Search arXivSearch

arXiv · 1704.01821

Frequency transitions in phononic four-wave mixing

Abstract

This work builds upon the recent demonstration of a phononic four-wave mixing (FWM) pathway mediated by parametric resonance. In such a process, drive tones f_d1 and f_d2 associated with a specific phonon mode interact such that one of the drive tones also parametrically excites a second mode at a sub-harmonic frequency and such interactions result in a frequency comb f_d1/2 +/- n(f_d1-f_d2 ). However, the specific behaviour associated with the case where both drive tones can independently excite the sub-harmonic phonon mode has not been studied or previously described. While it may be possible to expect the merger of two frequency combs f_d1/2 +/- n(f_d1-f_d2 ) and f_d2/2 +/- n(f_d1-f_d2 ), this paper indicates that only one of these mechanisms is selected and also shows an interesting transition linked to this process. Such frequency transitions from f_d1/2 +/- n(f_d1-f_d2 ) to f_d2/2 +/- n(f_d1-f_d2 ) holds potential promise for computing applications.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Adarsh Ganesan, Cuong Do, Ashwin Seshia. 2017-04-06. Frequency transitions in phononic four-wave mixing. https://doi.org/10.1063/1.4985266

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Routes to chaos in a mass-conserving two-species reaction-diffusion model

Mass-conserving reaction-diffusion systems with two species correspond to a seemingly simple case where pattern formation occurs under the influence of a conservation law. Here, we first revisit their linear stability behavior and point out that generically two instabilities can occur: a stationary large-scale mass-conserving (Cahn-Hilliard) instability and an instability that combines features of a stationary large-scale non-mass-conserving (Allen-Cahn) instability and a oscillatory large-scale mass-conserving (conserved-Hopf) instability. We term it an Allen-Cahn-Hopf instability. Second, we investigate the nonlinear dynamics for a specific model related to the formation of cell polarization where only a Cahn-Hilliard instability can occur, i.e., all primary bifurcations are stationary. We analyze how secondary and further bifurcations subsequently give rise to various oscillatory states. The emerging rich spectrum of spatiotemporal behavior includes several period-doubling cascades related to different forms of spatial and temporal symmetry breaking. Beside regular states, three types of low-dimensional spatiotemporal chaos occur and involve transitions like fusion and an outer crises. Our results demonstrate the importance of nonlinear interactions in the dynamics of mass-conserving reaction-diffusion systems, and show that even a simple two-species system with primary bifurcations of Cahn-Hilliard type can show complex spatiotemporal behavior.

nlin.PS

Duck hunting with quantum mechanics

We bridge two sides of singular perturbation theory: the classical theory of slow-fast systems and the semi-classical approach to quantum mechanical systems. For a specific but physically important class of dynamical systems, we show that purely classical and exotic objects, so-called canard solutions, are shadows of instantons in the corresponding quantum system. We demonstrate that canard solutions exist in a domain of parameter space whose boundaries are determined by an instanton action. We illustrate our statements analytically for the relevant example, the overdamped Josephson junction, and confirm them numerically. For the Josephson junction, the canard window is the exponentially narrow gap between consecutive Shapiro steps.

nlin.PS