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, we report the experimental observation of strong indirect coupling between separated mechanical resonators in a graphene-based electromechanical system. The coupling is mediated by a far-off-resonant phonon cavity through virtual excitations via a Raman-like process. By controlling the resonant frequency of the phonon cavity, the indirect coupling can be tuned in a wide range. Our results may lead to the development of gate-controlled all-mechanical devices and open up the possibility of long-distance quantum mechanical experiments.
A theory is presented showing that, under appropriate conditions, a ferroelectric in a cavity resonator can emit superradiant pulses. Initially, the ferroelectric has to be prepared in a nonequilibrium state from which it relaxes emitting a coherent pulse in the infrared region. Polarization dipolar waves play the role of the triggering mechanism initiating the beginning of the process.
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…
The resemblance between electrons and optical waves has strongly driven the advancement of mesoscopic physics. However, electron waves have yet to be understood in open cavity structures which have provided contemporary optics with rich insight towards non-Hermitian systems and complex interactions between resonance mode. Here, we report the realization of an open cavity resonator in a two-dimensional electronic system. We studied the resonant electron modes within the cavity and resolved the signatures of longitudinal and transverse quantization, showing that the modes are robust despite the …
We explore the prospects and benefits of combining the techniques of cavity optomechanics with efforts to image spins using magnetic resonance force microscopy (MRFM). In particular, we focus on a common mechanical resonator used in cavity optomechanics -- high-stress stoichiometric silicon nitride (Si$_3$N$_4$) membranes. We present experimental work with a trampoline membrane resonator that has a quality factor above $10^6$ and an order of magnitude lower mass than a comparable standard membrane resonators. Such high-stress resonators are on a trajectory to reach 0.1 $\rm{aN}/\sqrt{\rm{Hz}}$…
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…
We investigate long-range coherent and dissipative coupling between two spatially separated magnets while both are coupled to a microwave cavity. A careful examination of the system shows that the indirect interaction between two magnon modes is dependent on their individual mechanisms of direct coupling to the cavity. If both magnon modes share the same form of coupling to the cavity (either coherent or dissipative), then the indirect coupling between them will produce level repulsion. Conversely, if the magnon modes have different forms of coupling to the cavity (one coherent and one dissipa…
We investigate the regime of strong coupling of an ensemble of two-dimensional electrons to a single-mode cavity resonator. In particular, we realized such a regime of light-matter interaction by coupling the cyclotron motion of a collection of electrons on the surface of liquid helium to the microwave field in a semi-confocal Fabry-Perot resonator. For the co-rotating component of the microwave field, the strong coupling is pronouncedly manifested by the normal-mode splitting in the spectrum of coupled field-particle motion. We present a complete description of this phenomenon based on classi…
Nanomechanical resonators with increasingly high quality factors are enabled following recent insights into energy storage and loss mechanisms in nanoelectromechanical systems (NEMS). Consequently, efficient, non-dissipative transduction schemes are required to avoid the dominating influence of coupling losses. We present an integrated NEMS transducer based on a microwave cavity dielectrically coupled to an array of doubly-clamped pre-stressed silicon nitride beam resonators. This cavity-enhanced detection scheme allows resolving the resonators' Brownian motion at room temperature while preser…
