Deterministic multi-phonon entanglement between two mechanical resonators on separate substrates

Mechanical systems have emerged as a compelling platform for applications in quantum information, leveraging advances in the control of phonons, the quanta of mechanical vibrations. Experiments have demonstrated the control and measurement of phonon states in mechanical resonators, and while dual-resonator entanglement has been demonstrated, more complex entangled states remain a challenge. Here, we demonstrate rapid multi-phonon entanglement generation and subsequent tomographic analysis, using a scalable platform comprising two surface acoustic wave resonators on separate substrates, each connected to a superconducting qubit. We synthesize a mechanical Bell state with a fidelity of F = 0.872 ± 0.002 , and a multi-phonon entangled N = 2 N00N state with a fidelity of F = 0.748 ± 0.008 . The compact, modular, and scalable platform we demonstrate will enable further advances in the quantum control of complex mechanical systems.

Unconventional phonon blockade effect in array of three coupled weakly nonlinear nanomechanical resonators

Phonon antibunching, a phenomenon arising from the quantum statistics of mechanical vibrations, has attracted significant attention due to its potential applications in quantum information processing, sensing, and energy harvesting. Here, we present a comprehensive investigation of phonon antibunching in a system consisting of three weakly nonlinear coupled nanomechanical resonators. We analytically derive and study the antibunching behavior of phonons in the proposed system and bring insight into the underlying mechanisms. The optimal phonon blockade results from destructive quantum interference due to distinct two-phonon excitation pathways. Due to this quantum interference, these unconventional phonon blockade systems can achieve antibunched statistics even in weakly nonlinear regimes, in contrast to conventional phonon blockade systems that require strong nonlinearity. We show that with the inclusion of an additional resonator, there are multiple additional two-phonon excitation pathways compared to two resonator cases, which results in stronger phonon antibunching and supports single phonon for longer duration. These findings are interesting for practical phononics using coupled-resonator systems.

Highly Correlated Optomechanical Oscillations Manifested by an Anomalous Stabilization

Driven by a sufficiently powerful pump laser, a cavity optomechanical system will stabilize in coupled oscillations of its cavity field and mechanical resonator. It was assumed that the oscillation will be continuously magnified upon enhancing the driving laser further. However, based on the nonlinear dynamics of the system, we find that the dynamical behaviors of the system are much more complex than this intuitive picture, especially when it is operated near the blue detuning point by the mechanical resonator's intrinsic frequency. There exists an anomalous stabilization: depending on its intrinsic damping rate and the pump power, the mechanical resonator will metastably stay on one orbit of oscillation after another until it completely stabilizes on the final orbit it can reach. These orbits are consistent with the locked ones with almost fixed oscillation amplitudes, which are realized after the pump power becomes still higher. The oscillatory cavity field is seen to adjust its sidebands following the mechanical frequency shift due to optical spring effect, so that it always drives the mechanical resonator to near those locked orbits once the pump power is over a threshold. In the regimes with such correlation between cavity field sidebands and mechanical oscillation, the system's dynamical attractors are confined on the locked orbits and chaotic motion is also excluded.

Improving the Stationary Entanglement of a Laguerre-Gaussian Cavity Mode with a Rotating Mirror via Nonlinear Cross-Kerr Interactions and Parametric Interactions

Quantum entanglement is essential in performing many quantum information tasks. Here, we theoretically investigate the stationary entanglement between a Laguerre-Gaussian (LG) cavity field and a rotating end mirror in an LG-cavity optorotational system with a nonlinear cross-Kerr (CK) interaction and a degenerate optical parametric amplifier (OPA). We calculate the logarithmic negativity of the system to quantify the stationary entanglement. We examine the influence of various system parameters such as the cavity detuning, the strength of the nonlinear CK interaction, the parametric gain and phase of the OPA, the power of the input Gaussian laser, the topological charge of the LG-cavity field, the mass of the rotating end mirror, and the ambient temperature on the stationary entanglement. Under the combined effect of the nonlinear CK interaction and the OPA, we find that the stationary entanglement can be substantially enhanced at lower Gaussian laser powers, smaller topological charges of the LG-cavity field, and larger masses of the rotating end mirror. We show that the combination of the nonlinear CK interaction and the OPA can make the stationary entanglement more robust against the ambient temperature.

Entanglement and quantum coherence of two YIG spheres in a hybrid Laguerre-Gaussian cavity optomechanics

We theoretically investigate continuous variable entanglement and macroscopic quantum coherence in the hybrid L-G rotational cavity optomechanical system containing two YIG spheres. In this system, a single L-G cavity mode and both magnon modes (which are due to the collective excitation of spins in two YIG spheres) are coupled through the magnetic dipole interaction whereas the L-G cavity mode can also exchange orbital angular momentum (OAM) with the rotating mirror (RM). We study in detail the effects of various physical parameters like cavity and both magnon detunings, environment temperature, optorotational and magnon coupling strengths on the bipartite entanglement and the macroscopic quantum coherence as well. We also explore parameter regimes to achieve maximum values for both of these quantum correlations. We also observed that the parameters regime for achieving maximum bipartite entanglement is completely different from macroscopic quantum coherence. So, our present study shall provide a method to control various nonclassical quantum correlations of macroscopic objects in the hybrid L-G rotational cavity optomechanical system and have potential applications in quantum sensing, quantum meteorology, and quantum information science.

