Surpassing the Standard Quantum Limit Using an Optical Spring

Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements imposes a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a backaction evading measurement technique, reduce thermal noise to below the level of backaction, and exploit cancellations of any excess noise contributions at the detector. Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL sensitivity nearly two times better than previous measurements, and with an architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. We measure a total sensitivity below the SQL by 2.8 dB, corresponding to a reduction in the noise power by 72±5.1% below the quantum limit. Through the use of a detuned cavity and the optical spring effect, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the Universe.

Ground-state cooling of a mechanical oscillator by a noisy environment

Dissipation and the accompanying fluctuations are often seen as detrimental for quantum systems since they are associated with fast relaxation and loss of phase coherence. However, it has been proposed that a pure state can be prepared if external noise induces suitable downwards transitions, while exciting transitions are blocked. We demonstrate such a refrigeration mechanism in a cavity optomechanical system, where we prepare a mechanical oscillator in its ground state by injecting strong electromagnetic noise at frequencies around the red mechanical sideband of the cavity. The optimum cooling is reached with a noise bandwidth smaller than but on the order of the cavity decay rate. At higher bandwidths, cooling is less efficient as suitable transitions are not effectively activated. In the opposite regime where the noise bandwidth becomes comparable to the mechanical damping rate, damping follows the noise amplitude adiabatically, and the cooling is also suppressed.

Single-photon induced instabilities in a cavity electromechanical device

Cavity-electromechanical systems are extensively used for sensing and controlling the vibrations of mechanical resonators down to their quantum limit. The nonlinear radiation-pressure interaction in these systems could result in an unstable response of the mechanical resonator showing features such as frequency-combs, period-doubling bifurcations and chaos. However, due to weak light-matter interaction, typically these effects appear at very high driving strengths. By using polariton modes formed by a strongly coupled flux-tunable transmon and a microwave cavity, here we demonstrate an electromechanical device and achieve a single-photon coupling rateg 0 / 2 π of 160 kHz, which is nearly 4% of the mechanical frequency ωm. Due to large g0/ωm ratio, the device shows an unstable mechanical response resulting in frequency combs in sub-single photon limit. We systematically investigate the boundary of the unstable response and identify two important regimes governed by the optomechanical backaction and the nonlinearity of the electromagnetic mode. Such an improvement in the single-photon coupling rate and the observations of microwave frequency combs at single-photon levels may have applications in the quantum control of the motional states and critical parametric sensing. Our experiments strongly suggest the requirement of newer approaches to understand instabilities.

State Expansion of a Levitated Nanoparticle in a Dark Harmonic Potential

We spatially expand and subsequently contract the motional thermal state of a levitated nanoparticle using a hybrid trapping scheme. The particle's center-of-mass motion is initialized in a thermal state (temperature 155 mK) in an optical trap and then expanded by subsequent evolution in a much softer Paul trap in the absence of optical fields. We demonstrate expansion of the motional state's standard deviation in position by a factor of 24. In our system, state expansion occurs devoid of backaction from photon recoil, making this approach suitable for coherent wave function expansion.

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.

Coherent optical coupling to surface acoustic wave devices

Surface acoustic waves (SAW) and associated devices are ideal for sensing, metrology, and hybrid quantum devices. While the advances demonstrated to date are largely based on electromechanical coupling, a robust and customizable coherent optical coupling would unlock mature and powerful cavity optomechanical control techniques and an efficient optical pathway for long-distance quantum links. Here we demonstrate direct and robust coherent optical coupling to Gaussian surface acoustic wave cavities with small mode volumes and high quality factors (>105 measured here) through a Brillouin-like optomechanical interaction. High-frequency SAW cavities designed with curved metallic acoustic reflectors deposited on crystalline substrates are efficiently optically accessed along piezo-active directions, as well as non-piezo-active (electromechanically inaccessible) directions. The precise optical technique uniquely enables controlled analysis of dissipation mechanisms as well as detailed transverse spatial mode spectroscopy. These advantages combined with simple fabrication, large power handling, and strong coupling to quantum systems make SAW optomechanical platforms particularly attractive for sensing, material science, and hybrid quantum systems.

