Floquet Control of Optomechanical Bistability in Multimode Systems.

Cavity optomechanical systems make possible the fine manipulation of mechanical degrees of freedom with light, adding functionality and having broad appeal in photonic technologies. We show that distinct mechanical modes can be exploited with a temporally modulated Floquet drive to steer between distinct steady states induced by changes of cavity radiation pressure. We investigate the additional influence of the thermo-optic nonlinearity on these dynamics and find that it can suppress or amplify the control mechanism in contrast to its often performance-limiting character. Our results provide new techniques for the characterization of thermal properties of optomechanical systems and their control, sensing and computational applications.

Floquet Phonon Lasing in Multimode Optomechanical Systems.

Dynamical radiation pressure effects in cavity optomechanical systems give rise to self-sustained oscillations or 'phonon lasing' behavior, producing stable oscillators up to GHz frequencies in nanoscale devices. Like in photonic lasers, phonon lasing normally occurs in a single mechanical mode. We show here that mode-locked, multimode phonon lasing can be established in a multimode optomechanical system through Floquet dynamics induced by a temporally modulated laser drive. We demonstrate this concept in a suitably engineered silicon photonic nanocavity coupled to multiple GHz-frequency mechanical modes. We find that the long-term frequency stability is significantly improved in the multimode lasing state as a result of the mode locking. These results provide a path toward highly stable ultracompact oscillators, pulsed phonon lasing, coherent waveform synthesis, and emergent many-mode phenomena in oscillator arrays.

Prime number decomposition using the Talbot effect.

We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums. The latter are a mathematical tool from number theory used to analyze the properties of prime numbers as well as to decompose composite numbers into their prime factors. We employ the well-established connection between the Talbot effect and Gauss sums to implement prime number decompositions with a novel approach, making use of the longitudinal intensity profile of the Talbot carpet. The new algorithm is experimentally verified and the limits of the approach are discussed.