Steady motional entanglement between two distant levitated nanoparticles

Quantum entanglement in macroscopic systems is not only essential for practical quantum information processing, but also valuable for the study of the boundary between quantum and the classical world. However, it is very challenging to achieve the steady remote entanglement between distant macroscopic systems. We consider two distant nanoparticles, both of which are optically trapped in two cavities. Based on the coherent scattering mechanism, we find that the ultrastrong optomechanical coupling between the cavity modes and the motion of the levitated nanoparticles could be achieved. The large and steady entanglement between the filtered output cavity modes and the motion of nanoparticles can be generated if the trapping laser is under the red sideband. Then through entanglement swapping, the steady motional entanglement between the distant nanoparticles can be realized. We numerically simulate and find that the two nanoparticles with 10 km distance can be entangled for the experimentally feasible parameters, even in room temperature environments. The generated continuous variable multipartite entanglement is the key to realizing the quantum enhanced sensor network and the sensitivity beyond the standard quantum limit.

Nonlinear dynamics of cavity optomechanical-thermal systems

Cavity optomechanics is concerned with the interaction between optical cavities and mechanical resonators. Here, we present systematic research on the dynamic behaviors of cavity optomechanical systems incorporating the influence of thermal nonlinearity. A dimensionless theoretical model was established to describe the system and numerical simulations were performed to study the dynamic behaviors. We theoretically identify the staircase effect, which can abruptly alter the system parameters when adiabatically sweeping the pump laser frequency across the optical cavity resonance and driving the mechanical resonator into oscillation. Moreover, we found bistability effects in several detuning intervals when sweeping the laser forward and backward. Both effects are analyzed theoretically and the roots lie in the thermal instability between averaged cavity energy and laser detuning. Our study shows the dynamic behaviors in an optomechanical-thermal system and provides guidance in leveraging the systems for applications in optical frequency comb, phonon laser, etc.

Ultrasensitive Soft Sensor from Anisotropic Conductive Biphasic Liquid Metal-Polymer Gels

Subtle vibrations, such as sound and ambient noises, are common mechanical waves that can transmit energy and signals for modern technologies such as robotics and health management devices. However, soft electronics cannot accurately distinguish ultrasmall vibrations owing to their extremely small pressure, complex vibration waveforms, and high noise susceptibility. This study successfully recognizes signals from subtle vibrations using a highly flexible anisotropic conductive gel (ACG) based on biphasic liquid metals. The relationships between the anisotropic structure, subtle vibrations, and electrical performance are investigated using rheological-electrical experiments. The refined anisotropic design successfully realized low-cost flexible electronics with ultrahigh sensitivity (Gauge Factor: 12787), extremely low detection limit (strain: 0.01%), and excellent frequency recognition accuracy (>99%), significantly surpassing those of current flexible sensors. The ultrasensitive flexible electronics in this study are beneficial for diverse advanced technologies such as acoustic engineering, wearable electronics, and intelligent robotics.

Multi-field-driven optomechanical entanglement

Cavity optomechanical (COM) entanglement, playing an essential role in building quantum networks and enhancing quantum sensors, is usually weak and easily destroyed by noises. As feasible and effective ways to overcome this obstacle, optical or mechanical parametric modulations have been used to improve the quality of quantum squeezing or entanglement in various COM systems. However, the possibility of combining these powerful means to enhance COM entanglement has yet to be explored. Here, we fill this gap by studying a COM system containing an intra-cavity optical parametric amplifier (OPA), driven optically and mechanically. By tuning the relative strength and the frequency mismatch of optical and mechanical driving fields, we find that constructive interference can emerge and significantly improve the strength of COM entanglement and its robustness to thermal noises. This work sheds what we believe to be a new light on preparing and protecting quantum states with multi-field driven COM systems for diverse applications.

Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes

We propose an experimentally feasible optomechanical scheme to realize a negative cavity photon spectral function (CPSF) which is equivalent to a negative absorption. The system under consideration is an optomechanical system consisting of two mechanical (phononic) modes which are linearly coupled to a common cavity mode via the radiation pressure while parametrically driven through the coherent time-modulation of their spring coefficients. Using the equations of motion for the cavity retarded Green's function obtained in the framework of the generalized linear response theory, we show that in the red-detuned and weak-coupling regimes a frequency-dependent effective cavity damping rate (ECDR) corresponding to a negative CPSF can be realized by controlling the cooperativities and modulation parameters while the system still remains in the stable regime. Nevertheless, such a negativity which acts as an optomechanical gain never occurs in a standard (an unmodulated bare) cavity optomechanical system. Besides, we find that the presence of two modulated mechanical degrees of freedom provides more controllability over the magnitude and bandwidth of the negativity of CPSF, in comparison to the setup with a single modulated mechanical oscillator. Interestingly, the introduced negativity may open a new platform to realize an extraordinary (modified) optomechanically induced transparency (in which the input signal is amplified in the output) leading to a perfect tunable optomechanical filter with switchable bandwidth which can be used as an optical transistor.

Generation of multipartite entangled states based on a double-longitudinal-mode cavity optomechanical system

An optomechanical system is a promising platform to connect different "notes" of quantum networks. Therefore, entanglements generated from it is also of great importance. In this paper, the parameter dependence of optomechanical and optical-optical entanglements generated from the double-longitudinal-mode cavity optomechanical system are discussed and two quadrapartite entanglement generation schemes based on such a system are proposed. Furthermore, 2N and 4N-partite entangled states of optical modes can be obtained by coupling N cavities that used in the above two schemes with N-1 beamsplitters, respectively. Certain ladder or linear entanglement structures are included in the finally obtained entangled state, which are important for its application in one-way quantum computing.

