Sensitivity of the mixing-current technique in the detection of nano-mechanical displacement

Abstract : Detection of nanomechanical displacement by electronic transport techniques has reached a high level of sensitivity and versatility. In order to detect the amplitude of oscillation of a nanomechanical oscillator, a widely used technique consists of coupling this motion capacitively to a single-electron transistor or, more generally, to a transport device, and to detect the high-frequency modulation of the current through the nonlinear mixing with an electric signal at a slightly detuned frequency. This method, known as mixing-current technique, is employed in particular for the detection of suspended carbon nanotubes and has proven to be particularly successful leading to record sensitivities of mass and force detection. In this thesis we study theoretically the limiting conditions on the sensitivity of this method in different kind of transport devices. The sensitivity is a compromise between the noise, the back-action noise, and the response function. The latter is proportional to the electromechanical coupling. For these reasons in the thesis we study the response function, the effect of current and displacement (back-action) fluctuations for the following detection devices: (i) the metallic single electron transistor, (ii) the single-electronic level single electron transistor, and (iii) the coherent transport quantum dot. The optimal sensitivity is obtained, as usual, when the back-action of the detection device equals the intrinsic signal noise that, in our case, is the current noise. We found that the typical optimal values of the coupling are obtained in the strong coupling limit, where a strong renormalization of the resonating frequency is observed and a bistability of the mechanical oscillator is present [as discussed in G. Micchi, R. Avriller, F. Pistolesi, Phys. Rev. Lett. 115, 206802 (2015)]. We thus find upper bounds to the sensitivity of the mixing-current detection technique. We also consider how the mixing-current technique is modified in the limit where the tunneling rate becomes comparable to the resonating frequency of the mechanical oscillator.
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Yue Wang. Sensitivity of the mixing-current technique in the detection of nano-mechanical displacement. Other [cond-mat.other]. Université de Bordeaux, 2017. English. ⟨NNT : 2017BORD0659⟩. ⟨tel-01766467⟩

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