Coupled electromechanical resonators that can be independently driven/detected and easily integrated with external circuits are essential for exploring mechanical modes based signal processing. Here, we present a room temperature phonon-cavity electromechanical system, consisting of two distinct resonators: a silicon nitride electromechanical drum capacitively coupled to an aluminum one. We demonstrate electromechanically induced transparency and amplification in a two-tone driving scheme and observe the phonon-cavity force affecting the mechanical damping rates of both movable objects. We also develop an analytical model based on linearly coupled motion equations, which captures the optomechanical features in the classical limit and enables to fit quantitatively our measurements. Our results open up new possibilities in the study of phonon-cavity based signal processing in the classical and potentially in the future in the quantum regimes.
Light-matter interaction in optomechanical systems is the foundation for ultra-sensitive detection schemes [1,2] as well as the generation of phononic and photonic quantum states [3-10]. Electromechanical systems realize this optomechanical interaction in the microwave regime. In this context, capacitive coupling arrangements demonstrated interaction rates of up to 280 Hz [11]. Complementary, early proposals [12-15] and experiments [16,17] suggest that inductive coupling schemes are tunable and have the potential to reach the vacuum strong-coupling regime. Here, we follow the latter approach b…
Fabrication processes involving anhydrous hydrofluoric vapor etching are developed to create high-$Q$ aluminum superconducting microwave resonators on free-standing silicon membranes formed from a silicon-on-insulator wafer. Using this fabrication process, a high-impedance $8.9$GHz coil resonator is coupled capacitively with large participation ratio to a $9.7$MHz micromechanical resonator. Two-tone microwave spectroscopy and radiation pressure back-action are used to characterize the coupled system in a dilution refrigerator down to temperatures of $T_f = 11$~mK, yielding a measured electrome…
Evanescent coupling between a silica optical microbottle resonator and a GaAs electromechanical resonator is demonstrated. This coupling provides high optical sensitivity and efficient piezoelectric controllability of mechanical motion. Opto-electro-mechanical feedback control based on optomechanical detection and electromechanical control is performed in both heating and cooling regimes at room temperature. This feedback scheme can be extended to the efficient control of thermal mechanical motion in electromechanical resonators with arbitrary structures and materials.
We present a hybrid system consisting of a superconducting coplanar waveguide resonator coupled to a nanomechanical string and a transmon qubit acting as nonlinear circuit element. We perform spectroscopy for both the transmon qubit and the nanomechanical string. Measuring the ac-Stark shift on the transmon qubit as well as the electromechanically induced absorption on the string allows us to determine the average photon number in the microwave resonator in both the low and high power regimes. In this way, we measure photon numbers that are up to nine orders of magnitude apart. We find a quant…
Coupling an electromechanical resonator with carbon-nanotube quantum dots is a significant method to control both the electronic charge and the spin quantum states. By exploiting a novel micro-transfer technique, we fabricate two strongly-coupled and electrically-tunable mechanical resonators on a single carbon nanotube for the first time. The frequency of the two resonators can be individually tuned by the bottom gates, and strong coupling is observed between the electron charge and phonon modes of each resonator. Furthermore, the conductance of either resonator can be nonlocally modulated by…
We demonstrate squeezing of a strongly interacting opto-electromechanical system using a parametric drive. By employing real-time feedback on the phase of the pump at twice the resonance frequency the thermo-mechanical noise is squeezed beyond the 3 dB instability limit. Surprisingly, this method can also be used to generate highly nonlinear states. We show that using the parametric drive with feedback on, classical number-like and cat-like states can be prepared. This presents a valuable electro-optomechanical state-preparation protocol that is extendable to the quantum regime.
Using graphene resonator, we perform electromechanical measurements in quantum Hall regime to probe the coupling between a quantum Hall (QH) system and its mechanical motion. Mechanically perturbing the QH state through resonance modifies the DC resistance of the system and results in a Fano-lineshape due to electronic interference. Magnetization of the system modifies the resonator's equilibrium position and effective stiffness leading to changes in resonant frequency. Our experiments show that there is an intimate coupling between the quantum Hall state and mechanics - electron transport is …
Magnetically coupling a nano-mechanical resonator to a double quantum dot confining two electrons can enable the manipulation of a single electron spin and the readout of the resonator's natural frequency. When the Larmor frequency matches the resonator frequency, the electron spin in one of the dots can be selectively flipped by the magnetised resonator. By simultaneously measuring the charge state of the two-electron double quantum dots, this transition can be detected thus enabling the natural frequency of the mechanical resonator to be determined.