Splitting phonons: Building a platform for linear mechanical quantum computing

Linear optical quantum computing provides a desirable approach to quantum computing, with only a short list of required computational elements. The similarity between photons and phonons points to the interesting potential for linear mechanical quantum computing using phonons in place of photons. Although single-phonon sources and detectors have been demonstrated, a phononic beam splitter element remains an outstanding requirement. Here we demonstrate such an element, using two superconducting qubits to fully characterize a beam splitter with single phonons. We further use the beam splitter to demonstrate two-phonon interference, a requirement for two-qubit gates in linear computing. This advances a new solid-state system for implementing linear quantum computing, further providing straightforward conversion between itinerant phonons and superconducting qubits.

Nonlinear Sideband Cooling to a Cat State of Motion

The ability to prepare a macroscopic mechanical resonator into a quantum superposition state is an outstanding goal of cavity optomechanics. Here, we propose a technique to generate cat states of motion using the intrinsic nonlinearity of a dispersive optomechanical interaction. By applying a bichromatic drive to an optomechanical cavity, our protocol enhances the inherent second-order processes of the system, inducing the requisite two-phonon dissipation. We show that this nonlinear sideband cooling technique can dissipatively engineer a mechanical resonator into a cat state, which we verify using the full Hamiltonian and an adiabatically reduced model. While the fidelity of the cat state is maximized in the single-photon, strong-coupling regime, we demonstrate that Wigner negativity persists even for weak coupling. Finally, we show that our cat state generation protocol is robust to significant thermal decoherence of the mechanical mode, indicating that such a procedure may be feasible for near-term experimental systems.

Optomechanical force sensor operating over wide detection range

A detector with both broad operation range and high sensitivity is desirable in the measurement of weak periodic forces. Based on a nonlinear dynamical mechanism of locking the mechanical oscillation amplitude in optomechanical systems, we propose a force sensor that realizes the detection through the cavity field sidebands modified by an unknown external periodic force. Under the mechanical amplitude locking condition, the unknown external force happens to modify the locked oscillation amplitude linearly to its magnitude, thus achieving a linear scaling between the sideband changes read by the sensor and the magnitude of the force to be measured. This linear scaling range is found to be comparable to the applied pump drive amplitude, so the sensor can measure a wide range of force magnitude. Because the locked mechanical oscillation is rather robust against thermal perturbation, the sensor works well at room temperature. In addition to weak periodic forces, the same setup can as well detect static forces, though the detection ranges are much narrower.

Multipartite Entanglement in a Microwave Frequency Comb

Significant progress has been made with multipartite entanglement of discrete qubits, but continuous variable systems may provide a more scalable path toward entanglement of large ensembles. We demonstrate multipartite entanglement in a microwave frequency comb generated by a Josephson parametric amplifier subject to a bichromatic pump. We find 64 correlated modes in the transmission line using a multifrequency digital signal processing platform. Full inseparability is verified in a subset of seven modes. Our method can be expanded to generate even more entangled modes in the near future.

Generation of robust optical entanglement in cavity optomagnonics

We propose a scheme to realize robust optical entanglement in cavity optomagnonics, where two optical whispering gallery modes (WGMs) couple to a magnon mode in a yttrium iron garnet (YIG) sphere. The beam-splitter-like and two-mode squeezing magnon-photon interactions can be realized simultaneously when the two optical WGMs are driven by external fields. Entanglement between the two optical modes is then generated via their coupling with magnons. By exploiting the destructive quantum interference between the bright modes of the interface, the effects of initial thermal occupations of magnons can be eliminated. Moreover, the excitation of the Bogoliubov dark mode is capable of protecting the optical entanglement from thermal heating effects. Therefore, the generated optical entanglement is robust against thermal noise and the requirement of cooling the magnon mode is relaxed. Our scheme may find applications in the study of magnon-based quantum information processing.

2D-materials-integrated optoelectromechanics: recent progress and future perspectives

The discovery of two-dimensional (2D) materials has gained worldwide attention owing to their extraordinary optical, electrical, and mechanical properties. Due to their atomic layer thicknesses, the emerging 2D materials have great advantages of enhanced interaction strength, broad operating bandwidth, and ultralow power consumption for optoelectromechanical coupling. The van der Waals (vdW) epitaxy or multidimensional integration of 2D material family provides a promising platform for on-chip advanced nano-optoelectromechanical systems (NOEMS). Here, we provide a comprehensive review on the nanomechanical properties of 2D materials and the recent advances of 2D-materials-integrated nano-electromechanical systems and nano-optomechanical systems. By utilizing active nanophotonics and optoelectronics as the interface, 2D active NOEMS and their coupling effects are particularly highlighted at the 2D atomic scale. Finally, we share our viewpoints on the future perspectives and key challenges of scalable 2D-materials-integrated active NOEMS for on-chip miniaturized, lightweight, and multifunctional integration applications.

