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 01.07.2010   Карта сайта     Language По-русски По-английски
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01.07.2010

A macroscopic mechanical resonator driven by mesoscopic electrical back-action





Journal name:

Nature

Volume:

466,

Pages:

86–90

Date published:

(01 July 2010)

DOI:

doi:10.1038/nature09123


Received


Accepted







Systems with coupled mechanical and optical or electrical degrees of freedom1, 2 have fascinating dynamics that, through macroscopic manifestations of quantum behaviour3, provide new insights into the transition between the classical and quantum worlds. Of particular interest is the back-action of electrons and photons on mechanical oscillators, which can lead to cooling and amplification of mechanical motion4, 5, 6. Furthermore, feedback, which is naturally associated with back-action, has been predicted to have significant consequences for the noise of a detector coupled to a mechanical oscillator7, 8. Recently it has also been demonstrated that such feedback effects lead to strong coupling between single-electron transport and mechanical motion in carbon nanotube nanomechanical resonators9, 10. Here we present noise measurements which show that the mesoscopic back-action of electrons tunnelling through a radio-frequency quantum point contact11 causes driven vibrations of the host crystal. This effect is a remarkable macroscopic manifestation of microscopic quantum behaviour, where the motion of a mechanical oscillator—the host crystal, which consists of on the order of 1020 atoms—is determined by statistical fluctuations of tunnelling electrons.






Figures at a glance


left


  1. Figure 1: Current measurement and mechanical back-action in a QPC.


    a, Schematic of the measurement circuit. b, A lateral displacement by dy (blue arrows) with an associated contraction and expansion by dz in a GaAs crystal generates a shear strain Syz = 2dz/w at the upper surface that causes corresponding polarizations Pz and Px = Syz. The 2DEG free charge (+, −) will screen the Px polarization charge in most areas but not under the QPC or its gates, resulting in a potential difference ε across the QPC. c, Reservoirs L and R are usually treated as having a fixed chemical potential, which is ordinarily a good approximation. Here, however, we cannot ignore the presence of the ohmic contacts (shown in a) that may themselves have a non-negligible impedance of several kilo-ohms. We assume that the metallic wires E and C connected to the crystal are held at a fixed potential difference and that the potentials of L and R are free to change as electrons tunnel through the QPC. The electron distribution functions, left fencenEright fence and left fencenCright fence, for E and C are Fermi distributions, whereas the corresponding distributions, left fencenLright fence and left fencenRright fence, for L and R are not. We treat the QPC as a tunnel barrier with coupling ΩLR and the ohmic contacts as tunnel barriers with couplings ΩEL and ΩRC. d, The back-action associated with the measurement process naturally leads to the presence of a feedback loop. If a displacement dz of the crystal exists, piezoelectric transduction causes an energy difference between reservoirs L and R. The resulting flow of current, I, through the QPC can be used to obtain information regarding dz. Quantum statistical fluctuations in electron tunnelling invariably result in shot noise. Piezoelectric transduction leads to a fluctuating force, dF, that imparts a momentum kick to the lattice, affecting subsequent values of the displacement dz and closing the feedback loop. The energy needed to maintain the current I is provided by a bias voltage, VCE.




  2. Figure 2: Direct-current and radio-frequency characterization of the QPC.


    a, Measurements of GQPC versus gate voltage, Vg, at zero magnetic field, showing standard one-dimensional subbands. Inset, GQPC after exposure of the sample to light, showing multiple conductance plateaux. b, Nonlinear differential conductance, GQPC(Vdc,Vg). Each red trace corresponds to a different value of Vg (ΔVg = 1mV) and is plotted without offset. The vertical blue lines indicate the estimated root-mean-squared radio-frequency voltage, Vrf, applied to the QPC for noise measurements in c. c, Output power spectrum, Pn, of the RF-QPC for input power Pin = −78dBm and GQPC0.5G0. The frequency-dependent features are spontaneously generated and clearly exceed the noise floor of the cryogenic high-electron-mobility transistor (HEMT) amplifier, .