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 investigate spin states of few electrons in a double quantum dot by coupling them weakly to a magnetic field resilient NbTiN microwave resonator. We observe a reduced resonator transmission if resonator photons and spin singlet states interact. This response vanishes in a magnetic field once the quantum dot ground state changes from a spin singlet into a spin triplet state. Based on this observation, we map the two-electron singlet-triplet crossover by resonant spectroscopy. By measuring the resonator only, we observe Pauli spin blockade known from transport experiments at finite source-dra…
In an optomechanical setup, the coupling between cavity and resonator can be increased by tuning them to the same frequency. We study this interaction between a carbon nanotube resonator and a radio-frequency circuit. In this resonant regime, the vacuum optomechanical coupling is enhanced by the DC voltage coupling the cavity and the mechanical resonator. Using the cavity to detect the nanotube's motion, we observe and simulate interference between mechanical and electrical oscillations. We measure the mechanical ring-down and show that further improvements to the system could enable measureme…
The combination of low mass density, high frequency, and high quality-factor of mechanical resonators made of two-dimensional crystals such as graphene make them attractive for applications in force sensing/mass sensing, and exploring the quantum regime of mechanical motion. Microwave optomechanics with superconducting cavities offers exquisite position sensitivity and enables the preparation and detection of mechanical systems in the quantum ground state. Here, we demonstrate coupling between a multilayer graphene resonator with quality factors up to 220,000 and a high-$\textit{Q}$ supercondu…
We develop a theoretical method for solving Maxwell's equations to obtain the frequency spectra of inhomogeneous and asymmetric cavity resonators using a couple of effective Debye-type potentials. The structure we study specifically is the layered spherical cavity resonator with symmetrically or asymmetrically inserted inner dielectric sphere. The comparison of the exact numerical results obtained for the frequency spectrum of layered cavity resonator with centrosymmetrically inserted sphere and the spectrum found from the suggested theory reveals good agreement at the initial part of the freq…
Transition metal dichalcogenides (TMDs) is a promising platform for new generation optoelectronics and nanophotonics due to their unique optical properties. However, in contrast to direct bandgap TMDs monolayers, bulk samples have an indirect bandgap that restricts their application as light emitters. On the other hand, the high refractive index of these materials seems ideal for creating high-quality nanophotonic resonators with a strong Purcell effect. In this work, we fabricate Whispering-gallery mode (WGM) resonators from bulk (i.e., indirect bandgap) MoSe$_2$ using resistless scanning pro…
We present a monolithic integrated aluminum nitride (AlN) optomechanical resonator in which the mechanical motion is actuated by piezoelectric force and the displacement is transduced by a high-Q optical cavity. The AlN optomechanical resonator is excited from a radio-frequency electrode via a small air gap to eliminate resonator-to-electrode loss. We observe the electrically excited mechanical motion at 47.3 MHz, 1.04 GHz, and 3.12 GHz, corresponding to the 1st, 2nd, and 4th radial-contour mode of the wheel resonator respectively. An equivalent circuit model is developed to describe the obser…
Cavity cooling via quantum backaction force can extract thermal fluctuations from a mechanical resonator to reach the quantum ground state. Surface or bulk two-level-system (TLS) defects in a mechanical resonator can couple with the mechanical mode via deformation potential and affect the cooling process significantly. Here, we develop a theory to study the cavity cooling of a mechanical mode in the presence of a TLS defect using the adiabatic elimination technique. Our result shows that the cooling process depends strongly on the resonance and the damping rate of the TLS.
