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 electromechanical system, which provides additional functionality to the toolbox of microwave optomechanical devices. In addition to using the cavity as an interferometer to detect parametrically modulated mechanical displacement and squeezed thermomechanical motion, we demonstrate that parametric modulation of the nanobeam resonance frequency can realize a phase-sensitive parametric amplifier for intracavity microwave photons. In contrast to many other microwave amplification schemes using electromechanical circuits, the presented technique allows for simultaneous cooling of the mechanical element, which potentially enables this type of optomechanical microwave amplifier to be quantum-limited.
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 als…
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…
We implement a cavity opto-electromechanical system integrating electrical actuation capabilities of nanoelectromechanical devices with ultrasensitive mechanical transduction achieved via intra-cavity optomechanical coupling. Electrical gradient forces as large as 0.40 microN are realized, with simultaneous mechanical transduction sensitivity of 1.5 X 10^-18 m/rtHz representing a three orders of magnitude improvement over any nanoelectromechanical system to date. Opto-electromechanical feedback cooling is demonstrated, exhibiting strong squashing of the in-loop transduction signal. Out-of-loop…
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 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…
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…
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…
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 …
Demonstrating and exploiting the quantum nature of larger, more macroscopic mechanical objects would help us to directly investigate the limitations of quantum-based measurements and quantum information protocols, as well as test long standing questions about macroscopic quantum coherence. The field of cavity opto- and electro-mechanics, in which a mechanical oscillator is parametrically coupled to an electromagnetic resonance, provides a practical architecture for the manipulation and detection of motion at the quantum level. Reaching this quantum level requires strong coupling, interaction t…
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…
A detailed analysis of electromechanically induced absorption (EMIA) in a circuit nano-electromechanical hybrid system consisting of a superconducting microwave resonator coupled to a nanomechanical beam is presented. By performing two-tone spectroscopy experiments we have studied EMIA as a function of the drive power over a wide range of drive and probe tone detunings. We find good quantitative agreement between experiment and theoretical modeling based on the Hamiltonian formulation of a generic electromechanical system. We show that the absorption of microwave signals in an extremely narrow…
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…
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 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…
Two-photon loss mechanisms often accompany a Kerr nonlinearity. The kinetic inductance exhibited by superconducting transmission lines provides an example of a Kerr-like nonlinearity that is accompanied by a nonlinear resistance of the two-photon absorptive type. Such nonlinear dissipation can degrade the performance of amplifiers and mixers employing a Kerr-like nonlinearity as the gain or mixing medium. As an aid for parametric amplifier design, we provide a quantum analysis of a cavity parametric amplifier employing a Kerr nonlinearity that is accompanied by a two-photon absorptive loss. Be…
We present a platform based upon silicon nitride nanomembranes for integrating superconducting microwave circuits with planar acoustic and optical devices such as phononic and photonic crystals. Utilizing tensile stress and lithographic patterning of a silicon nitride nanomembrane we are able to reliably realize planar capacitors with vacuum gap sizes down to $s \approx 80$nm. In combination with spiral inductor coils of micron pitch, this yields microwave ($\approx 8$GHz) resonant circuits of high impedance ($Z_{0} \approx 3.4$k$Ω$) suitable for efficient electromechanical coupling to nanosca…
Radiation pressure within engineered structures has recently been used to couple the motion of nanomechanical objects with high sensitivity to optical and microwave electromagnetic fields. Here, we demonstrate a form of electromechanical crystal for coupling microwave photons and hypersonic phonons by embedding the vacuum-gap capacitor of a superconducting resonator within a phononic crystal acoustic cavity. Utilizing a two-photon resonance condition for efficient microwave pumping and a phononic bandgap shield to eliminate acoustic radiation, we demonstrate large cooperative coupling ($C \app…
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…
Phonon-cavity electromechanics allows the manipulation of mechanical oscillations similar to photon-cavity systems. Many advances on this subject have been achieved in various materials. In addition, the coherent phonon transfer (phonon Rabi oscillations) between the phonon cavity mode and another oscillation mode has attracted many interest in nano-science. Here we demonstrate coherent phonon transfer in a carbon nanotube phonon-cavity system with two mechanical modes exhibiting strong dynamical coupling. The gate-tunable phonon oscillation modes are manipulated and detected by extending the …
We present a theoretical analysis of a novel cavity electromechanical system where a mechanical resonator directly modulates the damping rate kappa of a driven electromagnetic cavity. We show that via a destructive interference of quantum noise, the driven cavity can effectively act like a zero-temperature bath irrespective of the ratio kappa / omega_M, where omega_M is the mechanical frequency. This scheme thus allows one to cool the mechanical resonator to its ground state without requiring the cavity to be in the so-called `good cavity' limit kappa << omega_M.