On-chip distribution of quantum information using traveling phonons

Distributing quantum entanglement on a chip is a crucial step toward realizing scalable quantum processors. Using traveling phonons-quantized guided mechanical wave packets-as a medium to transmit quantum states is now gaining substantial attention due to their small size and low propagation speed compared to other carriers, such as electrons or photons. Moreover, phonons are highly promising candidates to connect heterogeneous quantum systems on a chip, such as microwave and optical photons for long-distance transmission of quantum states via optical fibers. Here, we experimentally demonstrate the feasibility of distributing quantum information using phonons by realizing quantum entanglement between two traveling phonons and creating a time-bin-encoded traveling phononic qubit. The mechanical quantum state is generated in an optomechanical cavity and then launched into a phononic waveguide in which it propagates for around 200 micrometers. We further show how the phononic, together with a photonic qubit, can be used to violate a Bell-type inequality.

Generation of Schrödinger Cat States in a Hybrid Cavity Optomechanical System

We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom-cavity-oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, the proposed proposal consider the second order approximation on the Lamb-Dicke parameter, which is more universal in the experiment. Numerical simulations confirm the validity of our derivation.

Magnon-atom-optical photon entanglement via the microwave photon-mediated Raman interaction

We show that it is possible to generate magnon-atom-optical photon tripartite entanglement via the microwave photon-mediated Raman interaction. Magnons in a macroscopic ferromagnet and optical photons in a cavity are induced into a Raman interaction with an atomic spin ensemble when a microwave field couples the magnons to one Raman wing. The controllable magnon-atom entanglement, magnon-optical photon entanglement, and even genuine magnon-atom-optical photon tripartite entanglement can be generated simultaneously. In addition, these bipartite and tripartite entanglements are robust against the environment temperature. Our scheme paves the way for exploring a quantum interface bridging the microwave and optical domains, and may provide a promising building block for hybrid quantum networks.

Noise-Tolerant Optomechanical Entanglement via Synthetic Magnetism

Entanglement of light and multiple vibrations is a key resource for multichannel quantum information processing and memory. However, entanglement generation is generally suppressed, or even fully destroyed, by the dark-mode (DM) effect induced by the coupling of multiple degenerate or near-degenerate vibrational modes to a common optical mode. Here we propose how to generate optomechanical entanglement via DM breaking induced by synthetic magnetism. We find that at nonzero temperature, light and vibrations are separable in the DM-unbreaking regime but entangled in the DM-breaking regime. Remarkably, the threshold thermal phonon number for preserving entanglement in our simulations has been observed to be up to 3 orders of magnitude stronger than that in the DM-unbreaking regime. The application of the DM-breaking mechanism to optomechanical networks can make noise-tolerant entanglement networks feasible. These results are quite general and can initiate advances in quantum resources with immunity against both dark modes and thermal noise.

Cooling Effect and Cooling Speed for a Membrane-in-Middle Optomechanical System

Optomechanical systems are suitable for realizing the ground-state cooling of macroscopic objects. Based on a dynamical approach that goes beyond the validity of the standard linearization approach, we simulate the detailed cooling processes for a membrane-in-middle optomechanical system. In addition to the cooling results, we especially study the cooling speed, which is indicated by how soon the first minimum thermal phonon number is reached. Their relevance to the system parameters provides essential knowledge about how to achieve the best and/or fastest cooling under various combinations of different driving fields.

Ground state cooling of an ultracoherent electromechanical system

Cavity electromechanics relies on parametric coupling between microwave and mechanical modes to manipulate the mechanical quantum state, and provide a coherent interface between different parts of hybrid quantum systems. High coherence of the mechanical mode is of key importance in such applications, in order to protect the quantum states it hosts from thermal decoherence. Here, we introduce an electromechanical system based around a soft-clamped mechanical resonator with an extremely high Q-factor (>109) held at very low (30 mK) temperatures. This ultracoherent mechanical resonator is capacitively coupled to a microwave mode, strong enough to enable ground-state-cooling of the mechanics ([Formula: see text]). This paves the way towards exploiting the extremely long coherence times (tcoh > 100 ms) offered by such systems for quantum information processing and state conversion.

Vector optomechanical entanglement

The polarizations of optical fields, besides field intensities, provide more degrees of freedom to manipulate coherent light-matter interactions. Here, we propose how to achieve a coherent switch of optomechanical entanglement in a polarized-light-driven cavity system. We show that by tuning the polarizations of the driving field, the effective optomechanical coupling can be well controlled and, as a result, quantum entanglement between the mechanical oscillator and the optical transverse electric mode can be coherently and reversibly switched to that between the same phonon mode and the optical transverse magnetic mode. This ability to switch optomechanical entanglement with such a vectorial device can be important for building a quantum network being capable of efficient quantum information interchanges between processing nodes and flying photons.

Integrated Molecular Optomechanics with Hybrid Dielectric-Metallic Resonators

Molecular optomechanics describes surface-enhanced Raman scattering using the formalism of cavity optomechanics as a parametric coupling of the molecule's vibrational modes to the plasmonic resonance. Most of the predicted applications require intense electric field hotspots but spectrally narrow resonances, out of reach of standard plasmonic resonances. The Fano lineshapes resulting from the hybridization of dielectric-plasmonic resonators with a broad-band plasmon and narrow-band cavity mode allow reaching strong Raman enhancement with high-Q resonances, paving the way for sideband resolved molecular optomechanics. We extend the molecular optomechanics formalism to describe hybrid dielectric-plasmonic resonators with multiple optical resonances and with both free-space and waveguide addressing. We demonstrate how the Raman enhancement depends on the complex response functions of the hybrid system, and we retrieve the expression of Raman enhancement as a product of pump enhancement and the local density of states. The model allows prediction of the Raman emission ratio into different output ports and enables demonstrating a fully integrated high-Q Raman resonator exploiting multiple cavity modes coupled to the same waveguide.