Optomechanical squeezing with strong harmonic mechanical driving

In this paper, we propose an optomechanical scheme for generating mechanical squeezing over the 3 dB limit, with the mechanical mirror being driven by a strong and linear harmonic force. In contrast to parametric mechanical driving, the linearly driven force shakes the mechanical mirror periodically oscillating at twice the mechanical eigenfrequency with large amplitude, where the mechanical mirror can be dissipatively stabilized by the engineered cavity reservoir to a dynamical squeezed steady state with a maximum degree of squeezing over 8 dB. The mechanical squeezing of more than 3 dB can be achieved even for a mechanical thermal temperature larger than 100 mK. The scheme can be implemented in a cascaded optomechanical setup, with potential applications in engineering continuous variable entanglement and quantum sensing.

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.

Instabilities near Ultrastrong Coupling in a Microwave Optomechanical Cavity

With artificially engineered systems, it is now possible to realize the coherent interaction rate, which can become comparable to the mode frequencies, a regime known as ultrastrong coupling (USC). We experimentally realize a cavity-electromechanical device using a superconducting waveguide cavity and a mechanical resonator. In the presence of a strong pump, the mechanical-polaritons splitting can nearly reach 81% of the mechanical frequency, overwhelming all the dissipation rates. Approaching the USC limit, the steady-state response becomes unstable. We systematically measure the boundary of the unstable response while varying the pump parameters. The unstable dynamics display rich phases, such as self-induced oscillations, period-doubling bifurcation, and period-tripling oscillations, ultimately leading to the chaotic behavior. The experimental results and their theoretical modeling suggest the importance of residual nonlinear interaction terms in the weak-dissipative regime.

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.

Spectral Analysis of Quantum Field Fluctuations in a Strongly Coupled Optomechanical System

With a levitodynamics experiment in the strong and coherent quantum optomechanical coupling regime, we demonstrate that the oscillator acts as a broadband quantum spectrum analyzer. The asymmetry between positive and negative frequency branches in the displacement spectrum traces out the spectral features of the quantum fluctuations in the cavity field, which are thus explored over a wide spectral range. Moreover, in our two-dimensional mechanical system the quantum backaction, generated by such vacuum fluctuations, is strongly suppressed in a narrow spectral region due to a destructive interference in the overall susceptibility.

Beating thermal noise in a dynamic signal measurement by a nanofabricated cavity optomechanical sensor

Thermal fluctuations often impose both fundamental and practical measurement limits on high-performance sensors, motivating the development of techniques that bypass the limitations imposed by thermal noise outside cryogenic environments. Here, we theoretically propose and experimentally demonstrate a measurement method that reduces the effective transducer temperature and improves the measurement precision of a dynamic impulse response signal. Thermal noise-limited, integrated cavity optomechanical atomic force microscopy probes are used in a photothermal-induced resonance measurement to demonstrate an effective temperature reduction by a factor of ≈25, i.e., from room temperature down as low as ≈12 K, without cryogens. The method improves the experimental measurement precision and throughput by >2×, approaching the theoretical limit of ≈3.5× improvement for our experimental conditions. The general applicability of this method to dynamic measurements leveraging thermal noise-limited harmonic transducers will have a broad impact across a variety of measurement platforms and scientific fields.

Geometrical Bounds on Irreversibility in Squeezed Thermal Bath

Irreversible entropy production (IEP) plays an important role in quantum thermodynamic processes. Here, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a system coupled to a squeezed thermal bath subject to dissipation and dephasing, respectively. We find that the geometrical bounds of the IEP always shift in a contrary way under dissipation and dephasing, where the lower and upper bounds turning to be tighter occur in the situation of dephasing and dissipation, respectively. However, either under dissipation or under dephasing, we may reduce both the critical time of the IEP itself and the critical time of the bounds for reaching an equilibrium by harvesting the benefits of squeezing effects in which the values of the IEP, quantifying the degree of thermodynamic irreversibility, also become smaller. Therefore, due to the nonequilibrium nature of the squeezed thermal bath, the system-bath interaction energy has a prominent impact on the IEP, leading to tightness of its bounds. Our results are not contradictory with the second law of thermodynamics by involving squeezing of the bath as an available resource, which can improve the performance of quantum thermodynamic devices.

