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A Coherent Nanotube Oscillator Driven by Electromechanical Backaction Edward Laird a Coherent Nanotube Oscillator Driven by Electromechanical Backaction

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A Coherent Nanotube Oscillator Driven by Electromechanical Backaction Edward Laird a Coherent Nanotube Oscillator Driven by Electromechanical Backaction 1 A coherent nanotube oscillator driven by electromechanical backaction Edward Laird A coherent nanotube oscillator driven by electromechanical backaction Yutian Wen Natalia Ares Tian Pei Felix Schupp Andrew Briggs (at Oxford) ERC Consolidator Grant Panel 2016 Members of the ERC Peer Review Panels European Microkelvin The list below includes the panel members in the ERC Consolidator Grant 2016 peer review process, identified and invited by the ERC Scientific Council. There are in total 25 panels, divided Platform between the three domains as follows: 9 panels in Life Sciences (LS), 10 panels in Physical Sciences and Engineering (PE), and 6 panels in Social Sciences and Humanities (SH). 2 Panel chairs appear at the top of each panel list, followed by panel members in alphabetical order. Note to applicants: This information is given for reasons of transparency. Under no circumstances should peer reviewers be contacted by applicants, potential applicants or potential host institutions. Questions can be addressed to: - ERC Helpdesk http://ec.europa.eu/research/index.cfm?lg=en&pg=enquiries - ERC National Contact Points http://erc.europa.eu/ncp ERC- 2016-CoG Panel Members List – Release date: 01/02/2017 The limits of displacement sensing Suspended carbon nanotube ~106 nucleons Diameter ~5 nm Length ~800 nm • High mechanical quality factor • High frequency (200 MHz ≡ 10 mK) • Mechanically compliant • Can be integrated into electronic circuits 3 The limits of displacement sensing: Magnetic resonance microscopy Force per proton: ~10-20 N Review: Poggio & Harzheim (2018) 4 A coherent nanotube oscillator driven by electromechanical backaction 1. Measuring vibrations with a single-electron transistor 2. Creating a nanomechanical oscillator 3. Characterizing the oscillator 5 Question 1: How precisely can we measure nanomechanical vibrations? Standard quantum limit for continuous measurements (m/√Hz): Quality factor Mechanical frequency Theory: Caves et al. (RMP 1982) Mass Experiment: LaHaye et al. (Science 2004) Review: Clerk et al. (RMP 2010) 6 Question 2: Can we make a laser for sound? Microwave amplification by stimulated emission of radiation (Townes, 1955) 7 A vibrating carbon nanotube device Laird et al (2011) ~2 nm 1 µm 8 The single-electron transistor Energy levels ) nA Current ( Current Gate voltage (V) Hüttel et al (van der Zant group, 2009) 9 Sensing vibrations Motion Current Displacement Hüttel et al (2009) 10 Fast readout for nanotube vibrations SiGe amplifier Details: Wen et al. (2018) Schupp et al. (2018) 11 How precisely can we measure nanomechanical vibrations? 12 Is this a laser analogue? 13 REPORTS tions do not simply smooth the stepwise (G ~ f0), damping of the mechanical motion is addition to the overall softening of k yielding the transition from the static single-electron tuning minimized, and we observe the highest value of frequency dips of Fig. 2, the fluctuating charge on shifts. Instead, fluctuations caused dips in the Q.OnaCoulombpeak,chargefluctuationsare the dot also changes a,givingasofteningspring resonant frequency up to one order of magnitude maximized (G >> f0), and Q decreases to a few (a <0)outsideofthefrequencydip(Coulomb greater than the single-electron tuning shifts. As thousand. These results explicitly show that detec- valleys) and a hardening spring (a >0)insidethe shown in (13, 22)anddiscussedindetailinthe tor back-action can cause substantial mechanical frequency dip (Coulomb peaks), as shown in Fig. supporting online material (SOM) (20), the dy- damping. The underlying mechanism for the damp- 3. The sign of a follows the curvature of f0(Vg) namic force modifies the nanotube’sspringcon- ing is an energy transfer occasionally occurring induced by the fluctuating electron force, giving a stant (k)resultinginasofteningofthemechanical when a current-carrying electron is pushed up to change in sign at the inflection point of the fre- resonance. The shape of the frequency dip can be ahigher(electrostatic)energybythenanotube quency dip. Nonlinearity from the single-electron altered by applying a finite bias (Vsd)acrossthe motion before tunneling out of the dot. This gain force in our device dominates and is much stronger nanotube. Starting from deep and narrow at small in potential energy is later dissipated in the drain than that from the mechanical deformation (20). Vsd =0.5mV,thedipbecomesshallowerand contact. Figure 3, E and F, shows the regime of further broader with increasing Vsd.Thisdipshapelargely If we drive the system at higher RF powers enhanced RF driving. Now the nonlinearity is no resembles the broadening of Coulomb blockade (Fig. 3, C and D), we observe an asymmetric longer a perturbation of the spring constant, but peaks that occurs with increasing Vsd.Thus,we resonance peak, along with distinct hysteresis be- instead gives sharp peaks in the line shape and conclude