Nonlinear nanomechanical resonators for quantum optoelectromechanics

We present a scheme for tuning and controlling nano mechanical resonators by subjecting them to electrostatic gradient fields, provided by nearby tip electrodes. We show that this approach enables access to a novel regime of optomechanics, where the intrinsic nonlinearity of the nanoresonator can be explored. In this regime, one or several laser driven cavity modes coupled to the nanoresonator and suitably adjusted gradient fields allow to control the motional state of the nanoresonator at the single phonon level. Some applications of this platform have been presented previously [New J. Phys. 14, 023042 (2012), Phys. Rev. Lett. 110, 120503 (2013)]. Here, we provide a detailed description of the corresponding setup and its optomechanical coupling mechanisms, together with an in-depth analysis of possible sources of damping or decoherence and a discussion of the readout of the nanoresonator state.Comment: 15 pages, 6 figure

Failure of the Standard Coupled-Channels Method in Describing the Inelastic Reaction Data: On the Use of a New Shape for the Coupling Potential

We present the failure of the standard coupled-channels method in explaining the inelastic scattering together with other observables such as elastic scattering, excitation function and fusion data. We use both microscopic double-folding and phenomenological deep potentials with shallow imaginary components. We argue that the solution of the problems for the inelastic scattering data is not related to the central nuclear potential, but to the coupling potential between excited states. We present that these problems can be addressed in a systematic way by using a different shape for the coupling potential instead of the usual one based on Taylor expansion.Comment: 10 pages, 4 figures, 1 table, Latex:RevTex4 published in J. Phys. G: Nucl. Part. Phy

Laser cooling of a nanomechanical resonator mode to its quantum ground state

We show that it is possible to cool a nanomechanical resonator mode to its ground state. The proposed technique is based on resonant laser excitation of a phonon sideband of an embedded quantum dot. The strength of the sideband coupling is determined directly by the difference between the electron-phonon couplings of the initial and final states of the quantum dot optical transition. Possible applications of the technique we describe include generation of non-classical states of mechanical motion.Comment: 5 pages, 3 figures, revtex

Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion

We present a fully quantum theory describing the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the opto-mechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.Comment: 5 pages, 2 figure

On-Line Learning with Restricted Training Sets: An Exactly Solvable Case

We solve the dynamics of on-line Hebbian learning in large perceptrons exactly, for the regime where the size of the training set scales linearly with the number of inputs. We consider both noiseless and noisy teachers. Our calculation cannot be extended to non-Hebbian rules, but the solution provides a convenient and welcome benchmark with which to test more general and advanced theories for solving the dynamics of learning with restricted training sets.Comment: 19 pages, eps figures included, uses epsfig macr

Nonlinear damping in mechanical resonators based on graphene and carbon nanotubes

Carbon nanotubes and graphene allow fabricating outstanding nanomechanical resonators. They hold promise for various scientific and technological applications, including sensing of mass, force, and charge, as well as the study of quantum phenomena at the mesoscopic scale. Here, we have discovered that the dynamics of nanotube and graphene resonators is in fact highly exotic. We propose an unprecedented scenario where mechanical dissipation is entirely determined by nonlinear damping. As a striking consequence, the quality factor Q strongly depends on the amplitude of the motion. This scenario is radically different from that of other resonators, whose dissipation is dominated by a linear damping term. We believe that the difference stems from the reduced dimensionality of carbon nanotubes and graphene. Besides, we exploit the nonlinear nature of the damping to improve the figure of merit of nanotube/graphene resonators.Comment: main text with 4 figures, supplementary informatio

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