A nonlinear dynamics of stimulated phonon emission in a nonautonomous acoustic quantum generator under superlow-frequency-modulated pumping conditions

Abstract

An unusual nonlinear resonance was experimentally observed in a ruby phonon laser (phaser) operating at 9 GHz with an electromagnetic pumping at 23 GHz. The resonance is manifested by very slow cooperative self-detunings in the microwave spectra of stimulated phonon emission when pumping is modulated at a superlow frequency (less than 10 Hz). During the self-detuning cycle new and new narrow phonon modes are sequentially "fired" on one side of the spectrum and approximately the same number of modes are "extinguished" on the other side, up to a complete generation breakdown in a certain final portion of the frequency axis. This is usually followed by a short-time refractority, after which the generation is fired again in the opposite (starting) portion of the frequency axis. The entire process of such cooperative spectral motions is repeated with high degree of regularity. The self-detuning period strongly depends on difference between the modulation frequency and the resonance frequency. This period is incommensurable with period of modulation. It increases to very large values (more than 100 s) when pointed difference is less than 0.05 Hz. The revealed phenomenon is a kind of global spin-phonon self-organization. All microwave modes of phonon laser oscillate with the same period, but with different, strongly determined phase shifts -as in optical lasers with antiphase motions.PACS numbers: 05.65.+b, 42.65.Sf, 43.35.+d Phonon amplification by stimulated emission of radiation was predicted theoretically in [1] and experimentally observed in microwave range by several groups [2] in 1960-1970-th. This phenomenon is very similar to the usual paramagnetic maser gain of electromagnetic field [3,4]. But if the phonon gain is large enough to exceed the phonon losses in the solid-state resonator, the self-excitation of laser-like phonon emission is possible [5,6,7]. The wavelength of generated microwavefrequency phonons in such phonon laser lies usually in optical or near-infrared range (due to very small velocity of sound in crystals, which is about 5 orders less than the light velocity). In this sence microwave phonon laser (phaser) is more close relative of the optical laser, than terahertz phonon laser (saser), having much shorter wavelength (see [8] and references therein).Almost all early experiments with microwave phonon lasers [5,6,7] were carried out in autonomous regime, when the control parameters of the active system remain unchanged during the whole time of measurement. Various regular and chaotic processes of generation of microwave phonons in a multimode nonautonomous phaser was experimentally observed and studied [9] for ω m ≈ ω R ≈ 20-300 Hz, where ω m is the pumping modulation frequency, ω R is the relaxation frequency of a nonequilibrium autonomous acoustic system (ω R depends on pumping level). The existence of a single dominating component exp(iω R t) for the transient processes in the autonomous phonon laser reflects the collective character of a multimode stimulated emission [10] in the quantum ...

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

“…The ideas of quantum electronics have also deeply penetrated into adjacent branches of modern physics, especially into quantum acoustics [4][5][6][7][8][9][10][11][12][13]. A series of new nonlinear phenomena, which arise under the quantum amplification or generation of tera-, hyper-or ultrasonic oscillations in nonequilibrium (inverted) acoustic and nanomechanical dissipative systems of various origins, have been predicted theoretically and discovered experimentally during last years [14][15][16][17][18][19][20]. The researches concerning the conditions, under which the formation of inverted states and the purposeful control over nonlinear processes in such systems (the acoustic analogs of lasers) become possible, are of significant independent interest.…”

“…As has already been emphasized in works [14,15,21,22], if one confines the consideration to the quantum amplification and generation of hypersound, i.e. the acoustic waves within the microwave range of frequencies, the following circumstances invoke the greatest interest.…”

“…This conclusion has already been confirmed experimentally for a paramagnetic phaser with a pink ruby crystal (Cr 3+ : Al 2 O 3 ). In works [14,15,21,22], a new nonlinear resonance (λ-resonance), which is accompanied by a number of interesting dynamical phenomena, has been revealed experimentally in a non-autonomous ruby phaser and studied in details at liquid-helium temperatures and electromagnetic pumping with carrier frequency about 23 GHz. This λ-resonance arises at modulation of pumping (or Zeeman magnetic field) in the range of ultralow frequencies ω m ≈ ω λ , where ω λ /2π ≈ 10 Hz [14,15,21,22].…”

“…In works [14,15,21,22], a new nonlinear resonance (λ-resonance), which is accompanied by a number of interesting dynamical phenomena, has been revealed experimentally in a non-autonomous ruby phaser and studied in details at liquid-helium temperatures and electromagnetic pumping with carrier frequency about 23 GHz. This λ-resonance arises at modulation of pumping (or Zeeman magnetic field) in the range of ultralow frequencies ω m ≈ ω λ , where ω λ /2π ≈ 10 Hz [14,15,21,22]. It is considerably lower than the typical frequencies ω ν of the usual relaxational resonance (νresonance) in the ruby phaser (ω ν /2π ≈ 70-300 Hz), which was observed earlier in works [23,24] (note that ν-resonance in the ruby phaser is an acoustic analog of the well-known laser relaxational resonance).…”

“…In works [14,15,21,22], it has been discovered experimentally that a plenty of coexisting states of the spin-phonon system emerges in the domain of the λ-resonance and the very slow regular transitions, which remind autowave motions, occur between them. The period of the full cycle of such transitions reaches giant values and exceeds 10 3 − 10 4 s at ω m ≈ ω λ [14,15,21,22]. This is several orders of magnitude longer than the period τ m ≡ 2π/ω m of an external force that modulates phaser pumping (or Zeeman magnetic field).…”