Optomechanical Bell Test

Geometric interpretation and experimental test of Leggett inequalities with nonmaximally entangled states

Leggett inequality states that nonlocal hidden-variable models might still be incompatible with the predictions of quantum physics. However, its theoretical and experimental demonstration is only in the scenario of 2-dimensional maximally entangled systems. An open question remains as to whether the Leggett inequality can be violated by nonmaximally entangled states. Here, we answer this question both in theory and experiment. Specifically, from the point of view of geometry, we theoretically map the problem of maximizing the correlation measure in the Leggett inequality to maximizing the sum of an ellipse's diameter and semi-diameter axes, accordingly, demonstrating that the violation of the Leggett inequality requires a more robust entanglement than that of Bell's theory. Experimentally, by leveraging the controllable photonic orbital angular momentum entanglement, we demonstrate the violation of Leggett-type inequalities by more than 8.7 and 4.5 standard deviations under concurrence C = 0.95 and 0.9, respectively. Our observations indicate that, the requirement for quantum correlation should be increased to exclude a particular class of non-local hidden variable theories that abide by Leggett's model, providing insights into the boundaries of quantum correlation and the limitations imposed by non-local hidden variables.

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.

A microwave scattering spectral method to detect the nanomechanical vibrations embedded in a superconducting qubit

Nanomechanical resonators (NMRs), as the quantum mechanical sensing probers, have played the important roles for various high-precision quantum measurements. Differing from the previous emission spectral probes (i.e., the NMR modified the atomic emission), in this paper we propose an alternative approach, i.e., by probing the scattering spectra of the quantum mechanical prober coupled to the driving microwaves, to characterize the physical features of the NMR embedded in a rf-SQUID based superconducting qubit. It is shown that, from the observed specifical frequency points in the spectra, i.e., either the dips or the peaks, the vibrational features (i.e., they are classical vibration or quantum mechanical one) and the physical parameters (typically such as the vibrational frequency and displacements) of the NMR can be determined effectively. The proposal is feasible with the current technique and should be useful to design the desired NMRs for various quantum metrological 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.

Force-Gradient Sensing and Entanglement via Feedback Cooling of Interacting Nanoparticles

We show theoretically that feedback cooling of two levitated, interacting nanoparticles enables differential sensing of forces and the observation of stationary entanglement. The feedback drives the two particles into a stationary, nonthermal state which is susceptible to inhomogeneous force fields and which exhibits entanglement for sufficiently strong interparticle couplings. We predict that force-gradient sensing at the zepto-Newton per micron range is feasible and that entanglement due to the Coulomb interaction between charged particles can be realistically observed in state-of-the-art setups.

Enhanced Cavity Optomechanics with Quantum-Well Exciton Polaritons

Semiconductor microresonators embedding quantum wells can host tightly confined and mutually interacting excitonic, optical, and mechanical modes at once. We theoretically investigate the case where the system operates in the strong exciton-photon coupling regime, while the optical and excitonic resonances are parametrically modulated by the interaction with a mechanical mode. Owing to the large exciton-phonon coupling at play in semiconductors, we predict an enhancement of polariton-phonon interactions by 2 orders of magnitude with respect to mere optomechanical coupling: a near-unity single-polariton quantum cooperativity is within reach for current semiconductor resonator platforms. We further analyze how polariton nonlinearities affect dynamical backaction, modifying the capability to cool or amplify the mechanical motion.

Optomechanical crystal with bound states in the continuum

Chipscale micro- and nano-optomechanical systems, hinging on the intangible radiation-pressure force, have shown their unique strength in sensing, signal transduction, and exploration of quantum physics with mechanical resonators. Optomechanical crystals, as one of the leading device platforms, enable simultaneous molding of the band structure of optical photons and microwave phonons with strong optomechanical coupling. Here, we demonstrate a new breed of optomechanical crystals in two-dimensional slab-on-substrate structures empowered by mechanical bound states in the continuum (BICs) at 8 GHz. We show symmetry-induced BIC emergence with optomechanical couplings up to g/2π ≈ 2.5 MHz per unit cell, on par with low-dimensional optomechanical crystals. Our work paves the way towards exploration of photon-phonon interaction beyond suspended microcavities, which might lead to new applications of optomechanics from phonon sensing to quantum transduction.

Unsuspended optomechanical systems might enable unique applications for quantum sensing and transduction. Here, the authors demonstrate a two-dimensional slab-on-substrate optomechanical crystal empowered by mechanical bound states in the continuum.

Measuring High-Order Phonon Correlations in an Optomechanical Resonator

We use single photon detectors to probe the motional state of a superfluid ^{4}He resonator of mass ∼1  ng. The arrival times of Stokes and anti-Stokes photons (scattered by the resonator's acoustic mode) are used to measure the resonator's phonon coherences up to the fourth order. By postselecting on photon detection events, we also measure coherences in the resonator when ≤3 phonons have been added or subtracted. These measurements are found to be consistent with predictions that assume the acoustic mode to be in thermal equilibrium with a bath through a Markovian coupling.