Realization of a coupled-mode heat engine with cavity-mediated nanoresonators

We report an experimental demonstration of a coupled-mode heat engine in a two-membrane-in-the-middle cavity optomechanical system. The normal mode of the cavity-mediated strongly coupled nanoresonators is used as the working medium, and an Otto cycle is realized by extracting work between two phononic thermal reservoirs. The heat engine performance is characterized in both normal mode and bare mode pictures, which reveals that the correlation of two membranes plays a substantial role during the thermodynamic cycle. Moreover, a straight-twin nanomechanical engine is implemented by engineering the normal modes and operating two cylinders out of phase. Our results demonstrate an essential class of heat engine in cavity optomechanical systems and provide an ideal platform platform for investigating heat engines of interacting subsystems in small scales with controllability and scalability.

Improving few-photon optomechanical effects with coherent feedback

Few-photon effects such as photon blockade and tunneling have potential applications in modern quantum technology. To enhance the few-photon effects in an optomechanical system, we introduce a coherent feedback loop to cavity mode theoretically. By studying the second-order correlation function, we show that the photon blockade effect can be improved with feedback. Under appropriate parameters, the photon blockade effect exists even when cavity decay rate is larger than the single-photon optomechanical coupling coefficient, which may reduce the difficulty of realizing single-photon source in experiments. Through further study of the third-order correlation function, we show that the tunneling effect can also be enhanced by feedback. In addition, we discuss the application of feedback on Schrödinger-cat state generation in an optomechanical system. The result shows that the fidelity of cat state generation can be improved in the presence of feedback loop.

Room-Temperature Mechanical Resonator with a Single Added or Subtracted Phonon

A room-temperature mechanical oscillator undergoes thermal Brownian motion with an amplitude much larger than the amplitude associated with a single phonon of excitation. This motion can be read out and manipulated using laser light using a cavity-optomechanical approach. By performing a strong quantum measurement (i.e., counting single photons in the sidebands imparted on a laser), we herald the addition and subtraction of single phonons on the 300 K thermal motional state of a 4 GHz mechanical oscillator. To understand the resulting mechanical state, we implement a tomography scheme and observe highly non-Gaussian phase-space distributions. Using a maximum likelihood method, we infer the density matrix of the oscillator, and we confirm the counterintuitive doubling of the mean phonon number resulting from phonon addition and subtraction.

Quantum simulation of tunable and ultrastrong mixed-optomechanics

We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators.

Remote Generation of Magnon Schrödinger Cat State via Magnon-Photon Entanglement

The magnon cat state represents a macroscopic quantum superposition of collective magnetic excitations of large number spins that not only provides fundamental tests of macroscopic quantum effects but also finds applications in quantum metrology and quantum computation. In particular, remote generation and manipulation of Schrödinger cat states are particularly interesting for the development of long-distance and large-scale quantum information processing. Here, we propose an approach to remotely prepare magnon even or odd cat states by performing local non-Gaussian operations on the optical mode that is entangled with the magnon mode through pulsed optomagnonic interaction. By evaluating key properties of the resulting cat states, we show that for experimentally feasible parameters, they are generated with both high fidelity and nonclassicality, as well as with a size large enough to be useful for quantum technologies. Furthermore, the effects of experimental imperfections such as the error of projective measurements and dark count when performing single-photon operations have been discussed, where the lifetime of the created magnon cat states is expected to be t∼1  μs.

Polariton multistability in a nonlinear optomechanical cavity

We theoretically study the polariton multistability in a solid state based optomechanical resonator embedded with a quantum well and aχ⁽²⁾second order nonlinear medium. The excitonic transition inside the quantum well is strongly coupled to the optical cavity mode. The polariton formed due to the mixing of cavity photons and exciton states are coupled to the mechanical mode which gives rise to the bistable behavior. A transition from bistability to tristability occurs in the presence of a strongχ⁽²⁾nonlinearity. Switching between bistability and tristability can also be controlled using exciton-cavity and optomechanical coupling making the system highly tunable. Tristability appears at low input power making it a suitable candidate for polaritonic devices which requires low input power.

Nonlinear dynamic control of GaAs nanomechanical resonators using lasers

The ability to control, manipulate, and read out nanomechanical resonators is of great significance for many applications. In this work, we start by constructing a nonlinear dynamic model that is deduced from the fundamental beam-photon-electron interaction and energy band theories, with the aim of describing a complicated cavity-free optomechanical coupling process. Based on the model established, we first reveal the manipulation of a resonator's response, including softening and hardening effects due to laser injection. By driving the laser parametrically, we comprehensively investigate the control of the resonator's dynamics, in particular, in the nonlinear regime. It is found that both the laser power and frequency can be used to directly manipulate the NEMS resonator's dynamics, e.g., by amplitude amplification, periodicity changes, and periodic-chaotic state conversion. We then provide bifurcation diagrams, which evidence a deterministic evolution of dynamics. Finally, we perform a special study of the control of chaotic states of the nanomechanical resonator using laser parametric driving. The maximal Lyapunov exponents together with time series calculation show that the chaotic states can be controlled at a few specific frequency points of the injecting laser. This work not only provides guidance for using lasers to control nanoscale resonators, but also sheds light on the exploration of novel applications based on nonlinear NEMS resonators.

