Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation

Journal name:
Nature Nanotechnology
Year published:
Published online


The ability to control mechanical motion with optical forces has made it possible to cool mechanical resonators to their quantum ground states. The same techniques can also be used to amplify rather than reduce the mechanical motion of such systems. Here, we study nanomechanical resonators that are slightly buckled and therefore have two stable configurations, denoted ‘buckled up’ and ‘buckled down’, when they are at rest. The motion of these resonators can be described by a double-well potential with a large central energy barrier between the two stable configurations. We demonstrate the high-amplitude operation of a buckled resonator coupled to an optical cavity by using a highly efficient process to generate enough phonons in the resonator to overcome the energy barrier in the double-well potential. This allows us to observe the first evidence for nanomechanical slow-down and a zero-frequency singularity predicted by theorists. We also demonstrate a non-volatile mechanical memory element in which bits are written and reset by using optomechanical backaction to direct the relaxation of a resonator in the high-amplitude regime to a specific stable configuration.

At a glance


  1. The two states of a coupled mechanical resonator-optical cavity system.
    Figure 1: The two states of a coupled mechanical resonator–optical cavity system.

    a, Generic optomechanical system (top) in which one of the mirrors in an optical cavity illuminated by a pump laser of frequency ωp and power Pin is able to oscillate at a resonant frequency m. The power circulating inside the cavity, Pcirc, is enhanced by the finesse of the cavity (F = 20). Schematic of the experiment (bottom) showing a nanomechanical resonator embedded in a racetrack-shaped waveguide that serves as the optical cavity (without mirrors). The resonator and waveguide are made of a 110-nm-thick silicon layer. Light is coupled into the bus waveguide via grating couplers (triangles) and then into the cavity. The nanomechanical resonator is made by under-etching a part of the waveguide. The motion of the resonator changes the optical path length (and hence the resonant frequency of the cavity) by changing the effective refractive index of the optical mode. b, Scanning electron micrographs of the nanomechanical resonator in its buckled-up (left) and buckled-down (right) states. c, Optical transmission spectra of the cavity measured at low input power (–5 dBm on coupling bus waveguide) when the resonator is in the up state (blue curve) and the down state (red). The racetrack cavity optical resonances are separated by a free spectral range of 2 nm. d, Optical transmission spectrum of the cavity measured at high input power (green, left axis). When the input power exceeds a certain threshold, the spectrum no longer shows the Lorentzian shape seen at low power; rather, the resonance is dragged from the up state to the down state. Moreover, self-sustained oscillations (red, right axis) are observed when ωup < ωp < ωdown, where ωup and ωdown are the resonant frequency of the cavity when the resonator is in the up and down states, respectively. e, Thermomechanical noise spectra measured in the up (blue symbols) and down (red) states. Solid black lines are harmonic oscillator responses fitted to the data.

  2. Resolved and unresolved sideband regimes.
    Figure 2: Resolved and unresolved sideband regimes.

    a, Schematic plot of the optical transmission spectrum of the cavity as measured by a weak probe laser of frequency ω when the resonator is at rest (solid green line). The motion of the resonator modifies the effective path length of the optical cavity (Fig. 1a), so that the position of the peak (that is, the resonant frequency of the cavity) changes when the resonator moves (dashed lines). In the high-amplitude regime, the change in the resonance frequency can be larger than the width of the peak. Energy can be exchanged between the laser field and the mechanical motion of the resonator in units of hm/2π, where h is Planck's constant and m is the resonator frequency, which leads to optical fields (called sidebands) with frequencies of ωp ± nm, where ωp is the frequency of the pump laser and n is an integer. b, When the width of the cavity spectrum (green line) is smaller than m, only one sideband can lie inside the cavity linewidth, and this sideband will be enhanced by the coupling. In this regime, which is called the resolved sideband regime, only one phonon is exchanged between the optical field and the resonator. c, When the width of the cavity spectrum is much larger than m, many sidebands can lie inside the cavity linewidth. In this unresolved sideband regime, more than one phonon can be exchanged between the optical field and the resonator. d, Simulations showing the development of self-sustained oscillations over time for a blue-detuned pump laser. The plot at the back shows how the number of photons in the cavity varies with time. The middle plot shows how the resonant wavelength of the cavity varies with time; sometimes it is longer than the wavelength of the pump laser (shown by vertical yellow plane) and sometimes it is shorter. The front plot shows the energy gained (red regions) or lost (blue) by the resonator as a function of time and position.