We demonstrate a sideband-resolved cavity electromechanical system operating at room temperature. The mechanical resonator, a strongly pre-stressed silicon nitride string, is dielectrically coupled to a three-dimensional microwave cavity made of copper. The electromechanical coupling is characterized by two measurements, the cavity-induced eigenfrequency shift of the mechanical resonator and the optomechanically induced transparency. While the former is dominated by dielectric effects, the latter reveals a clear signature of the dynamical backaction of the cavity field on the resonator. This u…
A suspended, doubly clamped single wall carbon nanotube is characterized as driven nano-electromechanical resonator at cryogenic temperatures. Electronically, the carbon nanotube displays small bandgap behaviour with Coulomb blockade oscillations in electron conduction and transparent contacts in hole conduction. We observe the driven mechanical resonance in dc-transport, including multiple higher harmonic responses. The data shows a distinct negative frequency tuning at finite applied gate voltage, enabling us to electrostatically decrease the resonance frequency to 75% of its maximum value. …
The electrical response of two-dimensional electron gas to vibrations of a nanomechanical cantilever containing it is studied. Vibrations of perpendicularly oriented cantilevers are experimentally shown to change oppositely the conductivity near their bases. This indicates the piezoelectric nature of electromechanical coupling. A physical model is developed, which quantitatively explains the experiment. It shows that the main origin of the conductivity change is a rapid change in the mechanical stress on the boundary between suspended and non-suspended areas, rather than the stress itself.
In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that the coupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where …
Control over the quantum states of a massive oscillator is important for several technological applications and to test the fundamental limits of quantum mechanics. Addition of an internal degree of freedom to the oscillator could be a valuable resource for such control. Recently, hybrid electromechanical systems using superconducting qubits, based on electric-charge mediated coupling, have been quite successful. Here, we realize a hybrid device, consisting of a superconducting transmon qubit and a mechanical resonator coupled using the magnetic-flux. The coupling stems from the quantum-interf…
The widespread availability of quantum entanglement with photons, in the guise of two-mode squeezed states, can be attributed to the phenomenon of parametric down-conversion. A reinterpretation of this effect with macroscopic mechanical objects can offer a route towards a purely mechanical entanglement and the unique possibility of probing the quantum mechanical nature of our everyday classical world. In spite of this prospect, mechanical two-mode squeezed states have remained elusive due to the inability to recreate the nonlinear interaction at the heart of this phenomenon in the mechanical d…
We consider an electromechanical system where a microwave cavity is coupled to a mechanical resonator, with a mechanical frequency twice the microwave frequency. In this regime, the effective photon-phonon interaction is equivalent to that of a degenerate parametric amplifier, instead of the typical radiation pressure interaction. If the mechanical resonator is strongly driven, it undergoes a phase transition to a state where the energy pumped into the mechanical mode is entirely converted to the photonic mode. Quantum fluctuations smear this phase transition. We describe these effects with a …
We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.