from Fig. 2 that the single-electron tween upward and downward frequency sweeps. switching between several different metastable tuning oscillations are a mechanical effect that is Theoretically, this marks the onset of nonlinear modes [see further data in the SOM (20)]. At this adirectconsequenceofsingle-electrontunneling terms in the equation of motion, such as in the strong driving, we observe highly structured non- oscillations. well-studied Duffing oscillator (23, 24). k is mod- linear mechanical behavior that arises from the Besides softening, the charge fluctuations also ified by a large oscillation amplitude (x)thatis coupling of the resonator motion to the quantum provide a channel for dissipation of mechanical accounted for by replacing k with (k + ax2). The dot. energy. Figure 3A shows the resonance dip for time-averaged spring constant increases if a >0, In Fig. 3, we studied nonlinear coupling be- small RF power, with frequency traces in Fig. 3B. which is accompanied by a sharp edge at the high- tween the quantum dot and the mechanical res- In the Coulomb valleys, tunneling is suppressed frequency side of the peak; vice versa for a <0.In onator by applying a large RF driving force at a on April 26, 2010 Fig. 4. Spontaneous driving 05dI/dV (µS) 0 -10 dI/dV (µS) 5 Evidence for self-driven oscillations of the mechanical resonance sd by single-electron tunneling. A B D I (A)Differentialconductance 2 (dI/dVsd)showingridgesof 10 5 sharp positive (deep red) and (nA) sd negative (deep blue) spikes (ar- I B rows). ( )Similarridgesmea- ) sured on device two (trench Gate voltage-4.93 Vg nA www.sciencemag.org width = 430 nm) in the few- (mV) 5 (mV) 5 sd sd – – V hole regime (four-hole to V three-hole transition). Spikes in dI/dVsd appear as steplike ridges in current. (C)shows -10 Current ( the data from the upper half Self-oscillation of (B), but now as a three- -2 dimensional current plot. The threshold 0 0 ridges are entirely reproduc- Downloaded from ible. (D)(Inset)Coulombpeak -5.19 V (V) -5.17 -1.05 V (V) -0.95 Gate voltage g g E at V =0.5mVshowinglarge sd 284.5 switching-steps. (Main plot) From Steele et al (Kouwenhoven group, 2009) 14 Zoom-in view on data from C inset. (E)RFdrivenmechanical resonance measured for the 10 nA same Coulomb peak in (D) at adrivingpowerof–50 dB. Outside the switch region, the resonance has a narrow line shape and follows the soften- I f (MHz) ing dip from Figs. 2 and 3. At sd the first switch, the resonance position departs from the 283.5 expected position (indicated by dashed line). The mechan- 0.5 ical signal is strongly enhanced (nA) in amplitude and displays a sd I V ∆ broad asymmetric line shape. V sd At the second switch, the res- g -0.75 onance returns to the frequency -4.935 -4.93 Vg (V) and narrow line shape expected at these powers. 1106 28 AUGUST 2009 VOL 325 SCIENCE www.sciencemag.org A coherent nanotube oscillator driven by electromechanical backaction 1. Measuring vibrations with a single-electron transistor 2. Creating a nanomechanical oscillator 3. Characterizing the oscillator 15 Excitation off Bias on, excitation on Gate voltage (mV) Bias on, excitation off A coherent nanotube oscillator driven by electromechanical backaction 1. Measuring vibrations with a single-electron transistor 2. Creating a nanomechanical oscillator 3. Characterizing the oscillator 17 Measuring the output coherence 18 Statistics of the output coherence Emission histograms Correlation function 19 How the oscillator works Electrical charge Electrical Bennet & Clerk (2007) Usmani, Blanter, Nazarov (2007) 20 How the oscillator works Electrical charge Electrical Bennet & Clerk (2007) Usmani, Blanter, Nazarov (2007) 21 Laser physics I: Injection locking Principle Implementation Discovery: Huygens (1666) In lasers: Stover and Steier (1966) 22 Laser physics I: Injection locking 23 Laser physics II: Stabilising using feedback 24 Laser physics II: Stabilising using feedback 25 Why are nanomechanical lasers interesting? • They connect the physics of backaction with the physics of lasers. • They are amplifiers and transducers. Narrow linewidth means better sensitivity to perturbations. • They are on-chip phonon generators for microscopy, information transfer, etc. • They couple charge and motion on a mesoscopic scale. 26 Other nano-oscillators NATURE COMMUNICATIONS | DOI: 10.1038/ncomms2827 Electrical ARTICLE Spin transfer torque Double quantum dot micromaser Josephson laser (Pribiag 2007) (Liu 2017) (Cassidy 2017) elf-sustained oscillations (SSOs) are distinct from the forced B I motion of a resonator because the oscillation period does bias Snot depend on the frequency of the driving force. Resonators in the SSO regime typically produce signals with a F J spectral line width, which is narrower than the intrinsic line L u VLF VHF width of the resonator. The reduced line width enhances the Φa 1 ! sensitivity of resonance-based force-gradient sensors . On the 1 !2 other hand, these oscillations are not desirable in experiments I Mechanical that require observation of very small displacements, such as bias those induced by gravitational waves2 and quantum-mechanical Optomechanics 3–5 Optomechanics Vibrating SQUID (Grudininzero-point2010) fluctuations .
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