Superconducting Nanoelectromechanical Transducer Resilient to Magnetic Fields

Nanoscale electromechanical coupling provides a unique route toward control of mechanical motions and microwave fields in superconducting cavity electromechanical devices. However, conventional devices composed of aluminum have presented severe constraints on their operating conditions due to the low superconducting critical temperature (1.2 K) and magnetic field (0.01 T) of aluminum. To enhance their potential in device applications, we fabricate a superconducting electromechanical device employing niobium and demonstrate a set of cavity electromechanical dynamics, including back-action cooling and amplification, and electromechanically induced reflection at 4.2 K and in strong magnetic fields up to 0.8 T. Niobium-based electromechanical transducers operating at this temperature could potentially be employed to realize compact, nonreciprocal microwave devices in place of conventional isolators and cryogenic amplifiers. Moreover, with their resilience to magnetic fields, niobium devices utilizing the electromechanical back-action effects could be used to study spin-phonon interactions for nanomechanical spin-sensing.

Coupling of light and mechanics in a photonic crystal waveguide

High-Q mechanical modes of transverse oscillation at a few megahertz are characterized for a photonic crystal waveguide (PCW) consisting of parallel dielectric nanobeams. The transduction of thermally excited motion of 33 pm at 300 K results in phase modulation with high signal-to-noise ratio for light propagating in a guided mode of the PCW. Numerical modeling gives good agreement with experiment. With these measurements in hand, the system is assessed for possible applications in quantum information science and technology involving strong coupling of single phonons of vibration to single atoms and photons trapped within the PCW.

Observations of thermally driven transverse vibration of a photonic crystal waveguide (PCW) are reported. The PCW consists of two parallel nanobeams whose width is modulated symmetrically with a spatial period of 370 nm about a 240-nm vacuum gap between the beams. The resulting dielectric structure has a band gap (i.e., a photonic crystal stop band) with band edges in the near infrared that provide a regime for transduction of nanobeam motion to phase and amplitude modulation of an optical guided mode. This regime is in contrast to more conventional optomechanical coupling by way of moving end mirrors in resonant optical cavities. Models are developed and validated for this optomechanical mechanism in a PCW for probe frequencies far from and near to the dielectric band edge (i.e., stop band edge). The large optomechanical coupling strength predicted should make possible measurements with an imprecision below that at the standard quantum limit and well into the backaction-dominated regime. Since our PCW has been designed for near-field atom trapping, this research provides a foundation for evaluating possible deleterious effects of thermal motion on optical atomic traps near the surfaces of PCWs. Longer-term goals are to achieve strong atom-mediated links between individual phonons of vibration and single photons propagating in the guided modes (GMs) of the PCW, thereby enabling optomechanics at the quantum level with atoms, photons, and phonons. The experiments and models reported here provide a basis for assessing such goals.

Squeezed-light-driven force detection with an optomechanical cavity in a Mach-Zehnder interferometer

We analyze the performance of a force detector based on balanced measurements with a Mach–Zehnder interferometer incorporating a standard optomechanical cavity. The system is driven by a coherent superposition of coherent light and squeezed vacuum field, providing quantum correlation along with optical coherence in order to enhance the measurement sensitivity beyond the standard quantum limit. We analytically find the optimal measurement strength, squeezing direction, and squeezing strength at which the symmetrized power spectral density for the measurement noise is minimized below the standard quantum limit. This force detection scheme based on a balanced Mach–Zehnder interferometer provides better sensitivity compared to that based on balanced homodyne detection with a local oscillator in the low frequency regime.

Nonreciprocal Optomechanical Entanglement against Backscattering Losses

We propose how to achieve nonreciprocal quantum entanglement of light and motion and reveal its counterintuitive robustness against random losses. We find that by splitting the counterpropagating lights of a spinning resonator via the Sagnac effect, photons and phonons can be entangled strongly in a chosen direction but fully uncorrelated in the other. This makes it possible both to realize quantum nonreciprocity even in the absence of any classical nonreciprocity and also to achieve significant entanglement revival against backscattering losses in practical devices. Our work provides a way to protect and engineer quantum resources by utilizing diverse nonreciprocal devices, for building noise-tolerant quantum processors, realizing chiral networks, and backaction-immune quantum sensors.

A cavity optomechanical locking scheme based on the optical spring effect

We present a novel locking scheme for active length-stabilization and frequency detuning of a cavity optomechanical device based on the optical spring effect. The error signal is generated by utilizing the position measurement of a thermally driven intra-cavity nanomechanical device and employing its detuning-dependent frequency shift caused by the dispersive coupling to the cavity field. The scheme neither requires external modulation of the laser or the cavity nor does it demand for additional error signal readout, rendering its technical implementation rather simple for a large variety of existing optomechanical devices. Specifically, for large-linewidth microcavities or in situations where other locking schemes appear unfavorable conceptually or are hard to realize technically, the optical spring lock represents a potential alternative for stabilizing the cavity length. We explain the functional principle of the lock and characterize its performance in terms of bandwidth and gain profile.