We report on the experimental demonstration of atomically thin molybdenum disulfide (MoS2)-graphene van der Waals (vdW) heterostructure nanoelectromechanical resonators with ultrawide frequency tuning. With direct electrostatic gate tuning, these vdW resonators exhibit exceptional tunability, in general, Δf/f0 >200%, for continuously tuning the same device and the same mode (e.g., from ~23 to ~107MHz), up to Δf/f0 = 370%, the largest fractional tuning range in such resonators to date. This remarkable electromechanical resonance tuning is investigated by two different analytical models and fini…
We consider a single electron transistor where the central island can oscillate. It has been shown that for weak coupling of the elastic and electric degrees of freedom the position of the island fluctuates with a small variation of the current through the device. In this paper we consider the strong coupling limit. We show that the system undergoes a static mechanical instability that is responsible for the opening of a gap in the current voltage characteristics even at the degeneracy point. We provide an analytical description of the transition point. We also discuss how the mechanical natur…
We study nanoelectromechanical resonators fabricated from suspended flakes of NbSe$_2$ (thickness$\sim$30-50 nm) to probe charge density wave (CDW) physics at nanoscale. Variation of elastic and electronic properties accompanying the CDW phase transition (around 30 K) are investigated simultaneously using the devices as self-sensing heterodyne mixers. Elastic modulus is observed to change by 10 per cent, an amount significantly larger than what had been reported earlier in the case of bulk crystals. We also study the modulation of conductance by electric field effect, and examine its relation …
We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton--mechanical mode and a nonlinear transmon--mechanical mode interaction in the strong coupling regime. Together with the strong resonator--transmon interaction, these properties provide intriguing oppor…
Imaging the vibrations of nanomechanical resonators means measuring their flexural mode shapes from the dependence of their frequency response on in-plane position. Applied to two-dimensional resonators, this technique provides a wealth of information on the mechanical properties of atomically-thin membranes. We present a simple and robust system to image the vibrations of few layer graphene (FLG) resonators at room temperature and in vacuum with an in-plane displacement precision of $\approx0.20$ $μ$m. It consists of a sturdy vacuum enclosure mounted on a three-axis micropositioning stage and…
We consider the steady states of a harmonic oscillator coupled so strongly to a two-level system (a qubit) that the rotating wave approximation cannot be made. The Hamiltonian version of this model is known as the $E\otimesβ$ Jahn-Teller model. The semiclassical version of this system exhibits a fixed point bifurcation, which in the quantum model leads to a ground state with substantial entanglement between the oscillator and the qubit. We show that the dynamical bifurcation survives in a dissipative quantum description of the system, amidst an even richer bifurcation structure. We propose two…
The combination of high frequency vibrations and metallic transport in graphene makes it a unique material for nano-electromechanical devices. In this letter, we show that graphene-based nano-electromechanical devices are extremely well suited for charge pumping, due to the sensitivity of its transport coefficients to perturbations in electrostatic potential and mechanical deformations, with the potential for novel small scale devices with useful applications.
We use suspended graphene electromechanical resonators to study the variation of resonant frequency as a function of temperature. Measuring the change in frequency resulting from a change in tension, from 300 K to 30 K, allows us to extract information about the thermal expansion of monolayer graphene as a function of temperature, which is critical for strain engineering applications. We find that thermal expansion of graphene is negative for all temperatures between 300K and 30K. We also study the dispersion, the variation of resonant frequency with DC gate voltage, of the electromechanical m…
We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor $Q_i$. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure $Q_i$ as function of frequency, power and temperature. We observe a linear increase of $Q_i$ with frequency, as predicted by …
Recent achievements in the field of gate defined semiconductor quantum dots reinforce the concept of a spin-based quantum computer consisting of nodes of locally connected qubits which communicate with each other via superconducting circuit resonator photons. In this work we theoretically demonstrate a versatile set of quantum gates between adjacent spin qubits defined in semiconductor quantum dots situated within the same node of such a spin-based quantum computer. The electric dipole acquired by the spin of an electron that moves across a double quantum dot potential in a magnetic field grad…