We consider a superconducting qubit coupled to the nonstationary transmission line cavity with modulated frequency taking into account energy dissipation. Previously, it was demonstrated that in the case of a single nonadiabatical modulation of a cavity frequency there are two channels of a two-level system excitation which are due to the absorption of Casimir photons and due to the counterrotating wave processes responsible for the dynamical Lamb effect. We show that the parametric periodical modulation of the resonator frequency can increase dramatically the excitation probability. Remarkabl…
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…
Experiments to probe the basic quantum properties of motional degrees of freedom of mechanical systems have developed rapidly over the last decade. One promising approach is to use hybrid electromechanical systems incorporating superconducting qubits and microwave circuitry. However, a critical challenge facing the development of these systems is to achieve strong coupling between mechanics and qubits while simultaneously reducing coupling of both the qubit and mechanical mode to the environment. Here we report measurements of a qubit-coupled mechanical resonator system consisting of an ultra-…
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…
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…
Using a quantum noise approach, we discuss the physics of both normal metal and superconducting single electron transistors (SET) coupled to mechanical resonators. Particular attention is paid to the regime where transport occurs via incoherent Cooper-pair tunneling (either via the Josephson quasiparticle (JQP) or double Josephson quasiparticle (DJQP) process). We show that, surprisingly, the back-action of tunneling Cooper pairs (or superconducting quasiparticles) can be used to significantly cool the oscillator. We also discuss the physical origin of negative damping effects in this system, …
We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the SQUID attached to the cavity, and damping due to connection of the cavity to a transmission line are taken into consideration. We study in detail the nonlinear classical dynamics of the cavity field below and above the parametric threshold for the degenerate parametric resonance, featuring regimes of multistability and parametric radiation. We investigate the phase-sensitive amplification of external signals on resonance, as well as amplification of detuned signals, and relate th…
Cavity optomechanical phenomena, such as cooling, amplification or optomechanically induced transparency, emerge due to a strong imbalance in the dissipation rates of the parametrically coupled electromagnetic and mechanical resonators. Here we analyze the reversed dissipation regime where the mechanical energy relaxation rate exceeds the energy decay rate of the electromagnetic cavity. We demonstrate that this regime allows for mechanically-induced amplification (or cooling) of the electromagnetic mode. Gain, bandwidth, and added noise of this electromagnetic amplifier are derived and compare…
We study the parity-symmetry-breaking quantum phase transition (QPT) in a cavity magnonic system driven by a parametric field, where the magnons in a ferrimagnetic yttrium-iron-garnet sphere strongly couple to a microwave cavity. With appropriate parameters, this cavity magnonic system can exhibit a rich phase diagram, including the parity-symmetric phase, parity-symmetry-broken phase, and bistable phase. When increasing the drive strength beyond a critical threshold, the cavity magnonic system undergoes either a first- or second-order nonequilibrium QPT from the parity-symmetric phase with mi…
We address theoretically the optical parametric oscillator based on semiconductor cavity exciton-polaritons under a pulsed excitation. A "hyperspin" formalism is developed which allows, in the case of large number of polaritons, to reduce quantum dynamics of the parametric oscillator wavefunction to the Liouville equation for the classical probability distribution. Implications for the statistics of polariton ensembles are analyzed.
Recent experimental progress in cavity optomechanics has allowed cooling of mesoscopic mechanical oscillators via dynamic backaction provided by the parametric coupling to either an optical or an electrical resonator. Here we analyze the occurrence of normal-mode splitting in backaction cooling at high input power. We find that a hybridization of the oscillator's motion with the fluctuations of the driving field occurs and leads to a splitting of the mechanical and optical fluctuation spectra. Moreover, we find that cooling experiences a classical limitation through the cavity lifetime.