Cavity optomechanical chaos

Cavity optomechanics provides a powerful platform for observing many interesting classical and quantum nonlinear phenomena due to the radiation-pressure coupling between its optical and mechanical modes. In particular, the chaos induced by optomechanical nonlinearity has been of great concern because of its importance both in fundamental physics and potential applications ranging from secret information processing to optical communications. This review focuses on the chaotic dynamics in optomechanical systems. The basic theory of general nonlinear dynamics and the fundamental properties of chaos are introduced. Several nonlinear dynamical effects in optomechanical systems are demonstrated. Moreover, recent remarkable theoretical and experimental efforts in manipulating optomechanical chaotic motions are addressed. Future perspectives of chaos in hybrid systems are also discussed.

Mechanical squeezing in an active-passive-coupled double-cavity optomechanical system via pump modulation

We focus on the generation of mechanical squeezing by using periodically amplitude-modulated laser to drive an active-passive-coupled double-cavity optomechanical system, where the coupled gain cavity and loss cavity can form into a parity-time (P T)-symmetry system. The numerical analysis of the system stability shows that the system is more likely to be stable in the unbroken-P T-symmetry regime than in the broken-P T-symmetry regime. The mechanical squeezing in the active-passive system exhibits stronger robustness against the thermal noise than that in the passive-passive system, and the so-called 3 dB limit can be broken in the resolved-sideband regime. Furthermore, it is also found that the mechanical squeezing obtained in the unbroken-P T-symmetry region is stronger than that in the broken-P T-symmetry region. This work may be meaningful for the quantum state engineering in the gain-loss quantum system that contributes to the study of P T-symmetric physics in the quantum regime.

Topological lattices realized in superconducting circuit optomechanics

Cavity optomechanics enables the control of mechanical motion through the radiation-pressure interaction¹, and has contributed to the quantum control of engineered mechanical systems ranging from kilogramme-scale Laser Interferometer Gravitational-wave Observatory (LIGO) mirrors to nanomechanical systems, enabling ground-state preparation^2,3, entanglement^4,5, squeezing of mechanical objects⁶, position measurements at the standard quantum limit⁷ and quantum transduction⁸. Yet nearly all previous schemes have used single- or few-mode optomechanical systems. By contrast, new dynamics and applications are expected when using optomechanical lattices⁹, which enable the synthesis of non-trivial band structures, and these lattices have been actively studied in the field of circuit quantum electrodynamics¹⁰. Superconducting microwave optomechanical circuits² are a promising platform to implement such lattices, but have been compounded by strict scaling limitations. Here we overcome this challenge and demonstrate topological microwave modes in one-dimensional circuit optomechanical chains realizing the Su-Schrieffer-Heeger model^11,12. Furthermore, we realize the strained graphene model^13,14 in a two-dimensional optomechanical honeycomb lattice. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode functions of the hybridized modes without using any local probe^15,16. This enables us to reconstruct the full underlying lattice Hamiltonian and directly measure the existing residual disorder. Such optomechanical lattices, accompanied by the measurement techniques introduced, offer an avenue to explore collective^17,18, quantum many-body¹⁹ and quench²⁰ dynamics, topological properties^9,21 and, more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedom^22-24.

Optomechanical squeezing with pulse modulation

Quantum control technology provides an increasingly useful toolbox for quantum information tasks. In this Letter, by introducing a pulsed coupling to a standard optomechanical system, we show that stronger squeezing can be obtained with pulse modulation due to the reduction of the heating coefficient. Also, the general squeezed states, such as the squeezed vacuum, squeezed coherent, and squeezed cat states, can be obtained with their squeezing level exceeding 3 dB. Moreover, our scheme is robust to cavity decay, thermal temperature, and classical noise, which is friendly to experiments. The present work can extend the application of quantum engineering technology in optomechanical systems.