We fabricate a microscale electromechanical system, in which a suspended superconducting membrane, treated as a mechanical oscillator, capacitively couples to a superconducting microwave resonator. As the microwave driving power increases, nonmonotonic dependence of the resonance frequency of the mechanical oscillator on the driving power has been observed. We also demonstrate the optical switching of the resonance frequency of the mechanical oscillator. Theoretical models for qualitative understanding of our experimental observations are presented. Our experiment may pave the way for the appl…
Superconducting circuits present a promising platform with which to realize a quantum refrigerator. Motivated by this, we fabricate and perform spectroscopy of a gated Cooper-pair box, capacitively coupled to two superconducting coplanar waveguide resonators with different frequencies. We experimentally demonstrate the strong coupling of a charge qubit to two superconducting resonators, with the ability to perform voltage driving of the qubit at GHz frequencies. We go on to discuss how the measured device could be modified to operate as a cyclic quantum refrigerator by terminating the resonato…
We propose a circuit quantum electrodynamics (QED) realization of a protocol to generate a Greenberger-Horne-Zeilinger (GHZ) state for $N$ superconducting transmon qubits homogeneously coupled to a superconducting transmission line resonator in the dispersive limit. We derive an effective Hamiltonian with pairwise qubit exchange interactions of the XY type, $\tilde{g}(XX+YY)$, that can be globally controlled. Starting from a separable initial state, these interactions allow to generate a multi-qubit GHZ state within a time $t_{\text{GHZ}}\sim \tilde{g}^{-1}$. We discuss how to probe the non-lo…
We study InAs nanowire resonators fabricated on sapphire substrate with a local gate configuration. The key advantage of using an insulating sapphire substrate is that it results in a reduced parasitic capacitance thus allowing both wide bandwidth actuation and detection using a network analyzer as well as signal detection at room temperature. Both in-plane and out-of-plane vibrational modes of the nanowire can be driven and the non-linear response of the resonators studied. In addition this technique enables the study of variation of thermal strains due to heating in nanostructures
A suspended, doubly clamped single wall carbon nanotube is characterized at cryogenic temperatures. We observe specific switching effects in dc-current spectroscopy of the embedded quantum dot. These have been identified previously as nano-electromechanical self-excitation of the system, where positive feedback from single electron tunneling drives mechanical motion. A magnetic field suppresses this effect, by providing an additional damping mechanism. This is modeled by eddy current damping, and confirmed by measuring the resonance quality factor of the rf-driven nano-electromechanical resona…
Waveguide resonators are crucial elements in sensitive astrophysical detectors [1] and circuit quantum electrodynamics (cQED) [2]. Coupled to artificial atoms in the form of superconducting qubits [3, 4], they now provide a technologically promising and scalable platform for quantum information processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots [13] or mechanical oscillators [14, 15] has been explored to realize hybrid systems with extended functionality. Here, we couple a superconducting copla…
Chaos enables the emergence of randomness in deterministic physical systems. Therefore it can be exploited for the conception of true random number generators (RNG) mandatory in classical cryptography applications. Meanwhile, nanomechanical oscillators, at the core of many on-board functionalities such as sensing, reveal as excellent candidates to behave chaotically. This is made possible thanks to intrinsic mechanical nonlinearities emerging at the nanoscale. Here we present a platform gathering a nanomechanical oscillator and its integrated capacitive actuation. Using a modulation of the res…
We consider a parametrically driven Klein--Gordon system describing micro- and nano-devices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrodinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein--Gordon system through the discrete Schrodinger equation. We show that a parametric driving can not only destabilize onsite bright solitons, but also stabilize intersite bright discre…
Non-Hermitian Hamiltonians can give rise to exceptional points (EPs) which have been extensively explored with nominally identical coupled resonators. Here a non-Hermitian electromechanical system is developed which hosts vibration modes that differ massively in their spatial profile, frequency and even the sign of their dissipation. An optomechanical-like parametric modulation is employed to dynamically couple 2 of these disparate modes and in the appropriate parameter regime their imaginary eigenvalues coalesce whilst their normal modes split. The presence of this virtual EP is confirmed via…
The monolithic integration of electromechanical transduction at the nanoscale with advanced CMOS is among the most important challenges of semiconductor electronic systems to leverage the multi-domain sensing, actuation, and resonance properties of nano-mechanical systems. Here we report on the demonstration of vibrating devices enabled by atomically engineered ferroelectric Hf0.5Zr0.5O2 thin films with a variety of mechanical resonance modes with frequencies (f0) between 340kHz - 13GHz and frequency-quality (Q) factor products (f0 x Q) up to 3.97 x 10^12. Experiments based on electrical and o…