Achieving quantum correlations between two distant systems is a desirable feature for quantum networking. In this work, we study a system composed of two quantum emitter-cavity subsystems spatially separated. A mechanical resonator couples to either both quantum emitters or both cavities leading to quantum correlations between both subsystems such as non-local light-matter dressed states and cavity-cavity normal mode splitting. These indirect couplings can be explained by an effective Hamiltonian for large energy detuning between the mechanical resonator and the atoms/cavities. Moreover, it is…
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…
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…
Resonant photoelastic coupling in semiconductor nanostructures opens new perspectives for strongly enhanced light-sound interaction in optomechanical resonators. One potential problem, however, is the reduction of the cavity Q-factor induced by dissipation when the resonance is approached. We show in this letter that cavity-polariton mediation in the light-matter process overcomes this limitation allowing for a strongly enhanced photon-phonon coupling without significant lifetime reduction in the strongly-coupled regime. Huge optomechanical coupling factors in the PetaHz/nm range are envisaged…
We experimentally realize indirect coupling between two cavity modes via strong coupling with the ferromagnetic resonance in Yttrium Iron Garnet (YIG). We find that some indirectly coupled modes of our system can have a higher microwave transmission than the individual uncoupled modes. Using a coupled harmonic oscillator model, the influence of the oscillation phase difference between the two cavity modes on the nature of the indirect coupling is revealed. These indirectly coupled microwave modes can be controlled using an external magnetic field or by tuning the cavity height. This work has p…
We describe a cavity QED analogue for the coupling system of a spin and a nanomechanical resonator with a magnetic tip. For the quantized nanomechanical resonator, a spin-boson model for this coupling system can refer to a Jaynes-Cummings(JC) or an anti-JC model. These observations predict some quantum optical phenomena, such as squeezing and "collapse-revival" in the single oscillation mode of the nanomechanical resonator when it is initially prepared in the quasi-classical state. By modulating the phase of RF magnetic field one can switch the system between the JC and anti-JC model, which pr…
We theoretically analyse the cooling dynamics of a high-Q mode of a mechanical resonator, when the structure is also an optical cavity and is coupled with a NV center. The NV center is driven by a laser and interacts with the cavity photon field and with the strain field of the mechanical oscillator, while radiation pressure couples mechanical resonator and cavity field. Starting from the full master equation we derive the rate equation for the mechanical resonator's motion, whose coefficients depend on the system parameters and on the noise sources. We then determine the cooling regime, the c…
We investigate a general scheme for generating, either dynamically or in the steady state, continuous variable entanglement between two mechanical resonators with different frequencies. We employ an optomechanical system in which a single optical cavity mode driven by a suitably chosen two-tone field is coupled to the two resonators. Significantly large mechanical entanglement can be achieved, which is extremely robust with respect to temperature.
We have observed the dynamical bistability of a microwave superconducting Fabry-Perot cavity incorporating a non-linear element in the form of Josephson tunnel junction. The effect, which is the analog of optical bistability, manifests itself in the transmission and reflection characteristics of the cavity and is governed by a competition between the wave amplitude dependence of the resonant frequency and the finite residence time of the field energy inside the cavity. This finite residence time is solely due to extraction of radiation from the cavity by the measurement process. The tight quan…
A hybrid device comprising a (Al)GaAs quantum dot heterostructure and a LiNbO$_3$ surface acoustic wave resonator is fabricated by heterointegration. High acoustic quality factors $Q>4000$ are demonstrated for an operation frequency $f\approx 300$ MHz. The measured large quality factor-frequency products $Q\times f>10^{12}$ ensures the suppression of decoherence due to thermal noise for temperatures exceeding $T>50\,\mathrm{K}$. Frequency and position dependent optomechanical coupling of single quantum dots and the resonator modes is observed.
Using amplitude equations, we show that groups of identical nano-mechanical resonators, interacting with a common mode of a cavity microwave field, synchronize to form a single mechanical mode which couples to the cavity with a strength dependent on the square sum of the individual mechanical-microwave couplings. Classically this system is dominated by periodic behaviour which, when analyzed using amplitude equations, can be shown to exhibit multi-stability. In contrast groups of sufficiently dissimilar nano-mechanical oscillators may lose synchronization and oscillate out of phase at signific…
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…