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 present the design, measurement and analysis of a current sensor based on a process of Josephson parametric upconversion in a superconducting microwave cavity. Terminating a coplanar waveguide with a nanobridge constriction Josephson junction, we observe modulation sidebands from the cavity that enable highly sensitive, frequency-multiplexed output of small currents for applications such as transition-edge sensor array readout. We derive an analytical model to reproduce the measurements over a wide range of bias currents, detunings and input powers. Tuning the frequency of the cavity by mor…
Tunable nonlinear electromechanics at the zero-point motion scale
ICFO – Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（ICFO光子科学研究所，巴塞罗那科技研究院）；Center for Hybrid Quantum Networks (Hy-Q), Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔学院混合量子网络中心）；Université de Bordeaux, CNRS, LOMA, UMR 5798（波尔多大学）；Chiral Nano AG（手性纳米股份公司）
We consider the physics of an optomechanical cavity subject to coherent two-phonon driving, i.e. degenerate parametric amplification of the mechanical mode. We show that in such a system, the cavity mode can effectively "inherit" parametric driving from the mechanics, yielding phase-sensitive amplification and squeezing of optical signals reflected from the cavity. We also demonstrate how such a system can be used to perform single-quadrature detection of a near-resonant narrow-band force applied to the mechanics with extremely low added noise from the optics. The system also exhibits strong d…
We analyze the quantum regime of the dynamical backaction cooling of a mechanical resonator assisted by a driven harmonic oscillator (cavity). Our treatment applies to both optomechanical and electromechanical realizations and includes the effect of thermal noise in the driven oscillator. In the perturbative case, we derive the corresponding motional master equation using the Nakajima-Zwanzig formalism and calculate the corresponding output spectrum for the optomechanical case. Then we analyze the strong optomechanical coupling regime in the limit of small cavity linewidth. Finally we consider…
Electrically actuated optomechanical resonators provide a route to quantum-coherent, bidirectional conversion of microwave and optical photons. Such devices could enable optical interconnection of quantum computers based on qubits operating at microwave frequencies. Here we present a novel platform for microwave-to-optical conversion comprising a photonic crystal cavity made of single-crystal, piezoelectric gallium phosphide integrated on pre-fabricated niobium circuits on an intrinsic silicon substrate. The devices exploit spatially extended, sideband-resolved mechanical breathing modes at $\…
We demonstrate fast readout of a double quantum dot (DQD) that is coupled to a superconducting resonator. Utilizing parametric amplification in a nonlinear operational mode, we improve the signal-to-noise ratio (SNR) by a factor of 2000 compared to the situation with the parametric amplifier turned off. With an integration time of 400 ns we achieve a SNR of 76. By studying SNR as a function of the integration time we extract an equivalent charge sensitivity of 8 x 10^{-5} e/root(Hz). The high SNR allows us to acquire a DQD charge stability diagram in just 20 ms. At such a high data rate, it is…
Quantum corrections to transport through a chaotic ballistic cavity are known to be universal. The universality not only applies to the magnitude of quantum corrections, but also to their dependence on external parameters, such as the Fermi energy or an applied magnetic field. Here we consider such parameter dependence of quantum transport in a ballistic chaotic cavity in the semiclassical limit obtained by sending Planck's constant to zero without changing the classical dynamics of the open cavity. In this limit quantum corrections are shown to have a universal parametric dependence which is …
Within the framework of the mean-field approximation, a coherently excited two-dimensional system of weakly repulsive bosons is predicted to show a giant loop scattering when the rotational symmetry is reduced. The considered process combines (i) the parametric decay of the driven condensate into different k-states and (ii) their massive back scattering owing to spontaneous synchronization of several four-wave mixing channels. The hybridization of the direct and inverse scattering processes, which are different and thus do not balance each other, makes the condensate oscillate under constant o…
Mechanical resonators are promising systems for storing and manipulating information. To transfer information between mechanical modes, either direct coupling or an interface between these modes is needed. In previous works, strong coupling between different modes in a single mechanical resonator and direct interaction between neighboring mechanical resonators have been demonstrated. However, coupling between distant mechanical resonators, which is a crucial request for long-distance classical and quantum information processing using mechanical devices, remains an experimental challenge. Here,…
Generating non-reciprocal radio frequency transduction plays important roles in a wide range of research and applications, and an aspiration is to integrate this functionality into micro-circuit without introducing magnetic field, which, however, remains challenging. By designing a 1D artificial lattice structure with neighbor-interaction engineered parametrically, we predicted a non-reciprocity transduction with giant unidirectionality. We then experimentally demonstrated the phenomenon on a nano-electromechanical chip fabricated by conventional complementary metal-silicon processing. A unidi…