We study a resonator coupled to a generic detector and calculate the noise spectra of the two sub-systems. We describe the coupled system by a closed, linear, set of Langevin equations and derive a general form for the finite frequency noise of both the resonator and the detector. The resonator spectrum is the well-known thermal form with an effective damping, frequency shift and diffusion term. In contrast, the detector noise shows a rather striking Fano-like resonance, i.e. there is a resonance at the renormalized frequency, and an anti-resonance at the bare resonator frequency. As examples …
Efficient energy transfer often occurs between oscillation modes in a resonator when they are tuned to internal resonance. We design the eigenfrequencies of two vibrational modes of an electromechanical resonator to be close to a ratio of 3:1 and demonstrate that the energy supplied to the upper mode can be controllably transferred to the lower mode. With the lower mode vibrating with a period tripled that of the upper mode, the discrete time-translation symmetry imposed by the periodic drive is broken. The lower mode settles into one of three stable period-tripled states with different phases…
We have realized a nano-electromechanical hybrid system consisting of a silicon nitride beam dielectrically coupled to a superconducting microwave resonator. We characterize the sample by making use of the Duffing nonlinearity of the strongly driven beam. In particular, we calibrate the amplitude spectrum of the mechanical motion and determine the electromechanical vacuum coupling. A high quality factor of 480,000 at a resonance frequency of 14 MHz is achieved at 0.5 K. The experimentally determined electromechanical vacuum coupling of 11.5 mHz is quantitatively compared with finite element ba…
The studies of mechanical resonators in the quantum regime not only provide insight into the fundamental nature of quantum mechanics of massive objects, but also introduce promising platforms for novel hybrid quantum technologies. Here we demonstrate a configurable interaction between a superconducting qubit and many acoustic modes in the quantum regime. Specifically, we show how consecutive Landau-Zener-Stückelberg (LZS) tunneling type of transitions, which take place when a system is tuned through an avoided crossing of the coupled energy levels, interfere in a multimode system. The work pro…
We theoretically investigate the analog of electromagnetically induced transparency, absorption and parametric amplification in a hybrid opto-electromechanical system consisting of an optical cavity and a microwave cavity coupled to a common nanomechanical resonator. When the two cavity modes are driven on their respective red sidebands by two pump beams and a probe beam is applied to the optical cavity to monitor the optical response of the hybrid system, we find that a transparency window appears in the probe transmission spectrum due to destructive interference. When the optical cavity is p…
We present a scheme for photonic transistors based on photons and phonons in a cavity electromechanical system, which is consisted of a superconducting microwave cavity coupled to a nanomechanical resonator. Control of the propagation of photons is achieved through the interaction of microwave field (photons) and nanomechanical vibrations (phonons). By calculating the transmission spectrum of the signal field, we show that the signal field can be efficiently attenuated or amplified, depending on the power of a second `gating'(pump) field. This scheme may be a promising candidate for single-pho…
Due to their exceptional mechanical and optical properties, dielectric silicon nitride (SiN) micromembrane resonators have become the centerpiece of many optomechanical experiments. Efficient capacitive coupling of the membrane to an electrical system would facilitate exciting hybrid optoelectromechanical devices. However, capacitive coupling of such dielectric membranes is rather weak. Here we add a single layer of graphene on SiN micromembranes and compare electromechanical coupling and mechanical properties to bare dielectric membranes and to membranes metallized with an aluminium layer. Th…
Nanoelectromechanical systems (NEMS), utilising localised mechanical vibrations, were pioneered for sensors, signal processors and to study macroscopic quantum mechanics. Increasingly the concept of integrating multiple mechanical elements via electrical/optical means has emerged as a challenge towards NEMS circuits. Here we develop phononic crystal waveguides (PnC WGs), using a 1-dimensional array of suspended membranes, that offer purely mechanical means to integrate isolated NEMS resonators. In the first steps to this objective, we demonstrate the PnC WG can support and guide mechanical vib…
As the magnetic field penetrates the surface of a superconductor, it results in the formation of flux-vortices. It has been predicted that the flux-vortices will have a charged vortex core and create a dipolelike electric field. Such a charge trapping in vortices is particularly enhanced in high-T$_c$ superconductors (HTS). Here, we integrate a mechanical resonator made of a thin flake of HTS Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ into a microwave circuit to realize a cavity-electromechanical device. Due to the exquisite sensitivity of cavity-based devices to the external forces, we directly detect the…