The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-detuned GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quan…
We experimentally study an optomechanical cavity consisting of an oscillating mechanical resonator embedded in a superconducting microwave transmission line cavity. Tunable optomechanical coupling between the mechanical resonator and the microwave cavity is introduced by positioning a niobium-coated single mode optical fiber above the mechanical resonator. The capacitance between the mechanical resonator and the coated fiber gives rise to optomechanical coupling, which can be controlled by varying the fiber-resonator distance. We study radiation pressure induced self-excited oscillations as a …
Achieving strong coupling between light and matter is usually a challenge in Cavity Quantum Electrodynamics (cQED), especially in solid state systems. For this reason is useful taking advantage of alternative approaches to reach this regime, and then, generate reliable quantum polaritons. In this work we study a system composed of a quantized single mode of a mechanical resonator interacting linearly with both a single mode nanocavity and a two-level single quantum dot. In particular, we focus on the behavior of the indirect light-matter interaction when the phonon mode interfaces both parts. …
Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation properties and engineerable nonlinearities. Here we demonstrate synchronization of two nanomechanical oscillators via a photonic resonator, enabling optomechanical synchronization between mechanically isolated nanomechanical resonators. Optical backaction gives rise to both reactive and dissipative coupling of the mechanical resonators, leading to coherent os…
We investigate the magnon-photon couplings by employing a small magnet within an irregular resonant cavity, which leads to a desirable nonreciprocity with a big isolation ratio. Moreover, the higher-order couplings between the spin wave modes with the polarized photon modes also exhibit the nonreciprocity. These couplings between polarized photon and spin waves could be regarded as an indirect multi-modes coupling between the ferromagnetic resonance (FMR) mode and spin wave mode magnons mediated by the cavity mode photons. We also derive a coupling matrix to predict the characteristics of this…
Achieving coherent quantum control over massive mechanical resonators is a current research goal. Nano- and micromechanical devices can be coupled to a variety of systems, for example to single electrons by electrostatic or magnetic coupling, and to photons by radiation pressure or optical dipole forces. So far, all such experiments have operated in a regime of weak coupling, in which reversible energy exchange between the mechanical device and its coupled partner is suppressed by fast decoherence of the individual systems to their local environments. Controlled quantum experiments are in prin…
We describe a quantum computational architecture based on integrating nanomechanical resonators with Josephson junction phase qubits, with which we implement single- and multi-qubit operations. The nanomechanical resonator is a GHz-frequency, high-quality-factor dilatational resonator, coupled to the Josephson phase through a piezoelectric interaction. This system is analogous to one or more few-level atoms (the Josephson qubits) in a tunable electromagnetic cavity (the nanomechanical resonator). Our architecture combines the best features of solid-state and cavity-QED approaches, and may make…
We theoretically study a circuit QED architecture based on a superconducting flux qubit directly coupled to the center conductor of a coplanar waveguide transmission-line resonator. As already shown experimentally [Abdumalikov et al. Phys. Rev. B 78, 180502 (2008)], the strong coupling regime of cavity QED can readily be achieved by optimizing the local inductance of the resonator in the vicinity of the qubit. In addition to yielding stronger coupling with respect to other proposals for flux qubit based circuit QED, this approach leads to a qubit-resonator coupling strength g which does not sc…
We discuss the problem of magnetic-dipolar oscillations combined with microwave resonators. The energy density of magnetic-dipolar or magnetostatic (MS) oscillations in ferrite resonators is not the electromagnetic-wave density of the energy and not the exchange energy density as well. This fact reveals very special behaviors of the geometrical effects. Compared to other geometries, thin-film ferrite disk resonators exhibit very unique interactions of MS oscillations with the cavity electromagnetic fields. MS modes in a flat ferrite disk are characterized by a complete discrete spectrum of ene…
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…
The optical hybridization of the electronic states in strongly coupled molecule-cavity systems have revealed unique properties such as lasing, room temperature polariton condensation, and the modification of excited electronic landscapes involved in molecular isomerization. Here we show that molecular vibrational modes of the electronic ground state can also be coherently coupled with a micro-cavity mode at room temperature, given the low vibrational thermal occupation factors associated with molecular vibrations, and the collective coupling of a large ensemble of molecules immersed within the…