Beating the 3 dB Limit for Intracavity Squeezing and Its Application to Nondemolition Qubit Readout

While the squeezing of a propagating field can, in principle, be made arbitrarily strong, the cavity-field squeezing is subject to the well-known 3 dB limit, and thus has limited applications. Here, we propose the use of a fully quantum degenerate parametric amplifier (DPA) to beat this squeezing limit. Specifically, we show that by simply applying a two-tone driving to the signal mode, the pump mode can, counterintuitively, be driven by the photon loss of the signal mode into a squeezed steady state with, in principle, an arbitrarily high degree of squeezing. Furthermore, we demonstrate that this intracavity squeezing can increase the signal-to-noise ratio of longitudinal qubit readout exponentially with the degree of squeezing. Correspondingly, an improvement of the measurement error by many orders of magnitude can be achieved even for modest parameters. In stark contrast, using intracavity squeezing of the semiclassical DPA cannot practically increase the signal-to-noise ratio and thus improve the measurement error. Our results extend the range of applications of DPAs and open up new opportunities for modern quantum technologies.

Parametrically enhanced interactions and nonreciprocal bath dynamics in a photon-pressure Kerr amplifier

Photon-pressure coupling between two superconducting circuits is a promising platform for investigating radiation-pressure coupling in distinct parameter regimes and for the development of radio-frequency (RF) quantum photonics and quantum-limited RF sensing. Here, we implement photon-pressure coupling between two superconducting circuits, one of which can be operated as a parametric amplifier. We demonstrate a Kerr-based enhancement of the photon-pressure single-photon coupling rate and an increase of the cooperativity by one order of magnitude in the amplifier regime. In addition, we observe that the intracavity amplification reduces the measurement imprecision of RF signal detection. Last, we demonstrate that RF mode sideband cooling is unexpectedly not limited to the effective amplifier mode temperature arising from quantum noise amplification, which we interpret in the context of nonreciprocal heat transfer between the two circuits. Our results demonstrate how Kerr amplification can be used as resource for enhanced photon-pressure systems and Kerr cavity optomechanics.

Quantum fisher information of an optomechanical force sensor driven by a squeezed vacuum field

We investigate the enhancement in sensitivity when measuring a weak force through the optical response of an optomechanical oscillator driven by squeezed light. In the context of a quantum sensor based on cavity-optomechanics, the sensitivity scaling measured by the quantum Fisher information for a squeezed vacuum state pump is compared to that for a coherent state pump. We show that squeezed state inputs can produce noise levels below the standard quantum limit and even the Heisenberg limit in given regimes. This study shows that new pathways can be opened for enhanced quantum sensing with optomechanical systems conducive to measuring various physical quantities such as gravitational force, acceleration, and acoustics.

Unidirectional amplification in optomechanical system coupling with a structured bath

Nonreciprocity plays an indispensable role in quantum information transmission. We theoretically study the unidirectional amplification in the non-Markovian regime, in which a nanosphere surrounded by a structured bath is trapped in a single (dual)-mode cavity. The global mechanical response function of the nanosphere is markedly altered by the non-Markovian structured bath through shifting the effective frequency and magnifying the response function. Consequently, when there is a small difference in the transmission rate within the regime of Markovian, the unidirectional amplification is achieved in the super-Ohmic spectral environment. In the double-optomechanical coupling system, the phase difference between two optomechanical couplings can reverse the transmission direction. Meanwhile, the non-Markovian bath still can amplify the signal because of the XX-type coupling between nanosphere and its bath.

Simultaneous ground-state cooling of identical mechanical oscillators by Lyapunov control

The simultaneous cooling of multiple mechanical oscillators in the cavity optomechanical system has aroused people's attention and may be applicable in the quantum information process. In this paper, a scheme to realize the simultaneous ground-state cooling of two identical mechanical oscillators is proposed, where the frequency of one of the oscillators is designed according to Lyapunov control. By this method, the dark mode can effectively couple with the bright mode so that the two identical oscillators can be simultaneously cooled to their ground state. Extending this scheme into multiple identical mechanical oscillators, we show that simultaneous cooling can also be achieved.

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.

Nonlinearity-mediated digitization and amplification in electromechanical phonon-cavity systems

Electromechanical phonon-cavity systems are man-made micro-structures, in which vibrational energy can be coherently transferred between different degrees of freedom. In such devices, the energy transfer direction and coupling strength can be parametrically controlled, offering great opportunities for both fundamental studies and practical applications such as phonon manipulation and sensing. However, to date the investigation of such systems has largely been limited to linear vibrations, while their responses in the nonlinear regime remain yet to be explored. Here, we demonstrate nonlinear operation of electromechanical phonon-cavity systems, and show that the resonant response differs drastically from that in the linear regime. We further demonstrate that by controlling the parametric pump, one can achieve nonlinearity-mediated digitization and amplification in the frequency domain, which can be exploited to build high-performance MEMS sensing devices based on phonon-cavity systems. Our findings offer intriguing opportunities for creating frequency-shift-based sensors and transducers.