Enhanced Phonon Antibunching in a Circuit Quantum Acoustodynamical System Containing Two Surface Acoustic Wave Resonators

We propose a scheme to implement the phonon antibunching and phonon blockade in a circuit quantum acoustodynamical system containing two surface acoustic wave (SAW) resonators coupled to a superconducting qubit. In the cases of driving only one SAW resonator and two SAW resonators, we investigate the phonon statistics by numerically calculating the second-order correlation function. It is found that, when only one SAW cavity is resonantly driven, the phonon antibunching effect can be achieved even when the qubit–phonon coupling strength is smaller than the decay rates of acoustic cavities. This result physically originates from the quantum interference between super-Poissonian statistics and Poissonian statistics of phonons. In particular, when the two SAW resonators are simultaneously driven under the mechanical resonant condition, the phonon antibunching effect can be significantly enhanced, which ultimately allows for the generation of a phonon blockade. Moreover, the obtained phonon blockade can be optimized by regulating the intensity ratio of the two SAW driving fields. In addition, we also discuss in detail the effect of system parameters on the phonon statistics. Our work provides an alternative way for manipulating and controlling the nonclassical effects of SAW phonons. It may inspire the engineering of new SAW-based phonon devices and extend their applications in quantum information processing.

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.

Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.

Quasinormal-Mode Perturbation Theory for Dissipative and Dispersive Optomechanics

Despite the several novel features arising from the dissipative optomechanical coupling, such effect remains vastly unexplored due to the lack of a simple formalism that captures non-Hermiticity in the engineering of optomechanical systems. In this Letter, we show that quasinormal-mode-based perturbation theory is capable of correctly predicting both dispersive and dissipative optomechanical couplings. We validate our model through simulations and also by comparison with experimental results reported in the literature. Finally, we apply this formalism to plasmonic systems, used for molecular optomechanics, where strong dissipative coupling signatures in the amplification of vibrational modes could be observed.

Bell correlations between light and vibration at ambient conditions

Time-resolved Raman spectroscopy techniques offer various ways to study the dynamics of molecular vibrations in liquids or gases and optical phonons in crystals. While these techniques give access to the coherence time of the vibrational modes, they are not able to reveal the fragile quantum correlations that are spontaneously created between light and vibration during the Raman interaction. Here, we present a scheme leveraging universal properties of spontaneous Raman scattering to demonstrate Bell correlations between light and a collective molecular vibration. We measure the decay of these hybrid photon-phonon Bell correlations with sub-picosecond time resolution and find that they survive over several hundred oscillations at ambient conditions. Our method offers a universal approach to generate entanglement between light and molecular vibrations. Moreover, our results pave the way for the study of quantum correlations in more complex solid-state and molecular systems in their natural state.

Two-dimensional optomechanical crystal cavity with high quantum cooperativity

Optomechanical systems offer new opportunities in quantum information processing and quantum sensing. Many solid-state quantum devices operate at millikelvin temperatures—however, it has proven challenging to operate nanoscale optomechanical devices at these ultralow temperatures due to their limited thermal conductance and parasitic optical absorption. Here, we present a two-dimensional optomechanical crystal resonator capable of achieving large cooperativity C and small effective bath occupancy n_b, resulting in a quantum cooperativity C_eff ≡ C/n_b > 1 under continuous-wave optical driving. This is realized using a two-dimensional phononic bandgap structure to host the optomechanical cavity, simultaneously isolating the acoustic mode of interest in the bandgap while allowing heat to be removed by phonon modes outside of the bandgap. This achievement paves the way for a variety of applications requiring quantum-coherent optomechanical interactions, such as transducers capable of bi-directional conversion of quantum states between microwave frequency superconducting quantum circuits and optical photons in a fiber optic network.

The authors demonstrate a two-dimensional optomechanical crystal cavity which traps a phonon mode within a phononic bandgap while yielding large thermal conductivity to the environment. High quantum cooperativity at millikelvin temperatures is realized, suitable for quantum coherent control.

Giant Tunable Mechanical Nonlinearity in Graphene-Silicon Nitride Hybrid Resonator

High quality factor mechanical resonators have shown great promise in the development of classical and quantum technologies. Simultaneously, progress has been made in developing controlled mechanical nonlinearity. Here, we combine these two directions of progress in a single platform consisting of coupled silicon nitride (SiNx) and graphene mechanical resonators. We show that nonlinear response can be induced on a large area SiNx resonator mode and can be efficiently controlled by coupling it to a gate-tunable, freely suspended graphene mode. The induced nonlinear response of the hybrid modes, as measured on the SiNx resonator surface is giant, with one of the highest measured Duffing constants. We observe a novel phononic frequency comb which we use as an alternate validation of the measured values, along with numerical simulations which are in overall agreement with the measurements.

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.

Enhanced photon blockade in an optomechanical system with parametric amplification

We propose a scheme to enhance the single- and two-photon blockade effects significantly in a nonlinear hybrid optomechanical system with optical parametric amplification (OPA). The scheme does not rely on strong single-photon optomechanical coupling and can eliminate the disadvantages of suppressing multi-photon excitation incompletely. Through analyzing the single-photon blockade (1PB) mechanism and optimizing the system parameters, we obtain a perfect 1PB with a high occupancy probability of single-photon excitation, which means that a high-quality and efficient single-photon source can be generated. Moreover, we find that not only the two-photon blockade (2PB) effect is significantly enhanced, but also the region where 2PB occurs is widened when OPA exists, where we also derive the optimal parameter condition to maximize two-photon emission and higher photon excitations intensely suppressed at the same time.

