The combination of low mass density, high frequency, and high quality-factor of mechanical resonators made of two-dimensional crystals such as graphene 1-8 make them attractive for applications in force sensing/mass sensing, and exploring the quantum regime of mechanical motion. Microwave optomechanics with superconducting cavities 9-14 offers exquisite position sensitivity 10 and enables the preparation and detection of mechanical systems in the quantum ground state 15,16 . Here, we demonstrate coupling between a multilayer graphene resonator with quality factors up to 220,000 and a high-Q superconducting cavity. Using thermo-mechanical noise as calibration, we achieve a displacement sensitivity of 17 fm/ √ Hz. Optomechanical coupling is demonstrated by optomechanically induced reflection (OMIR) and absorption (OMIA) of microwave photons [17][18][19] . We observe 17 dB of mechanical microwave amplification 13 and signatures of strong optomechanical backaction. We extract the cooperativity C, a characterization of coupling strength, quantitatively from the measurement with no free parameters and find C = 8, promising for the quantum regime of graphene motion. Here, we present a multilayer graphene mechanical resonator coupled to a superconducting cavity. Using a deterministic all-dry transfer technique 22 and a novel microwave coupling design, we are able to combine these two without sacrificing the exceptional intrinsic properties of either. Although multilayer graphene has a higher mass than a monolayer, it could be advantageous for coupling to a superconducting cavity due to its lower electrical resistance. In Figure 2, we characterize the mechanical properties of the multilayer graphene resonator using a homodyne measurement scheme 9 . Here, the cavity is used as an interferometer to detect motion while injecting a microwave signal near ω c and exciting the mechanical resonator with an AC voltage applied to the gate. The mechanical resonance frequency is much larger than the cavity linewidth (ω m /κ ∼ 150), placing us in the sideband resolved limit, a prerequisite for ground state cooling. The cavity can also be used to detect the undriven motion, such as thermomechanical noise of the drum shown in the inset of Figure 2(a) corresponding to a mechanical mode temperature of 96 mK (see SI for additional details). The thermal motion peak serves as a calibration for the displacement sensitivity. While driving the cavity at its resonance and utilizing its full dynamic range before the electrical nonlinearity set in (-41 dBm injected power) we estimate a displacement sensitivity for mechanical motion of 17 fm/ √ Hz. Using a DC voltage applied to the gate electrode, we can also tune the frequency of the multilayer graphene resonator shown in Figure 2(b). The decrease in resonance frequency ω m for non-zero gate voltage is due to electrostatic softening of the spring constant and has been observed before 3 .In Figure 3, we demonstrate optomechanical coupling between the multilayer graphene mechanical resona...
We have used the mechanical motion of a carbon nanotube (CNT) as a probe of the average charge on a quantum dot. Variations of the resonance frequency and the quality factor are determined by the change in average charge on the quantum dot during a mechanical oscillation. The average charge, in turn, is influenced by the gate voltage, the bias voltage, and the tunnel rates of the barriers to the leads. At bias voltages that exceed the broadening due to tunnel coupling, the resonance frequency and quality factor show a double dip as a function of gate voltage. We find that increasing the current flowing through the CNT at the Coulomb peak does not increase the damping, but in fact decreases damping. Using a model with energy-dependent tunnel rates, we obtain quantitative agreement between the experimental observations and the model. We theoretically compare different contributions to the single-electron induced nonlinearity, and show that only one term is significant for both the Duffing parameter and the mode coupling parameter. We also present additional measurements which support the model we develop: Tuning the tunnel barriers of the quantum dot to the leads gives a 200-fold decrease of the quality factor. Single-electron tunneling through an excited state of the CNT quantum dot also changes the average charge on the quantum dot, bringing about a decrease in the resonance frequency. In the Fabry-Pérot regime, the absence of charge quantization results in a spring behavior without resonance frequency dips, which could be used, for example, to probe the transition from quantized to continuous charge with a nanomechanical resonator.