We propose and analyze a hybrid device by integrating a microscale diamond beam with a single built-in nitrogen-vacancy (NV) center spin to a superconducting coplanar waveguide (CPW) cavity. We find that under an ac electric field the quantized motion of the diamond beam can strongly couple to the single cavity photons via dielectric interaction. Together with the strong spin-motion interaction via a large magnetic field gradient, it provides a hybrid quantum device where the dia- mond resonator can strongly couple both to the single microwave cavity photons and to the single NV center spin. T…
The interaction between two magnetic spheres in microwave cavities is studied by Mie scattering theory beyond the magnetostatic and rotating wave approximations. We demonstrate that two spatially separated dielectric and magnetic spheres can be strongly coupled over a long distance by standing cavity modes. The interactions splits acoustical (dark) and optical (bright) modes in a way that can be mapped on a molecular orbital theory of the hydrogen molecule. Breaking the symmetry by assigning different radii to the two spheres introduces "ionic" character to the magnonic bonds. These results il…
We study a single-mode cavity weakly coupled to a voltage-biased quantum point contact. In a perturbative analysis, the lowest order predicts a thermal state for the cavity photons, driven by the emission noise of the conductor. The cavity is thus emptied as all transmission probabilities of the quantum point contact approach one or zero. Two-photon processes are identified at higher coupling, and pair absorption dominates over pair emission for all bias voltages. As a result, the number of cavity photons, the cavity damping rate and the second order coherence $g^{(2)}$ are all reduced and exh…
We investigate the quantum versus classical dynamics of a microwave cavity-coupled-Cooper pair transistor (CPT) system, where an applied dc bias causes the system to self-oscillate via the ac Josephson effect. Varying the dc bias allows the self-oscillation frequency to be tuned. An unusual feature of the system design is that the dc bias does not significantly affect the high quality factor of the cavity mode to which the CPT predominantly couples. The CPT-cavity mode system has a mechanical analogue involving a driven coupled pendulum-oscillator system. The corresponding, nonlinear classical…
We investigate theoretically in detail the non-linear effects in the response of an optical/microwave cavity coupled to a Duffing mechanical resonator. The cavity is driven by a laser at a red or blue mechanical subband, and a probe laser measures the reflection close to the cavity resonance. Under these conditions, we find that the cavity exhibits optomechanically induced reflection (OMIR) or absorption (OMIA) and investigate the optomechanical response in the limit of non-linear driving of the mechanics. Similar to linear mechanical drive, an overcoupled cavity the red-sideband drive may lea…
Nonlinear phenomena in superconducting resonator circuits are of great significance in the field of quantum technology. We observe thermal self-oscillations in a monolayer graphene flake coupled to Molybdenum-Rhenium superconducting resonator. The graphene flake forms a SINIS junction coupled to the resonator with strong temperature dependent resistance. In certain conditions of pump power and frequency, this nonlinearity leads to thermal self-oscillations appearing as sidebands in cavity transmission measurements with strong temperature dependence and gate tunability. The experimental observa…
It was shown [New J. Phys. 17, 103037 (2015)] that large and robust entanglement between two different mechanical resonators could be achieved, either dynamically or in the steady state, in an optomechanical system in which the two mechanical resonators are coupled to a single cavity mode driven by a suitably chosen two-tone field. An important limitation of the scheme is that the cavity decay rate must be much smaller than the two mechanical frequencies and their difference. Here we show that the entanglement can be remarkably enhanced, and the validity of the scheme can be largely extended, …
The generation and control of quantum states of light constitute fundamental tasks in cavity quantum electrodynamics (QED). The superconducting realization of cavity QED, circuit QED, enables on-chip microwave photonics, where superconducting qubits control and measure individual photon states. A long-standing issue in cavity QED is the coherent transfer of photons between two or more resonators. Here, we use circuit QED to implement a three-resonator architecture on a single chip, where the resonators are interconnected by two superconducting phase qubits. We use this circuit to shuffle one- …
We experimentally demonstrate coupling of an atomically thin, free-standing graphene membrane to an optical cavity. By changing the position of the membrane along the standing-wave field of the cavity we tailor the dissipative coupling between the membrane and the cavity, and we show that the dissipative coupling can outweigh the dispersive coupling. Such a system, for which controlled dissipation prevails dispersion, will prove useful for novel laser-cooling schemes in optomechanics. In addition, we have determined the continuous-wave optical damage threshold of free-standing monolayer graphe…
