Non-linear Frequency Transduction of Nano-mechanical Brownian Motion

We report on experiments addressing the non-linear interaction between a nano-mechanical mode and position fluctuations. The Duffing non-linearity transduces the Brownian motion of the mode, and of other non-linearly coupled ones, into frequency noise. This mechanism, ubiquitous to all weakly-nonlinear resonators thermalized to a bath, results in a phase diffusion process altering the motion: two limit behaviors appear, analogous to motional narrowing and inhomogeneous broadening in NMR. Their crossover is found to depend non-trivially on the ratio of the frequency noise correlation time to its magnitude. Our measurements obtained over an unprecedented range covering the two limits match the theory of Y. Zhang and M. I. Dykman, Phys. Rev. B 92, 165419 (2015), with no free parameters. We finally discuss the fundamental bound on frequency resolution set by this mechanism, which is not marginal for bottom-up nanostructures.Comment: Article plus Supplementary Materia

Electric circuit model of microwave optomechanics

We report on the generic classical electric circuit modeling that describes standard single-tone microwave optomechanics. Based on a parallel RLC circuit in which a mechanical oscillator acts as a movable capacitor, derivations of analytical expressions are presented, including key features such as the back-action force, the input-output expressions, and the spectral densities associated, all in the classical regime. These expressions coincide with the standard quantum treatment performed in optomechanics when the occupation number of both cavity and mechanical oscillator are large. Besides, the derived analytics transposes optical elements and properties into electronics terms, which is mandatory for quantitative measurement and design purposes. Finally, the direct comparison between the standard quantum treatment and the classical model addresses the bounds between quantum and classical regimes, highlighting the features which are truly quantum, and those which are not

Modal Decomposition in Goalpost Micro/nano Electro-mechanical Devices

We have studied the first three symmetric out-of-plane flexural resonance modes of a goalpost silicon micro-mechanical device. Measurements have been performed at 4.2K in vacuum, demonstrating high Qs and good linear properties. Numerical simulations have been realized to fit the resonance frequencies and produce the mode shapes. These mode shapes are complex, since they involve distortions of two coupled orthogonal bars. Nonetheless, analytic expressions have been developed to reproduce these numerical results, with no free parameters. Owing to their generality they are extremely helpful, in particular to identify the parameters which may limit the performances of the device. The overall agreement is very good, and has been verified on our nano-mechanical version of the device.Comment: Journal of Low Temperature Physics (2013

Evidence for magnon BEC in superfluid 3He-A

International audienceThe phenomenon of phase-coherent precession of magnetization in superfluid 3He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different states of coherent precession have been observed in 3He-B: homogeneously precessing domain (HPD); persistent signal formed byQ-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of the coherent precession in compressed aerogel. Here we demonstrate the evidence of magnons Bose-Einstein condensation in 3He-A in a compressed aerogel

Fully suspended nano-beams for quantum fluids

Non-invasive probes are keystones of fundamental research. Their size, and maneuverability (in terms of e.g. speed, dissipated power) define their applicability range for a specific use. As such, solid state physics possesses e.g. Atomic Force Microscopy (AFM), Scanning Tunneling Microscopy (STM), or Scanning SQUID Microscopy. In comparison, quantum fluids (superfluid $^3$He, $^4$He) are still lacking probes able to sense them (in a fully controllable manner) down to their smallest relevant lengthscales, namely the coherence length $\xi_0$. In this work we report on the fabrication and cryogenic characterization of fully suspended (hanging over an open window, with no substrate underneath) Si$_3$N$_4$ nano-beams, of width down to 50 nm and quality factor up to $10^5$. As a benchmark experiment we used them to investigate the Knudsen boundary layer of a rarefied gas: $^4$He at very low pressures. The absence of the rarefaction effect due to the nearby chip surface discussed in Gazizulin et al. [1] is attested, while we report on the effect of the probe size itself

Finite size effects in ferromagnetic 3He nano-clusters

International audience3He adsorbed on Graphite enables to create model 2D ferromagnetic Heisenberg systems. The exchange énergies are of the order of 2mK, typical sizes on the order of a thousand spins. By adding 4He (which is non magnetic) to the system, one can tune the effective size of one ferromagnetic domain. Up to now, the theoretical tools available did not allow a quantitative understanding of themagnetism of these clusters. For the first time, "engineered" ferromagnetic nano-clusters are compared to accurate theoretical models in order to understand the finite size effects. The experimental magnetization of a cluster of about 16 spins is compared to exact diagonalization and Monte-Carlo simulations based on the Heisenberg Hamiltonian