Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer

Coherent optical control of a superconducting microwave cavity via electro-optical dynamical back-action

Recent quantum technologies have established precise quantum control of various microscopic systems using electromagnetic waves. Interfaces based on cryogenic cavity electro-optic systems are particularly promising, due to the direct interaction between microwave and optical fields in the quantum regime. Quantum optical control of superconducting microwave circuits has been precluded so far due to the weak electro-optical coupling as well as quasi-particles induced by the pump laser. Here we report the coherent control of a superconducting microwave cavity using laser pulses in a multimode electro-optical device at millikelvin temperature with near-unity cooperativity. Both the stationary and instantaneous responses of the microwave and optical modes comply with the coherent electro-optical interaction, and reveal only minuscule amount of excess back-action with an unanticipated time delay. Our demonstration enables wide ranges of applications beyond quantum transductions, from squeezing and quantum non-demolition measurements of microwave fields, to entanglement generation and hybrid quantum networks.

Enhanced nonlinear optomechanics in a coupled-mode photonic crystal device

The nonlinear component of the optomechanical interaction between light and mechanical vibration promises many exciting classical and quantum mechanical applications, but is generally weak. Here we demonstrate enhancement of nonlinear optomechanical measurement of mechanical motion by using pairs of coupled optical and mechanical modes in a photonic crystal device. In the same device we show linear optomechanical measurement with a strongly reduced input power and reveal how both enhancements are related. Our design exploits anisotropic mechanical elasticity to create strong coupling between mechanical modes while not changing optical properties. Additional thermo-optic tuning of the optical modes is performed with an auxiliary laser and a thermally-optimised device design. We envision broad use of this enhancement scheme in multimode phonon lasing, two-phonon heralding and eventually nonlinear quantum optomechanics.

Generation and enhancement of sum sideband in a quadratically coupled optomechanical system with parametric interactions

We investigate theoretically the generation and enhancement of sum sideband in a quadratically coupled optomechanical system with parametric interactions. It is shown that the generation of frequency components at the sum sideband stems from the nonlinear optomechanical interactions via two-phonon processes in the quadratically coupled optomechanical system, while an optical parametric amplifier (OPA) inside the system can considerably improve the sum sideband generation (SSG). The dependence of SSG on the system parameters, including the power of the control field, the frequency detuning of the probe fields and the nonlinear gain of OPA are analyzed in detail. Our analytic calculation indicates that the SSG can be obtained even under weak driven fields and greatly enhanced via meeting the matching conditions. The effect of SSG may have potential applications for achieving measurement of electric charge (or other weak forces) with higher precision and on-chip manipulation of light propagation.

Quantum electromechanics of a hypersonic crystal

Recent technical developments in the fields of quantum electromechanics and optomechanics have spawned nanoscale mechanical transducers with the sensitivity to measure mechanical displacements at the femtometre scale and the ability to convert electromagnetic signals at the single photon level. A key challenge in this field is obtaining strong coupling between motion and electromagnetic fields without adding additional decoherence. Here we present an electromechanical transducer that integrates a high-frequency (0.42 GHz) hypersonic phononic crystal with a superconducting microwave circuit. The use of a phononic bandgap crystal enables quantum-level transduction of hypersonic mechanical motion and concurrently eliminates decoherence caused by acoustic radiation. Devices with hypersonic mechanical frequencies provide a natural pathway for integration with Josephson junction quantum circuits, a leading quantum computing technology, and nanophotonic systems capable of optical networking and distributing quantum information.

Coherent interaction of orthogonal polarization modes in a photonic crystal nanofiber cavity

We show that coherent interaction between two sets of multiple resonances leads to exotic resonant effects, such as Fano-type resonances, optical analogue of electro-magnetically induced transparency, and avoided crossing between modes, under different coupling regimes. We experimentally demonstrate such resonant effects in a photonic crystal nanofiber cavity using two sets of cavity modes with orthogonal polarizations. The interaction between the modes arises due to intra-cavity polarization mixing. The observed line shapes are reproduced using a multiple-mode interaction model. Such spectral characteristics may further enhance the capabilities of the nanofiber cavity as a fiber-in-line platform for nanophotonics and quantum photonics applications.

