Nanometre-scale displacement sensing using a single electron transistor

Knobel, R.; Cleland, A. N.

doi:10.1038/nature01773

Cited by 598 publications

(581 citation statements)

References 27 publications

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“…Several experimental groups have observed the behavior described by the classical Duffing oscillator [27,28,29,30]. The transition to the quantum regime is currently in the focus of intense research [31,32,33,34,35,36]. Once, such kind of truly quantum-'mechanical' systems on the nanoscale have been shown to exist, macroscopic quantum effects [33] should be readily observable.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

Peano

Thorwart

2006

Chemical Physics

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We investigate the nonlinear response of an anharmonic monostable quantum mechanical resonator to strong external periodic driving. The driving thereby induces an effective bistability in which resonant tunneling can be identified. Within the framework of a Floquet analysis, an effective Floquet-Born-Markovian master equation with time-independent coefficients can be established which can be solved straightforwardly. Various effects including resonant tunneling and multi-photon transitions will be described. Our model finds applications in nano-electromechanical devices such as vibrating suspended nano-wires as well as in non-destructive readout procedures for superconducting quantum bits involving the nonlinear response of the read-out SQUID.

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Section: Discussionmentioning

confidence: 99%

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

Peano

Thorwart

2006

Chemical Physics

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“…Nanotube oscillation is excited by applying a voltage signal at frequency u to the gate, via electrostatic interaction with the bottom gate electrode. The nanotube is used as a mixer (Knobel & Cleland 2003) allowing the motion to be detected by simply measuring the amplitude of the source-drain current (figure 15b). The device can also be tuned by applying a DC voltage to the gate, which produces an electrostatic force that changes the tension in the nanotube (figure 15c).…”

Section: (C ) Oscillatorsmentioning

confidence: 99%

Nanomechanics of carbon nanotubes

Kis

Zettl

2008

Phil. Trans. R. Soc. A.

110

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Some of the most important potential applications of carbon nanotubes are related to their mechanical properties. Stiff sp 2 bonds result in a Young's modulus close to that of diamond, while the relatively weak van der Waals interaction between the graphitic shells acts as a form of lubrication. Previous characterization of the mechanical properties of nanotubes includes a rich variety of experiments involving mechanical deformation of nanotubes using scanning probe microscopes. These results have led to promising prototypes of nanoelectromechanical devices such as high-performance nanomotors, switches and oscillators based on carbon nanotubes.

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“…By detuning the cavity, we have observed a drastic cooling of the microresonator by intracavity radiation pressure, down to an effective temperature of 10 K. We have also obtained an efficient heating for an opposite detuning, up to the observation of a radiation-pressure induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a mechanical resonator [12,13,14], either by passive [15] or active cooling techniques [16,17,18].…”

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Radiation-pressure cooling and optomechanical instability of a micromirror

Arcizet

Cohadon

Briant

et al. 2006

Nature

966

969

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PACS numbers:Recent experimental progress in table-top experiments [1,2] or gravitational-wave interferometers [3] has enlightened the unique displacement sensitivity offered by optical interferometry. As the mirrors move in response to radiation pressure, higher power operation, though crucial for further sensitivity enhancement, will however increase quantum effects of radiation pressure, or even jeopardize the stable operation of the detuned cavities proposed for next-generation interferometers [4,5,6]. The appearance of such optomechanical instabilities [7,8] is the result of the nonlinear interplay between the motion of the mirrors and the optical field dynamics. In a detuned cavity indeed, the displacements of the mirror are coupled to intensity fluctuations, which modifies the effective dynamics of the mirror. Such "optical spring" effects have already been demonstrated on the mechanical damping of an electromagnetic waveguide with a moving wall [9], on the resonance frequency of a specially designed flexure oscillator [10], and through the optomechanical instability of a silica micro-toroidal resonator [11]. We present here an experiment where a micro-mechanical resonator is used as a mirror in a very high-finesse optical cavity and its displacements monitored with an unprecedented sensitivity. By detuning the cavity, we have observed a drastic cooling of the microresonator by intracavity radiation pressure, down to an effective temperature of 10 K. We have also obtained an efficient heating for an opposite detuning, up to the observation of a radiation-pressure induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a mechanical resonator [12,13,14], either by passive [15] or active cooling techniques [16,17,18].The resonator is placed at the end of a linear cavity, along with a conventional coupling mirror (Fig. 1a). As we are only interested in the motion at frequencies Ω close to a resonance frequency Ω m of the resonator, the mirror dynamics can be approximated as the one of a single harmonic oscillator, with resonance frequency Ω m , mass M , damping Γ m and mechanical susceptibility:The resonator is submitted to a radiation pressure force F rad induced by the intracavity field. Depending on the detuning Ψ ≡ 4πL/λ [2π], where L is the cavity length and λ the laser wavelength, any small displacement x of the resonator induces a variation of the intracavity power P and of the radiation pressure (see Fig. 1b). As a consequence, the spring constant k = M Ω 2 m of the resonator is balanced by the radiation pressure force: for a positive detuning, the displacement creates a negative linear force and thereby an additional binding force, increasing the effective spring constant, whereas for a negative detuning, the force corresponds to a softening of the oscillator. Effects are null at resonance, maximum at half-width of the optical resonance, and proportional to the incident power. These effects hav...

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Nanometre-scale displacement sensing using a single electron transistor

Cited by 598 publications

References 27 publications

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

Nanomechanics of carbon nanotubes

Radiation-pressure cooling and optomechanical instability of a micromirror

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