Improving the Stochastic Feedback Cooling of a Mechanical Oscillator Using a Degenerate Parametric Amplifier

Cooling of a macroscopic mechanical resonator to extremely low temperatures is a necessary condition to observe a variety of macroscopic quantum phenomena. Here, we study the stochastic feedback cooling of a mechanical resonator in an optomechanical system with a degenerate optical parametric amplifier (OPA). In the bad-cavity limit, we find that the OPA can enhance the cooling of the movable mirror in the stochastic feedback cooling scheme. The movable mirror can be cooled from 132 mK to 0.033 mK, which is lower than that without the OPA by a factor of about 5.

Mechanical Squeezing via Unstable Dynamics in a Microcavity

We theoretically show that strong mechanical quantum squeezing in a linear optomechanical system can be rapidly generated through the dynamical instability reached in the far red-detuned and ultrastrong coupling regime. We show that this mechanism, which harnesses unstable multimode quantum dynamics, is particularly suited to levitated optomechanics, and we argue for its feasibility for the case of a levitated nanoparticle coupled to a microcavity via coherent scattering. We predict that for submillimeter-sized cavities the particle motion, initially thermal and well above its ground state, becomes mechanically squeezed by tens of decibels on a microsecond timescale. Our results bring forth optical microcavities in the unresolved sideband regime as powerful mechanical squeezers for levitated nanoparticles, and hence as key tools for quantum-enhanced inertial and force sensing.

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.

Mechanical frequency control in inductively coupled electromechanical systems

Nano-electromechanical systems implement the opto-mechanical interaction combining electromagnetic circuits and mechanical elements. We investigate an inductively coupled nano-electromechanical system, where a superconducting quantum interference device (SQUID) realizes the coupling. We show that the resonance frequency of the mechanically compliant string embedded into the SQUID loop can be controlled in two different ways: (1) the bias magnetic flux applied perpendicular to the SQUID loop, (2) the magnitude of the in-plane bias magnetic field contributing to the nano-electromechanical coupling. These findings are quantitatively explained by the inductive interaction contributing to the effective spring constant of the mechanical resonator. In addition, we observe a residual field dependent shift of the mechanical resonance frequency, which we attribute to the finite flux pinning of vortices trapped in the magnetic field biased nanostring.

Quantum-coherent nanoscience

For the past three decades nanoscience has widely affected many areas in physics, chemistry and engineering, and has led to numerous fundamental discoveries, as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing, has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this Review according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system, such as charge, spin, mechanical motion and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations.

Rapid Quantum Squeezing by Jumping the Harmonic Oscillator Frequency

Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic oscillators, the rate of generating squeezing is set by a quantum speed limit. Therefore, the degree to which a quantum advantage can be used in practice is limited by the time needed to create the state relative to the rate of unavoidable decoherence. Alternatively, a sudden change of harmonic oscillator's frequency projects a ground state into a squeezed state which can circumvent the time constraint. Here, we create squeezed states of atomic motion by sudden changes of the harmonic oscillation frequency of atoms in an optical lattice. Building on this protocol, we demonstrate rapid quantum amplification of a displacement operator that could be used for detecting motion. Our results can speed up quantum gates and enable quantum sensing and quantum information processing in noisy environments.

Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators

We investigate the sideband spectra of a driven nonlinear mode with its eigenfrequency being modulated at a low frequency (<1  kHz). This additional parametric modulation leads to prominent antiresonance line shapes in the sideband spectra, which can be controlled through the vibration state of the driven mode. We also establish a direct connection between the antiresonance frequency and the squeezing of thermal fluctuation in the system. Our Letter not only provides a simple and robust method for squeezing characterization, but also opens a new possibility toward sideband applications.

