the experiments with weak and strong electromagnetic pumping. The clearly depined increase of the number of the independently co-existing SE states as the pumping level rise has been observed both in physical and computer experiments. This confirms the analytical estimations of the branching density in the phase space. The nature of the SE pulses refractority is closely connected with such branching and reflects the crises of strange attractors, i.e. their collisions with unstable periodic components of the higher branches.The stimulated emission (SE) of microwave phonons has been first observed in experiments on quantum hypersound amplification, when in 1960-ies it was reported for dielectric single crystals doped with paramagnetic ions of the iron group [1] - [3]. The hypersound amplification is due to inversed population of the ion spin levels, transitions between which are allowed for the spin-phonon interaction, and is, in fact, an acoustic analog of the linear maser amplification of electromagnetic fields [4], [5].At the same time, the nature of this effect -quantum generation of microwave phonons -has remained not fully understood for a long time. There was some inertia of thinking, with analogies proposed [6] between the photon quantum generator (phaser) and electromagnetic maser generator in the same way as it had been done for amplifiers.Experimental studies of phonon SE in Ni 2+ :Al 2 O 3 and Cr 3+ :Al 2 O 3 crystals ([7] -[10]) have shown that phaser generation mechanism is actually much closer to the processes in optical lasers than those in maser generators. Really, due to very low velocity of hypersound (as compared with the velocity of light) the wavelength of acoustic SE in a microwave solid-state resonator is about 1-3 µm, i.e., it corresponds to the near-infrared range of electromagnetic radiation. The resonator Q-factor CAV

Self-Organized Bottleneck and Coexistence of Incongruous States in a Microwave Phonon Laser (Phaser)

“…Therefore, if the phaser system is finely tuned and the pumping is powerful enough, the transient process is rather fast (τ tran ≈ τ 1 ). This experimental fact agrees with theoretical estimations [23,24] of τ tran made in the framework of the elementary (balance) model of SE [41,42]: τ tran ≈ τ 1 /A P , where A P is the pumping parameter (for our system, A P ≈ 2 [23,24]). In other words, under the conditions specified above, the process of formation of the stationary CS of the phaser power spectra terminates approximately within the same time interval, over which the stationary resonant absorption in a passive (non-inverted) paramagnetic system becomes settled.…”

“…In this work, we use the term "chaotic FS", not specifying the kind of the disorder observed, because it is not still clear, whether this is a multi-dimensional deterministic chaos or some form of a small-scale spin-phonon turbulence. The experimental data presented below allow us to assert only that the dimension of the phase space, which is necessary to describe the observed chaotic FS, should be much higher than that in the case of the ordinarylow-dimension deterministic chaos which was studied in phasers whith periodic pump modulation [23,24,41,42].…”