  3. Optomechanical amplification and relaxation of a nanomechanical resonator in a double-well potential.
    Figure 3: Optomechanical amplification and relaxation of a nanomechanical resonator in a double-well potential.

    After the resonator has been excited into a high-amplitude state (left panels) and the pump laser has been turned off, it can relax into the down (middle panels) or up (right panels) states. ac, Schematic representation of the amplification and relaxation processes. df, Photodetected voltage versus time, showing an increase in mechanical motion as the pump laser is turned on (d), and then a decrease in mechanical motion when the pump laser is turned off (e,f). gi, Fourier spectra of the traces shown in df at different times (indicated by different colours). The wavelength of the probe laser used in panels f and i differed from that used in the other panels to provide a good transduction in the up state.

  4. Ring-down and zero-frequency singularity.
    Figure 4: Ring-down and zero-frequency singularity.

    a,b, Oscillation frequency (a) and amplitude (b) versus time during free decay into the up (blue curve) and down (red) states. The two curves in a represent the instantaneous frequency of the resonator obtained from the time traces; the open symbols show the frequency determined from the digital Fourier transform spectra at different times (Fig. 3). The zero-frequency singularity appears as a pronounced dip in the oscillation frequency at 0.02 ms, which coincides with a large change in the oscillation amplitude. c, Simulated phase portrait of a resonator relaxing from a high-amplitude state into the up state. The symbols indicate the values at a fixed interval. The parameters used for simulation are extracted from the experiment; however, for clarity, a smaller mechanical quality factor (Qm = 50) was used.

  5. All-optical, non-volatile nanomechanical memory.
    Figure 5: All-optical, non-volatile nanomechanical memory.

    a, Probability of the resonator relaxing to the up state (blue) or down state (red) versus wavelength of the cooling laser (Pin = 7.5 dBm). For certain ranges of wavelengths there is a 100% probability of the resonator relaxing to a given state, so lasers with these wavelengths are used to write data to the nanomechanical memory. An optomechanical instability around 1,560.6 nm is highlighted. b, Writing a ‘1’ (left) and a ‘0’ (right) to a nanomechanical memory. First, a reset pulse (blue) excites the resonator to a high-amplitude state. A write pulse of wavelength λ1 (pink, left) or λ0 (red, right) then cools the motion of the resonator into the up state (which represents ‘1’, left) or the down state (‘0’, right). A weak probe laser (dark blue) then reads the state of the resonator. c, Non-volatile memory operation of the resonator. The upper panel shows a series of 10101… written onto the state of the resonator, while in the lower panel a series of 01001… bits are stored in the memory element. The blue time traces show the series of pulses that reset the memory by exciting large-amplitude oscillations in the resonator. The red (pink) pulses then cool the resonator from the high-amplitude regime into the selected down (up) state; the green time sequence shows the weak probe signal that traces the state of the mechanical resonator. The dark blue shows the state of the memory element.


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Author information


  1. Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, USA

    • Mahmood Bagheri,
    • Menno Poot,
    • Mo Li,
    • Wolfram P. H. Pernice &
    • Hong X. Tang
  2. Present address: Department of Electrical and Computer Engineering, University of Minnesota, Minnesota 55455, USA

    • Mo Li


M.B. performed the device fabrication and carried out measurements and data analysis under the supervision of H.X.T. M.B. and M.P. contributed to numerical analysis of the coupled optomechanical system. M.B., M.P., M.L., W.P.H.P. and H.X.T. discussed the results and all authors contributed to the writing of the manuscript.

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