The quantum behaviour of mechanical resonators is a new and emerging field driven by recent experiments reaching the quantum ground state. The high frequency, small mass, and large quality-factor of carbon nanotube resonators make them attractive for quantum nanomechanical applications. A common element in experiments achieving the resonator ground state is a second quantum system, such as coherent photons or a superconducting device, coupled to the resonators motion. For nanotubes, however, this is a challenge due to their small size. Here, we couple a carbon nanoelectromechanical (NEMS) device to a superconducting circuit. Suspended carbon nanotubes act as both superconducting junctions and moving elements in a Superconducting Quantum Interference Device (SQUID). We observe a strong modulation of the flux through the SQUID from displacements of the nanotube. Incorporating this SQUID into superconducting resonators and qubits should enable the detection and manipulation of nanotube mechanical quantum states at the single-phonon level.
In physical systems, decoherence can arise from both dissipative and dephasing processes. In mechanical resonators, the driven frequency response measures a combination of both, whereas 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 nonlinear dephasing mechanism. Our results highlight the importance of time-domain techniques for understanding dissipation in nanomechanical resonators, and the relevance of decoherence mechanisms in nanotube mechanics.
Superconducting microwave resonators (SMR) with high quality factors have become an important technology in a wide range of applications. Molybdenum-Rhenium (MoRe) is a disordered superconducting alloy with a noble surface chemistry and a relatively high transition temperature.These properties make it attractive for SMR applications, but characterization of MoRe SMR has not yet been reported. Here, we present the fabrication and characterization of SMR fabricated with a MoRe 60-40 alloy. At low drive powers, we observe internal quality-factors as high as 700,000. Temperature and power dependence of the internal quality-factors suggest the presence of the two level systems from the dielectric substrate dominating the internal loss at low temperatures. We further test the compatibility of these resonators with high temperature processes such as for carbon nanotube CVD growth, and their performance in the magnetic field, an important characterization for hybrid systems. The SMR were designed in a coplanar waveguide geometry and fabricated on a sapphire wafer (substrate thickness ∼ 430 µm) in order to minimize dielectric losses. As cleaning of the substrate surface seems to play an important role in minimizing two-level systems 24 , an extensive cleaning of the sapphire wafer is performed with phosphoric acid (H 3 PO 4 )at 75 ℃ for 30 minutes followed by rinsing in DI water for 2 hours. After exposing the fresh surface of the wafer, it was immediately loaded in the vacuum chamber for MoRe film 2 deposition. Using an RF sputtering system, we deposit a 145 nm thick MoRe film with a continuous flow of Ar (pressure 1.5 × 10 −3 mTorr) from a ∼ 99.95 % purity, single target of MoRe. The SMR designs were patterned using e-beam lithography on a three layer mask (S1813/W(Tungsten)/PMMA-950) followed by the etching of MoRe by SF 6 /He plasma. We use a frequency multiplexing scheme to side-couple multiple quarter wavelength resonators of different frequencies to a common transmission line. Figure 1(a) shows an optical microscope image of such a resonator after the fabrication process. The quarter-wavelength coplanar waveguide resonator is formed by terminating a transmission line (characteristic impedance of 50 Ω and 10 µm wide trace) to the ground plane. For microwave measurements, the samples were mounted in a light-tight microwave box and were cooled down in a dilution fridge or a He-3 cryostat with sufficient attenuation at each temperature stage to thermalize the microwave photons reaching the sample. A schematic of the attenuation scheme in the dilution refrigerator is shown in Figure 1(b). For these sputtered thin films, we measure a typical room temperature resistivity of 88 µΩ-cm, RRR ∼ 1.2 and T c ∼ 9.2 K.The low power transmission response S 21 for a side-coupled quarter wavelength resonator near its resonance frequency f 0 can be modeled bywhereis the loaded quality-factor, Q c is the coupling quality-factor and Q i is the internal quality-factor of the resonator. Figure 1(c) shows the measurement of the tr...
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