Optical Cooling of Magnons

Inelastic scattering of light by spin waves generates an energy flow between the light and magnetization fields, a process that can be enhanced and controlled by concentrating the light in magneto-optical resonators. Here, we model the cooling of a sphere made of a magnetic insulator, such as yttrium iron garnet, using a monochromatic laser source. When the magnon lifetimes are much larger than the optical ones, we can treat the latter as a Markovian bath for magnons. The steady-state magnons are canonically distributed with a temperature that is controlled by the light intensity. We predict that such a cooling process can significantly reduce the temperature of the magnetic order within current technology.

Metrology with PT-Symmetric Cavities: Enhanced Sensitivity near the PT-Phase Transition

We propose and analyze a new approach based on parity-time (PT) symmetric microcavities with balanced gain and loss to enhance the performance of cavity-assisted metrology. We identify the conditions under which PT-symmetric microcavities allow us to improve sensitivity beyond what is achievable in loss-only systems. We discuss the application of PT-symmetric microcavities to the detection of mechanical motion, and show that the sensitivity is significantly enhanced near the transition point from unbroken- to broken-PT regimes. Our results open a new direction for PT-symmetric physical systems and it may find use in ultrahigh precision metrology and sensing.

Quantum electromechanics on silicon nitride nanomembranes

Radiation pressure has recently been used to effectively couple the quantum motion of mechanical elements to the fields of optical or microwave light. Integration of all three degrees of freedom—mechanical, optical and microwave—would enable a quantum interconnect between microwave and optical quantum systems. We present a platform based on silicon nitride nanomembranes for integrating superconducting microwave circuits with planar acoustic and optical devices such as phononic and photonic crystals. Using planar capacitors with vacuum gaps of 60 nm and spiral inductor coils of micron pitch we realize microwave resonant circuits with large electromechanical coupling to planar acoustic structures of nanoscale dimensions and femtoFarad motional capacitance. Using this enhanced coupling, we demonstrate microwave backaction cooling of the 4.48 MHz mechanical resonance of a nanobeam to an occupancy as low as 0.32. These results indicate the viability of silicon nitride nanomembranes as an all-in-one substrate for quantum electro-opto-mechanical experiments.

Preparation and detection of mechanical objects at the quantum zero-point level has been achieved in both the optical and microwave regimes. Here, the authors develop silicon nitride nanomembranes that are suitable for integrating nanophotonic, nanomechanical and superconducting microwave circuits together.

Macroscopic Quantum Superposition in Cavity Optomechanics

Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct mechanical superposition states in a two-mode optomechanical system. Photon hopping between the two cavity modes is modulated sinusoidally. The modulated photon tunneling enables an ultrastrong radiation-pressure force acting on the mechanical resonator, and hence significantly increases the mechanical displacement induced by a single photon. We study systematically the generation of the Yurke-Stoler-like states in the presence of system dissipations. We also discuss the experimental implementation of this scheme.

Fluctuation-dissipation and energy properties of a finite bath

This paper expands a recent proposal by the authors to rederive the Langevin equation for a test particle in a finite-size thermal bath using a perturbation approach that yields a cascade of Langevin-type equations. Such an approach produces a different viewpoint for the fluctuation-dissipation duality by expressing them on similar scales. General properties of energy sharing between the test particle and the bath are outlined, investigating the resonant and nonresonant conditions.