Spectrometric detection of weak forces in cavity optomechanics

We propose a spectrometric method to detect a classical weak force acting upon the moving end mirror in a cavity optomechanical system. The force changes the equilibrium position of the end mirror, and thus the resonance frequency of the cavity field depends on the force to be detected. As a result, the magnitude of the force can be inferred by analyzing the single-photon emission and scattering spectra of the optomechanical cavity. Since the emission and scattering processes are much faster than the characteristic mechanical dissipation, the influence of the mechanical thermal noise is negligible in this spectrometric detection scheme. We also extent this spectrometric method to detect a monochromatic oscillating force by utilizing an optomechanical coupling modulated at the same frequency as the force.

Single-Photon Cooling in Microwave Magnetomechanics

Cavity optomechanics, where photons are coupled to mechanical motion, provides the tools to control mechanical motion near the fundamental quantum limits. Reaching single-photon strong coupling would allow to prepare the mechanical resonator in non-Gaussian quantum states. Preparing massive mechanical resonators in such states is of particular interest for testing the boundaries of quantum mechanics. This goal remains however challenging due to the small optomechanical couplings usually achieved with massive devices. Here we demonstrate a novel approach where a mechanical resonator is magnetically coupled to a microwave cavity. We measure a single-photon coupling of g_{0}/2π∼3  kHz, an improvement of one order of magnitude over current microwave optomechanical systems. At this coupling we measure a large single-photon cooperativity with C_{0}≳10, an important step to reach single-photon strong coupling. Such a strong interaction allows us to cool the massive mechanical resonator to a third of its steady state phonon population with less than two photons in the microwave cavity. Beyond tests for quantum foundations, our approach is also well suited as a quantum sensor or a microwave to optical transducer.

Cavity piezo-mechanics for superconducting-nanophotonic quantum interface

Hybrid quantum systems are essential for the realization of distributed quantum networks. In particular, piezo-mechanics operating at typical superconducting qubit frequencies features low thermal excitations, and offers an appealing platform to bridge superconducting quantum processors and optical telecommunication channels. However, integrating superconducting and optomechanical elements at cryogenic temperatures with sufficiently strong interactions remains a tremendous challenge. Here, we report an integrated superconducting cavity piezo-optomechanical platform where 10 GHz phonons are resonantly coupled with photons in a superconducting cavity and a nanophotonic cavity at the same time. Taking advantage of the large piezo-mechanical cooperativity (Cem ~7) and the enhanced optomechanical coupling boosted by a pulsed optical pump, we demonstrate coherent interactions at cryogenic temperatures via the observation of efficient microwave-optical photon conversion. This hybrid interface makes a substantial step towards quantum communication at large scale, as well as novel explorations in microwave-optical photon entanglement and quantum sensing mediated by gigahertz phonons.

Magnetostrictively Induced Stationary Entanglement between Two Microwave Fields

We present a scheme to entangle two microwave fields by using the nonlinear magnetostrictive interaction in a ferrimagnet. The magnetostrictive interaction enables the coupling between a magnon mode (spin wave) and a mechanical mode in the ferrimagnet, and the magnon mode simultaneously couples to two microwave cavity fields via the magnetic dipole interaction. The magnon-phonon coupling is enhanced by directly driving the ferrimagnet with a strong red-detuned microwave field, and the driving photons are scattered onto two sidebands induced by the mechanical motion. We show that two cavity fields can be prepared in a stationary entangled state if they are, respectively, resonant with two mechanical sidebands. The present scheme illustrates a new mechanism for creating entangled states of optical fields and enables potential applications in quantum information science and quantum tasks that require entangled microwave fields.

Laser Cooling of a Nanomechanical Oscillator to Its Zero-Point Energy

Optomechanical systems in the well-resolved-sideband regime are ideal for studying a myriad of quantum phenomena with mechanical systems, including backaction-evading measurements, mechanical squeezing, and nonclassical states generation. For these experiments, the mechanical oscillator should be prepared in its ground state, i.e., exhibit negligible residual excess motion compared to its zero-point motion. This can be achieved using the radiation pressure of laser light in the cavity by selectively driving the lower motional sideband, leading to sideband cooling. To date, the preparation of sideband-resolved optical systems to their zero-point energy has eluded laser cooling because of strong optical absorption heating. The alternative method of passive cooling suffers from the same problem, as the requisite milliKelvin environment is incompatible with the strong optical driving needed by many quantum protocols. Here, we employ a highly sideband-resolved silicon optomechanical crystal in a ^{3}He buffer-gas environment at ∼2  K to demonstrate laser sideband cooling to a mean thermal phonon occupancy of 0.09_{-0.01}^{+0.02} quantum (self-calibrated using motional sideband asymmetry), which is -7.4  dB of the oscillator's zero-point energy and corresponds to 92% ground state probability. Achieving such low occupancy by laser cooling opens the door to a wide range of quantum-optomechanical experiments in the optical domain.

Quantum Acoustomechanics with a Micromagnet

We show theoretically how to strongly couple the center-of-mass motion of a micromagnet in a harmonic potential to one of its acoustic phononic modes. The coupling is induced by a combination of an oscillating magnetic field gradient and a static homogeneous magnetic field. The former parametrically couples the center-of-mass motion to a magnonic mode while the latter tunes the magnonic mode in resonance with a given acoustic phononic mode. The magnetic fields can be adjusted to either cool the center-of-mass motion to the ground state or to enter into the strong quantum coupling regime. The center of mass can thus be used to probe and manipulate an acoustic mode, thereby opening new possibilities for out-of-equilibrium quantum mesoscopic physics. Our results hold for experimentally feasible parameters and apply to levitated micromagnets as well as micromagnets deposited on a clamped nanomechanical oscillator.

