The detection of mechanical vibrations near the quantum limit is a formidable challenge since the displacement becomes vanishingly small when the number of phonon quanta tends towards zero. An interesting setup for on-chip nanomechanical resonators is that of coupling them to electrical microwave cavities for detection and manipulation. Here we show how to achieve a large cavity coupling energy of up to (2π) 1 MHz/nm for metallic beam resonators at tens of MHz. We used focused ion beam (FIB) cutting to produce uniform slits down to 10 nm, separating patterned resonators from their gate electrodes, in suspended aluminum films. We measured the thermomechanical vibrations down to a temperature of 25 mK, and we obtained a low number of about twenty phonons at the equilibrium bath temperature. The mechanical properties of Al were excellent after FIB cutting and we recorded a quality factor of Q ∼ 3 × 10 5 for a 67 MHz resonator at a temperature of 25 mK. Between 0.2K and 2K we find that the dissipation is linearly proportional to the temperature. Keywords nanomechanics, NEMS, quantum limit, detection, dissipationThe measurement of small-amplitude vibrations in mechanical systems is becoming an increasingly interesting problem [1,2]. From the point of view of basic science, the study of mechanical systems close to the quantum limit has attracted a lot of interest recently [3,4]. The endeavor towards the ground state of the harmonic phonon oscillations has been going on in various physical systems such as in optomechanics [5][6][7], or in electrically coupled beam resonators which have been measured using single-electron transistors [4,8], or lately, with on-chip microwave cavities [9][10][11][12].The quantum challenge is posed by several issues, including the relatively low frequency (f 0 ∼ 10 MHz), of the lowest modes in suspended beams. The quantum limit implies stringent requirements on temperature, since hf 0 needs to be small in comparison to k B T . On the other hand, at higher frequencies, the coupling to measuring systems diminishes rapidly. Third, the zero-point vibration amplitudes x ZP = /2mω 0 , where m is the effective mass and ω 0 = 2πf 0 is the angular frequency, are vanishingly small even at the atomic scale. Very recently, O'Connell et al.[13] demonstrated a piezoelectric mechanical mode at the quantum ground state by using a coupling to a superconducting qubit. However, bringing a purely mechanical mode to the quantum limit remains an ongoing quest, with the goal becoming a reality probably in the near future.Micromechanical resonators are also used in applications as detectors. The best devices take advantage of the trend to smaller size and higher frequencies, and will soon approach sensing at the atomic mass unit level [14,15]. They could also be operated as sensors of position, force, or high-frequency electromagnetic fields.For conductive resonators, capacitive coupling to an electrical measuring apparatus is useful for readout. In contrast to magnetomotive or optical detection, one can obtain v...

The measurement of micron-sized mechanical resonators by electrical techniques is difficult, because of the combination of a high frequency and a small mechanical displacement which together suppress the electromechanical coupling. The only electromagnetic technique proven up to the range of several hundred MHz requires the usage of heavy magnetic fields and cryogenic conditions. Here we show how, without the need of either of them, to fully electrically detect the vibrations of conductive nanomechanical resonators up to the microwave regime. We use the electrically actuated vibrations to modulate an LC tank circuit which blocks the stray capacitance, and detect the created sideband voltage by a microwave analyzer. We show the novel technique up to mechanical frequencies of 200 MHz. Finally, we estimate how one could approach the quantum limit of mechanical systems

Single electron transistors (SETs) fabricated from single-walled carbon nanotubes (SWNTs) can be operated as highly sensitive charge detectors reaching sensitivity levels comparable to metallic radio frequency SETs (rf-SETs). Here, we demonstrate how the charge sensitivity of the device can be improved by using the mechanical oscillations of a single-walled carbon nanotube quantum dot. To optimize the charge sensitivity δQ, we drive the mechanical resonator far into the nonlinear regime and bias it to an operating point where the mechanical third order nonlinearity is canceled out. This way we enhance δQ, from 6 μe/(Hz)(1/2) for the static case to 0.97 μe/(Hz)(1/2) at a probe frequency of ∼1.3 kHz.

† these authors contributed equally to this work A capacitive coupling between mechanical resonator and a microwave cavity enables readout and manipulation of the vibrations. We present a setup to carry out such experiments with aluminum membranes fabricated as stamps and transferred in place with micromanipulation. The membrane is held in place by van der Waals forces, and is supported by three microscopic points. We measure the lowest mechanical modes, and conclude the membrane vibrates as an essentially free-free resonator. Sliding clamping conditions are identified via a softening Duffing nonlinearity. The method will enable reduction of clamping losses, while maintaining a narrow vacuum gap for strong capacitive coupling.