We propose a scheme for entangling the motion of two massive objects in a hybrid electromechanical architecture. The entanglement is generated due to the interaction of two mechanical oscillators with a mediating superconducting qubit. We show that the generated macroscopic entangled states are non-Gaussian and its lifetime is limited by coherence time of the qubit. The entanglement is attainable in a wide range of parameters with appropriate control of the qubit. We confirm performance of our scheme by numerically solving the quantum optical master equation including sources of noise. The eff…
Under a strong quantum measurement, the motion of an oscillator is disturbed by the measurement back-action, as required by the Heisenberg uncertainty principle. When a mechanical oscillator is continuously monitored via an electromagnetic cavity, as in a cavity optomechanical measurement, the back-action is manifest by the shot noise of incoming photons that becomes imprinted onto the motion of the oscillator. Following the photons leaving the cavity, the correlations appear as squeezing of quantum noise in the emitted field. Here we observe such "ponderomotive" squeezing in the microwave dom…
We investigate the electromechanical actuation of a pair of suspended silicon nitride membranes forming a monolithic optomechanical array. By controlling the membrane resonators' tensile stress via a piezoelectrically controlled compressive force applied to the membrane chip we demonstrate noninvasive tuning of their mechanical mode spectrum, as well as strong intermode electromechanical coupling. Piezoelectric actuation is also shown to enhance the nonlinear response of the membranes, which is evidenced either by parametric amplification of the fundamental mode thermal fluctuations or by reso…
Superconducting systems have a long history of use in experiments that push the frontiers of mechanical sensing. This includes both applied and fundamental research, which at present day ranges from quantum computing research and efforts to explore Planck-scale physics to fundamental studies on the nature of motion and the quantum limits on our ability to measure it. In this paper, we first provide a short history of the role of superconducting circuitry and devices in mechanical sensing, focusing primarily on efforts in the last decade to push the study of quantum mechanics to include motion …
Microwave optomechanical circuits have been demonstrated in the past years to be extremely powerfool tools for both, exploring fundamental physics of macroscopic mechanical oscillators as well as being promising candidates for novel on-chip quantum limited microwave devices. In most experiments so far, the mechanical oscillator is either used as a passive device element and its displacement is detected using the superconducting cavity or manipulated by intracavity fields. Here, we explore the possibility to directly and parametrically manipulate the mechanical nanobeam resonator of a cavity el…
In this report, we study electromechanical properties of a suspended InAs nanowire (NW) resonator. At low temperatures, the NW acts as the island of a single electron transistor (SET) and we observe a strong coupling between electrons and mechanical modes at resonance; the rate of electron tunneling is approximately 10 times the resonant frequency. Above and below the mechanical resonance, the magnitude of Coulomb peaks is different and we observe Fano resonance in conductance due to the interference between two contributions to potential of the SET. The quality factor ($Q$) of these devices i…
We study the quantum measurement of a cantilever using a parametrically-coupled electromagnetic cavity which is driven at the two sidebands corresponding to the mechanical motion. This scheme, originally due to Braginsky et al. [V. Braginsky, Y. I. Vorontsov, and K. P. Thorne, Science 209, 547 (1980)], allows a back-action free measurement of one quadrature of the cantilever's motion, and hence the possibility of generating a squeezed state. We present a complete quantum theory of this system, and derive simple conditions on when the quantum limit on the added noise can be surpassed. We also s…
We propose a scheme involving a Cooper pair transistor (CPT) embedded in a superconducting microwave cavity, where the CPT serves as a charge tunable quantum inductor to facilitate ultra-strong coupling between photons in the cavity and a nano- to meso-scale mechanical resonator. The mechanical resonator is capacitively coupled to the CPT, such that mechanical displacements of the resonator cause a shift in the CPT inductance and hence the cavity's resonant frequency. The amplification provided by the CPT is sufficient for the zero point motion of the mechanical resonator alone to cause a sign…
We develop an all-integrated optoelectromechanical system that operates in the superhigh frequency band. This system is based on an ultrahigh-Q slotted photonic crystal (PhC) nanocavity formed by two PhC membranes, one of which is patterned with electrode and capacitively driven. The strong simultaneous electromechanical and optomechanical interactions yield efficient electrical excitation and sensitive optical transduction of the bulk acoustic modes of the PhC membrane. These modes are identified up to a frequency of 4.20 GHz, with their mechanical Q factors ranging from 240 to 1,730. Directl…