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.

Microwave-to-optics conversion using a mechanical oscillator in its quantum groundstate

Conversion between signals in the microwave and optical domains is of great interest both for classical telecommunication, as well as for connecting future superconducting quantum computers into a global quantum network. For quantum applications, the conversion has to be both efficient, as well as operate in a regime of minimal added classical noise. While efficient conversion has been demonstrated using mechanical transducers, they have so far all operated with a substantial thermal noise background. Here, we overcome this limitation and demonstrate coherent conversion between GHz microwave signals and the optical telecom band with a thermal background of less than one phonon. We use an integrated, on-chip electro-opto-mechanical device that couples surface acoustic waves driven by a resonant microwave signal to an optomechanical crystal featuring a 2.7 GHz mechanical mode. We initialize the mechanical mode in its quantum groundstate, which allows us to perform the transduction process with minimal added thermal noise, while maintaining an optomechanical cooperativity >1, so that microwave photons mapped into the mechanical resonator are effectively upconverted to the optical domain. We further verify the preservation of the coherence of the microwave signal throughout the transduction process.

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.

Gallium Phosphide as a Piezoelectric Platform for Quantum Optomechanics

Recent years have seen extraordinary progress in creating quantum states of mechanical oscillators, leading to great interest in potential applications for such systems in both fundamental as well as applied quantum science. One example is the use of these devices as transducers between otherwise disparate quantum systems. In this regard, a promising approach is to build integrated piezoelectric optomechanical devices that are then coupled to microwave circuits. Optical absorption, low quality factors, and other challenges have up to now prevented operation in the quantum regime, however. Here, we design and characterize such a piezoelectric optomechanical device fabricated from gallium phosphide in which a 2.9 GHz mechanical mode is coupled to a high quality factor optical resonator in the telecom band. The large electronic band gap and the resulting low optical absorption of this new material, on par with devices fabricated from silicon, allows us to demonstrate quantum behavior of the structure. This not only opens the way for realizing noise-free quantum transduction between microwaves and optics, but in principle also from various color centers with optical transitions in the near visible to the telecom band.

Quantifying the Mesoscopic Nature of Einstein-Podolsky-Rosen Nonlocality

Evidence for Bell's nonlocality is so far mainly restricted to microscopic systems, where the elements of reality that are negated predetermine results of measurements to within one spin unit. Any observed nonlocal effect (or lack of classical predetermination) is then limited to no more than the difference of a single photon or electron being detected or not (at a given detector). In this paper, we analyze experiments that report the Einstein-Podolsky-Rosen (EPR) steering form of nonlocality for mesoscopic photonic or Bose-Einstein condensate systems. Using an EPR steering parameter, we show how the EPR nonlocalities involved can be quantified for four-mode states, to give evidence of EPR-nonlocal effects corresponding to a two-mode number difference of 10^{5} photons, or of several tens of atoms (at a given site). Applying to experiments, we also show how the variance criterion of Duan, Giedke, Cirac and Zoller for EPR entanglement can be used to determine a lower bound on the number of particles in a pure two-mode EPR-entangled or steerable state.

Flexure-tuned membrane-at-the-edge optomechanical system

We introduce a passively-aligned, flexure-tuned cavity optomechanical system in which a membrane is positioned microns from one end mirror of a Fabry-Perot optical cavity. By displacing the membrane through gentle flexure of its silicon supporting frame (i.e., to ∼80 m radius of curvature (ROC)), we gain access to the full range of available optomechanical couplings, finding also that the optical spectrum exhibits none of the abrupt discontinuities normally found in "membrane-in-the-middle" (MIM) systems. More aggressive flexure (3 m ROC) enables >15 μm membrane travel, milliradian tilt tuning, and a wavelength-scale (1.64 ± 0.78 μm) membrane-mirror separation. We also provide a complete set of analytical expressions for this system's leading-order dispersive and dissipative optomechanical couplings. Notably, this system can potentially generate orders of magnitude larger linear dissipative or quadratic dispersive strong coupling parameters than is possible with a MIM system. Additionally, it can generate the same purely quadratic dispersive coupling as a MIM system, but with significantly suppressed linear dissipative back-action (and force noise).

Optimal Feedback Cooling of a Charged Levitated Nanoparticle with Adaptive Control

We use an optimal control protocol to cool one mode of the center-of-mass motion of an optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force on a charged particle with a pair of electrodes and follows the control law of a linear quadratic regulator, whose gains are optimized by a machine learning algorithm in under 5 s. With a simpler and more robust setup than optical feedback schemes, we achieve a minimum center-of-mass temperature of 5 mK at 3×10^{-7}  mbar and transients 10-600 times faster than cold damping. This cooling technique can be easily extended to 3D cooling and is particularly relevant for studies demanding high repetition rates and force sensing experiments with levitated objects.