Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced nano-electromechanical membrane by evidencing the enhancement of a weak phase modulated signal thanks to the addition of phase noise. Based on a general forced Duffing oscillator model, we demonstrate experimentally and theoretically that phase noise acts multiplicatively inducing important physical consequences. These results may open interesting prospects for phase noise metrology or coherent signal transmission applications in nanomechanical oscillators. Moreover, our approach, due to its general character, may apply to various systems.Stochastic resonance whereby a small signal gets amplified resonantly by application of external noise has been introduced originally in paleoclimatology [1,19] to explain the recurrence of ice ages and has then been observed in many other areas including neurobiology [6,16] [3,33,34,42]. Implementation of stochastic resonances involves generally three ingredients : (i) the existence of metastable states separated by an activation energy, as in excitable or bistable nonlinear systems, (ii) a coherent excitation, whose amplitude is however too weak to induce deterministic hopping between the states, and (iii) stochastic processes inducing random jumps over the potential barrier. In the classical picture of a bistable system, this corresponds to the motion of a fictive particle in a double-well potential periodically modulated in amplitude by the signal and subjected to noise [21]. When an optimal level of noise is reached, the system's response power spectrum displays a peak in the signal to noise ratio, unveiling the stochastic resonance phenomenon. The resonance occurs as a 'bona-fide' resonance in a frequency band around a signal frequency approximately given by the time-matching condition [5,22], i.e. when the potential modulation period is twice the mean residence time of the noise-driven particle. Experimental works on stochastic resonance are almost exclusively using amplitude modulation going along with additive amplitude noise or multiplicative amplitude noise [10,20,37,44,45]. In this case, it corresponds to a pure one dimensional effect. Few studies take advantage of a bidimensional phase space by e.g. using phase modulation and/or phase noise (i.e. phase random fluctuations of input signal) [15,23]. Most of them use amplitude noise to demonstrate amplitude stochastic resonance, or introduce noise in the form of the response of a stochastic oscillator [39]. However in the latter scheme, neither the noise nor the modulation are controlled, thus preventing to unveil the specific roles of phase modulation and phase noise in stochastic resonance.In this Letter, stochastic resonance is implemented in a nonlinear nanomechanical oscillator forced close to its resonant frequency. It enables, in a bidimensionnal phase space, the implementation of phase...

Some predictions of quantum mechanics are in contrast with the macroscopic realm of everyday experience, in particular those originated by the Heisenberg uncertainty principle, encoded in the non-commutativity of some measurable operators. Nonetheless, in the last decade opto-mechanical experiments have actualized macroscopic mechanical oscillators exhibiting such non-classical properties. A key indicator is the asymmetry in the strength of the motional sidebands generated in