Intracavity Squeezing Can Enhance Quantum-Limited Optomechanical Position Detection through Deamplification

It has been predicted and experimentally demonstrated that by injecting squeezed light into an optomechanical device, it is possible to enhance the precision of a position measurement. Here, we present a fundamentally different approach where the squeezing is created directly inside the cavity by a nonlinear medium. Counterintuitively, the enhancement of the signal-to-noise ratio works by deamplifying precisely the quadrature that is sensitive to the mechanical motion without losing quantum information. This enhancement works for systems with a weak optomechanical coupling and/or strong mechanical damping. This can allow for larger mechanical bandwidth of quantum-limited detectors based on optomechanical devices. Our approach can be straightforwardly extended to quantum nondemolition qubit detection.

Integrated III-V Photonic Crystal--Si waveguide platform with tailored optomechanical coupling

Optomechanical systems, in which the vibrations of a mechanical resonator are coupled to an electromagnetic radiation, have permitted the investigation of a wealth of novel physical effects. To fully exploit these phenomena in realistic circuits and to achieve different functionalities on a single chip, the integration of optomechanical resonators is mandatory. Here, we propose a novel approach to heterogeneously integrate arrays of two-dimensional photonic crystal defect cavities on top of silicon-on-insulator waveguides. The optomechanical response of these devices is investigated and evidences an optomechanical coupling involving both dispersive and dissipative mechanisms. By controlling the optical coupling between the waveguide and the photonic crystal, we were able to vary and understand the relative strength of these couplings. This scalable platform allows for an unprecedented control on the optomechanical coupling mechanisms, with a potential benefit in cooling experiments, and for the development of multi-element optomechanical circuits in the framework of optomechanically-driven signal-processing applications.

Spatial mapping of multimode Brownian motions in high-frequency silicon carbide microdisk resonators

High-order and multiple modes in high-frequency micro/nanomechanical resonators are attractive for empowering signal processing and sensing with multi-modalities, yet many challenges remain in identifying and manipulating these modes, and in developing constitutive materials and structures that efficiently support high-order modes. Here we demonstrate high-frequency multimode silicon carbide microdisk resonators and spatial mapping of the intrinsic Brownian thermomechanical vibrations, up to the ninth flexural mode, with displacement sensitivities of ~7-14 fm Hz(-1/2). The microdisks are made in a 500-nm-carbide on 500-nm-oxide thin-film technology that facilitates ultrasensitive motion detection via scanning laser interferometry with high spectral and spatial resolutions. Mapping of these thermomechanical vibrations vividly visualizes the shapes and textures of high-order Brownian motions in the microdisks. Measurements on devices with varying dimensions provide deterministic information for precisely identifying the mode sequence and characteristics, and for examining mode degeneracy, spatial asymmetry and other effects, which can be exploited for encoding information with increasing complexity.

Enhanced interaction between a mechanical oscillator and two coupled resonant electrical circuits

This paper reports result of calculation and experimental realization of an electromechanical system that consists of a high-Q mechanical oscillator parametrically coupled in the manner of a capacitive transducer with a radio frequency (RF) circuit, which is in turn inductively coupled with another RF circuit. The system operates in the resolved sideband regime when the mechanical oscillator's frequency is larger than the electrical circuits' bandwidths. Using two coupled RF circuits allowed one to enhance the interaction between them and the mechanical oscillator which is one of flexural vibrational modes of a free-edge circular silicon wafer. Such a coupled electromechanical system can be used as a high-sensitive capacitive vibration sensor.

Reconfigurable long-range phonon dynamics in optomechanical arrays

We investigate periodic optomechanical arrays as reconfigurable platforms for engineering the coupling between multiple mechanical and electromagnetic modes and for exploring many-body phonon dynamics. Exploiting structural resonances in the coupling between light fields and collective motional modes of the array, we show that tunable effective long-range interactions between mechanical modes can be achieved. This paves the way towards the implementation of controlled phononic walks and heat transfer on densely connected graphs as well as the coherent transfer of excitations between distant elements of optomechanical arrays.

