Quantum Optics Seminar by Eva M. Weig

Nonlinear dynamics of high Q nanomechanical resonators

Doubly-clamped pre-stressed silicon nitride string resonators room temperature quality factors of several 100,000 in the 10 MHz eigenfrequency range. Dielectrically controlled silicon nitride strings are an ideal testbed to explore a variety of dynamical phenomena ranging from multimode coupling to coherent control. Here I will focus on the nonlinear dynamics of a driven string which is described in the framework of the well-established Duffing model. As a result of the large mechanical quality factor of the nonlinear string near-resonant driving results in classical squeezing of its thermal fluctuations as theoretically predicted [1]. The power spectrum of the driven resonator reveals two well-resolved satellite peaks, the areas of which encode the squeezing ratio [2]. Further insights into noise-induced nonlinear dynamics include nonlinear switching between the two stable solutions of the Duffing resonator. Under stronger near-resonant driving, negative friction is observed which leads to self-sustained oscillation of the string in its rotating frame, and to the subsequent formation of a nanomechanical frequency comb, as recently theoretically predicted [3,4]


[1]                      M. I. Dykman & M. A. Krivoglaz, Theory of fluctuational transitions
                           between stable states of a non linear oscillator.
                           Sov. Phys. JETP 50, 30 (1979)

[2]                      J. Huber et al., Detecting squeezing from the fluctuation spectrum
                          of a driven nanomechanical mode 

[3]                      M. I. Dykman et al., Resonantly induced friction and frequency combs
                           in driven nanomechanical systems
                           Phys. Rev. Lett. 122, 254301 (2019)

[4]                      J. Huber et al., Frequency comb from a single driven nanomechanical
                          mode, (in preparation)