  3. Figure 3: Frequency-dependent shot noise.


    a, The reference modulation signal, Ps, is generated by applying an a.c. excitation to the QPC gates. b, Power dependence. The dashed lines are guides to the eye showing that Ps (red squares) scales as ~Pin whereas the integrated excess noise, (blue circles), scales as , the first signature of shot noise. c, Partition dependence. The reflected power spectra, Pn, for Pin = −88dBm and GQPC0 (red), GQPC0.5G0 (black) and GQPCG0 (green), showing that Pn is minimal for fully open or closed channels and maximal for half-open channels, the second signature of shot noise. d, Quantitative comparison of measured shot noise with theory. The measured integrated excess noise, (blue circles), and the calculated integrated noise power, ∫(2L/CpZ0)SI(ω,ω0) df (blue dashes), as functions of QPC differential conductance, GQPC. We shift the calculated noise power downward by 3.9dB but use no other fitting parameter. The suppression of the measured shot noise relative to the single-particle theory for GQPC 0.5 has been observed by others and attributed to the many-body physics of the 0.7 structure30. All data are from sample A.




  4. Figure 4: A macroscopic mechanical resonance driven by mesoscopic shot noise.


    a, The reflected power spectrum, Pn, from sample A reproduced with the inclusion of data from an addition input power excitation (Pin = −98dBm). The diagram of the sample geometry includes the ohmic contacts (blue boxes), the QPC (yellow rectangles) and the linear dimensions. The calculated value for the excited three-dimensional acoustic mode (fa = 510kHz) falls almost exactly on the shot noise peak. As the power is increased (from red to black) the broadband shot noise decreases whereas the total increases, becoming concentrated at the resonant frequency. b, The shot noise spectrum for sample B, whose dimensions were chosen to provide ~1MHz of bandwidth in which the shot noise is suppressed. The sample dimensions shown in the diagram correspond to a predicted resonant frequency (fb = 1.07MHz) remarkably close to the shot noise peak. The sharp features marked with asterisks are modulation noise rather than shot noise and scale as Pin, not . c, The reflected power spectra, Pn, for QPC 1 and QPC 2 (inset) in sample C when GQPC0 (red), GQPC0.5G0 (black) and GQPCG0 (green), showing partition dependence for QPC 1 but no shot noise features for QPC 2. This confirms the existence of a back-action-mediated feedback loop between the shot noise and the normal vibrational mode. Without a bias across QPC 2, energy transferred to the Ey-1 mode cannot be returned to the current, thereby breaking the feedback loop. The sample dimensions shown in the diagram again correctly predict the location of the peak in the shot noise. d, Left axis: frequency-dependent Fano factor, , for sample A for Pin = −68dBm, showing drastically super-Poissonian ( 100) and sub-Poissonian ( ) noise as a function of frequency (on a logarithmic scale). The red dotted line indicates Poissonian noise and the green dashed line gives the Fano factor expected for an uncoupled detector. Right axis: displacement dy versus frequency, showing the strongly non-thermal nature of the resonator dynamics. Inset, displacements dy and dz versus input power for sample A. The dashed line is a guide to the eye showing scaling as . In the diagram of the sample, blue arrows indicate the dy and dz deformations of the crystal in the Ey-1 mode.






right







Author information







  1. These authors contributed equally to this work.



    • Joel Stettenheim &

    • Madhu Thalakulam




Affiliations




  1. Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA



    • Joel Stettenheim,

    • Feng Pan,

    • Mustafa Bal,

    • Weiwei Xue,

    • M. P. Blencowe &

    • A. J. Rimberg




  2. Rice Quantum Institute, Rice University, Houston, Texas 77005, USA



    • Madhu Thalakulam




  3. Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA



    • Zhonqing Ji




  4. Bell Laboratories, Alcatel–Lucent, Murray Hill, New Jersey 07974, USA



    • Loren Pfeiffer &

    • K. W. West






Contributions


A.J.R. initiated the project. M.T. fabricated and measured sample A. J.S. fabricated and measured five samples including samples B and C. F.P., M.B., J.Z. and W.X. fabricated and measured two additional samples. L.P. and K.W.W. grew the GaAs/AlGaAs heterostructure material. A.J.R. and M.P.B. developed the theoretical model used to describe the system. M.T. analysed data for sample A. A.J.R. and J.S. analysed data for all samples and co-wrote the paper with input from M.P.B.


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