Optomechanics with levitated particles

Optomechanics is concerned with the use of light to control mechanical objects. As a field, it has been hugely successful in the production of precise and novel sensors, the development of low-dissipation nanomechanical devices, and the manipulation of quantum signals. Micro- and nano-particles levitated in optical fields act as nanoscale oscillators, making them excellent low-dissipation optomechanical objects, with minimal thermal contact to the environment when operating in vacuum. Levitated optomechanics is seen as the most promising route for studying high-mass quantum physics, with the promise of creating macroscopically separated superposition states at masses of 10⁶ amu and above. Optical feedback, both using active monitoring or the passive interaction with an optical cavity, can be used to cool the centre-of-mass of levitated nanoparticles well below 1 mK, paving the way to operation in the quantum regime. In addition, trapped mesoscopic particles are the paradigmatic system for studying nanoscale stochastic processes, and have already demonstrated their utility in state-of-the-art force sensing.

Spin-Phonon Interfaces in Coupled Nanomechanical Cantilevers

Coupled micro- and nanomechanical oscillators are of fundamental and technical interest for emerging quantum technologies. Upon interfacing with long-lived solid-state spins, the coherent manipulation of the quantum hybrid system becomes possible even at ambient conditions. Although the ability of these systems to act as a quantum bus inducing long-range spin-spin interactions has been known, the possibility to coherently couple electron/nuclear spins to the common modes of multiple oscillators and map their mechanical motion to spin-polarization has not been experimentally demonstrated. We here report experiments on interfacing spins to the common modes of a coupled cantilever system and show their correlation by translating ultralow forces induced by radiation from one oscillator to a distant spin. Further, we analyze the coherent spin-spin coupling induced by the common modes and estimate the entanglement generation among distant spins.

Manipulation of optomechanically induced transparency and absorption by indirectly coupling to an auxiliary cavity mode

We theoretically study the optomechanically induced transparency (OMIT) and absorption (OMIA) phenomena in a single microcavity optomechanical system, assisted by an indirectly coupled auxiliary cavity mode. We show that the interference effect between the two optical modes plays an important role and can be used to control the multiple-pathway induced destructive or constructive interference effect. The three-pathway interference could induce an absorption dip within the transparent window in the red sideband driving regime, while we can switch back and forth between OMIT and OMIA with the four-pathway interference. The conversion between the transparency peak and absorption dip can be achieved by tuning the relative amplitude and phase of the multiple light paths interference. Our system proposes a new platform to realize multiple pathways induced transparency and absorption in a single microcavity and a feasible way for realizing all-optical information processing.

Ultrastrong Parametric Coupling between a Superconducting Cavity and a Mechanical Resonator

We present a new optomechanical device where the motion of a micromechanical membrane couples to a microwave resonance of a three-dimensional superconducting cavity. With this architecture, we realize ultrastrong parametric coupling, where the coupling not only exceeds the dissipation in the system but also rivals the mechanical frequency itself. In this regime, the optomechanical interaction induces a frequency splitting between the hybridized normal modes that reaches 88% of the bare mechanical frequency, limited by the fundamental parametric instability. The coupling also exceeds the mechanical thermal decoherence rate, enabling new applications in ultrafast quantum state transfer and entanglement generation.

Feedback Cooling of a Room Temperature Mechanical Oscillator close to its Motional Ground State

Preparing mechanical systems in their lowest possible entropy state, the quantum ground state, starting from a room temperature environment is a key challenge in quantum optomechanics. This would not only enable creating quantum states of truly macroscopic systems, but at the same time also lay the groundwork for a new generation of quantum-limited mechanical sensors in ambient environments. Laser cooling of optomechanical devices using the radiation pressure force combined with cryogenic precooling has been successful at demonstrating ground state preparation of various devices, while a similar demonstration starting from a room temperature environment remains an outstanding goal. Here, we combine integrated nanophotonics with phononic band gap engineering to simultaneously overcome prior limitations in the isolation from the surrounding environment and the achievable mechanical frequencies, as well as limited optomechanical coupling strength, demonstrating a single-photon cooperativity of 200. This new microchip technology allows us to feedback cool a mechanical resonator to around 1 mK, near its motional ground state, from room temperature. Our experiment marks a major step toward accessible, widespread quantum technologies with mechanical resonators.

Measurement of Motion beyond the Quantum Limit by Transient Amplification

Through simultaneous but unequal electromechanical amplification and cooling processes, we create a method for a nearly noiseless pulsed measurement of mechanical motion. We use transient electromechanical amplification (TEA) to monitor a single motional quadrature with a total added noise -8.5±2.0  dB relative to the zero-point motion of the oscillator, or equivalently the quantum limit for simultaneous measurement of both mechanical quadratures. We demonstrate that TEA can be used to resolve fine structure in the phase space of a mechanical oscillator by tomographically reconstructing the density matrix of a squeezed state of motion. Without any inference or subtraction of noise, we directly observe a squeezed variance 2.8±0.3  dB below the oscillator's zero-point motion.