Near-self-imaging cavity for three-mode optoacoustic parametric amplifiers using silicon microresonators

Three-mode optoacoustic parametric amplifiers (OAPAs), in which a pair of photon modes are strongly coupled to an acoustic mode, provide a general platform for investigating self-cooling, parametric instability and very sensitive transducers. Their realization requires an optical cavity with tunable transverse modes and a high quality-factor mirror resonator. This paper presents the design of a table-top OAPA based on a near-self-imaging cavity design, using a silicon torsional microresonator. The design achieves a tuning coefficient for the optical mode spacing of 2.46  MHz/mm. This allows tuning of the mode spacing between amplification and self-cooling regimes of the OAPA device. Based on demonstrated resonator parameters (frequencies ∼400  kHz and quality-factors ∼7.5×10(5) we predict that the OAPA can achieve parametric instability with 1.6 μW of input power and mode cooling by a factor of 1.9×10(4) with 30 mW of input power.

Electromagnetically induced transparency and slow light in two-mode optomechanics

We theoretically demonstrate the mechanically mediated electromagnetically induced transparency in a two-mode cavity optomechanical system, where two cavity modes are coupled to a common mechanical resonator. When the two cavity modes are driven on their respective red sidebands by two pump beams, a transparency window appears in the probe transmission spectrum due to destructive interference. Under this situation the transmitted probe beam can be delayed as much as 4 μs, which can be easily controlled by the power of the pump beams.

Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light

We show that distributed Bragg reflector GaAs/AlAs vertical cavities designed to confine photons are automatically optimal to confine phonons of the same wavelength, strongly enhancing their interaction. We study the impulsive generation of intense coherent and monochromatic acoustic phonons by following the time evolution of the elastic strain in picosecond-laser experiments. Efficient optical detection is assured by the strong phonon backaction on the high-Q optical cavity mode. Large optomechanical factors are reported (~THz/nm range). Pillar cavities based in these structures are predicted to display picogram effective masses, almost perfect sound extraction, and threshold powers for the stimulated emission of phonons in the range μW-mW, opening the way for the demonstration of phonon "lasing" by parametric instability in these devices.

Multimode circuit optomechanics near the quantum limit

The coupling of distinct systems underlies nearly all physical phenomena. A basic instance is that of interacting harmonic oscillators, giving rise to, for example, the phonon eigenmodes in a lattice. Of particular importance are the interactions in hybrid quantum systems, which can combine the benefits of each part in quantum technologies. Here we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering of entangled motional states.

Optomechanical systems allow for the exploration of macroscopic behaviour at or near the quantum limit. Massel et al. use micromechanical resonators to study the hybridisation of one photonic and two phononic modes with phonon numbers down to 1.8, showing a coupling between all three degrees of freedom.

Optomechanical quantum information processing with photons and phonons

We describe how strong resonant interactions in multimode optomechanical systems can be used to induce controlled nonlinear couplings between single photons and phonons. Combined with linear mapping schemes between photons and phonons, these techniques provide a universal building block for various classical and quantum information processing applications. Our approach is especially suited for nano-optomechanical devices, where strong optomechanical interactions on a single photon level are within experimental reach.

Dissipative optomechanics in a Michelson-Sagnac interferometer

Dissipative optomechanics studies the coupling of the motion of an optical element to the decay rate of a cavity. We propose and theoretically explore a realization of this system in the optical domain, using a combined Michelson-Sagnac interferometer, which enables a strong and tunable dissipative coupling. Quantum interference in such a setup results in the suppression of the lower motional sideband, leading to strongly enhanced cooling in the non-sideband-resolved regime. With state-of-the-art parameters, ground-state cooling and low-power quantum-limited position transduction are both possible. The possibility of a strong, tunable dissipative coupling opens up a new route towards observation of such fundamental optomechanical effects as nonlinear dynamics. Beyond optomechanics, the suggested method can be readily transferred to other setups involving nonlinear media, atomic ensembles, or single atoms.