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Since the advent of atomic force microscopy, mechanical resonators have been used to study a wide variety of phenomena, such as the dynamics of individual electron spins, persistent currents in normal metal rings, and the Casimir force. Key to these experiments is the ability to measure weak forces. Here, we report on force sensing experiments with a sensitivity of 12 zN Hz^(-1/2) at a temperature of 1.2 K using a resonator made of a carbon nanotube. An ultra-sensitive method based on cross-correlated electrical noise measurements, in combination with parametric downconversion, is used to detect the low-amplitude vibrations of the nanotube induced by weak forces. The force sensitivity is quantified by applying a known capacitive force. This detection method also allows us to measure the Brownian vibrations of the nanotube down to cryogenic temperatures. Force sensing with nanotube resonators offers new opportunities for detecting and manipulating individual nuclear spins as well as for magnetometry measurements.
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We report on the nonlinear coupling between the mechanical modes of a nanotube resonator. The coupling is revealed in a pump-probe experiment where a mode driven by a pump force is shown to modify the motion of a second mode measured with a probe force. In a second series of experiments, we actuate the resonator with only one oscillating force. Mechanical resonances feature exotic lineshapes with reproducible dips, peaks, and jumps when the measured mode is commensurate with another mode with a frequency ratio of either 2 or 3. Conventional lineshapes are recovered by detuning the frequency ratio using the voltage on a nearby gate electrode. The exotic lineshapes are attributed to strong coupling between the mechanical modes. The possibility to control the strength of the coupling with the gate voltage holds promise for various experiments, such as quantum manipulation, mechanical signal processing, and the study of the quantum-toclassical transition.
In physical systems, decoherence can arise from both dissipative and dephasing processes. In mechanical resonators, the driven frequency response measures a combination of both, while time domain techniques such as ringdown measurements can separate the two. Here, we report the first observation of the mechanical ringdown of a carbon nanotube mechanical resonator. Comparing the mechanical quality factor obtained from frequency- and time-domain measurements, we find a spectral quality factor four times smaller than that measured in ringdown, demonstrating dephasing-induced decoherence of the nanomechanical motion. This decoherence is seen to arise at high driving amplitudes, pointing to a non-linear dephasing mechanism. Our results highlight the importance of time-domain techniques for understanding dissipation in nano-mechanical resonators, and the relevance of decoherence mechanisms in nanotube mechanics.
Sensitive detection of weak magnetic moments is an essential capability in many areas of nanoscale science and technology, including nanomagnetism, quantum readout of spins, and nanoscale magnetic resonance imaging. Here, we show that the write head of a commercial hard drive may enable significant advances in nanoscale spin detection. By approaching a sharp diamond tip to within 5 nm from the pole and measuring the induced diamagnetic moment with a nanomechanical force transducer, we demonstrate a spin sensitivity of 0.032 Bohr magnetons per root Hz, equivalent to 21 proton magnetic moments. The high sensitivity is enabled in part by the poles strong magnetic gradient of up to 28 million Tesla per meter and in part by the absence of non-contact friction due to the extremely flat writer surface. In addition, we demonstrate quantitative imaging of the pole field with about 10 nm spatial resolution. We foresee diverse applications for write heads in experimental condensed matter physics, especially in spintronics, ultrafast spin manipulation, and mesoscopic physics.
We report on measurements of the spin lifetime of nuclear spins strongly coupled to a micromechanical cantilever as used in magnetic resonance force microscopy. We find that the rotating-frame correlation time of the statistical nuclear polarization is set by the magneto-mechanical noise originating from the thermal motion of the cantilever. Evidence is based on the effect of three parameters: (1) the magnetic field gradient (the coupling strength), (2) the Rabi frequency of the spins (the transition energy), and (3) the temperature of the low-frequency mechanical modes. Experimental results are compared to relaxation rates calculated from the spectral density of the magneto-mechanical noise.
We experimentally investigate the nonlinear response of a multilayer graphene resonator using a superconducting microwave cavity to detect its motion. The radiation pressure force is used to drive the mechanical resonator in an optomechanically induced transparency configuration. By varying the amplitudes of drive and probe tones, the mechanical resonator can be brought into a nonlinear limit. Using the calibration of the optomechanical coupling, we quantify the mechanical Duffing nonlinearity. By increasing the drive force, we observe a decrease in the mechanical dissipation rate at large amplitudes, suggesting a negative nonlinear damping mechanism in the graphene resonator. Increasing the optomechanical backaction, we observe a nonlinear regime not described by a Duffing response that includes new instabilities of the mechanical response.
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