Cooling photon-pressure circuits into the quantum regime

Quantum control of electromagnetic fields was initially established in the optical domain and has been advanced to lower frequencies in the gigahertz range during the past decades extending quantum photonics to broader frequency regimes. In standard cryogenic systems, however, thermal decoherence prevents access to the quantum regime for photon frequencies below the gigahertz domain. Here, we engineer two superconducting LC circuits coupled by a photon-pressure interaction and demonstrate sideband cooling of a hot radio frequency (RF) circuit using a microwave cavity. Because of a substantially increased coupling strength, we obtain a large single-photon quantum cooperativity 𝒞_q0 ∼ 1 and reduce the thermal RF occupancy by 75% with less than one pump photon. For larger pump powers, the coupling rate exceeds the RF thermal decoherence rate by a factor of 3, and the RF circuit is cooled into the quantum ground state. Our results lay the foundation for RF quantum photonics.

Levitodynamics: Levitation and control of microscopic objects in vacuum

[Figure: see text].

Experimental demonstration of strong unitary uncertainty relations

Uncertainty relations are one of the most important foundations of quantum physics. In the textbook literatures, uncertainty relations usually refer to the preparation uncertainty. Its original formulation based on variances of two observables limits on the ability to prepare an ensemble of quantum systems for which non-commuting observables will have arbitrary uncertainty. The preparation uncertainty relation has been widely investigated. On the other hand, a unitary operator is a fundamental tenet of quantum theory. Every evolution of a closed quantum system is governed by acting unitary operators on the state of the system and the evolution of an open system can be represented by acting unitary operators on an enlarged system consisting of the quantum system as a subsystem. Therefore, naturally, to understand and quantitatively capture the essence of uncertainty relations for unitary operators is important and timely. Here we report an experimental investigation of a set of uncertainty relations for two unitary operators, which are theoretically derived by using a sequence of fine-grained inequalities. We test these uncertainty relations with single photons and interferometric networks. The unitary uncertainty relation is saturated by any pure qubit state. For higher-dimensional states, it is stronger than the best known bound introduced in the previous literatures. The lower bounds of the unitary uncertainty relations can be even further strengthened by the symmetry of permutation. The experimental findings agree with the predictions of quantum theory and respect the new uncertainty relations.

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.

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.

Large and robust mechanical squeezing of optomechanical systems in a highly unresolved sideband regime via Duffing nonlinearity and intracavity squeezed light

We propose a scheme to generate strong and robust mechanical squeezing in an optomechanical system in the highly unresolved sideband (HURSB) regime with the help of the Duffing nonlinearity and intracavity squeezed light. The system is formed by a standard optomechanical system with the Duffing nonlinearity (mechanical nonlinearity) and a second-order nonlinear medium (optical nonlinearity). In the resolved sideband regime, the second-order nonlinear medium may play a destructive role in the generation of mechanical squeezing. However, it can significantly increase the mechanical squeezing (larger than 3dB) in the HURSB regime when the parameters are chosen appropriately. Finally, we show the mechanical squeezing is robust against the thermal fluctuations of the mechanical resonator. The generation of large and robust mechanical squeezing in the HURSB regime is a combined effect of the mechanical and optical nonlinearities.

Enhancing Spin-Phonon and Spin-Spin Interactions Using Linear Resources in a Hybrid Quantum System

Hybrid spin-mechanical setups offer a versatile platform for quantum science and technology, but improving the spin-phonon as well as the spin-spin couplings of such systems remains a crucial challenge. Here, we propose and analyze an experimentally feasible and simple method for exponentially enhancing the spin-phonon and the phonon-mediated spin-spin interactions in a hybrid spin-mechanical setup, using only linear resources. Through modulating the spring constant of the mechanical cantilever with a time-dependent pump, we can acquire a tunable and nonlinear (two-phonon) drive to the mechanical mode, thus amplifying the mechanical zero-point fluctuations and directly enhancing the spin-phonon coupling. This method allows the spin-mechanical system to be driven from the weak-coupling regime to the strong-coupling regime, and even the ultrastrong coupling regime. In the dispersive regime, this method gives rise to a large enhancement of the phonon-mediated spin-spin interactions between distant solid-state spins, typically two orders of magnitude larger than that without modulation. As an example, we show that the proposed scheme can apply to generating entangled states of multiple spins with high fidelities even in the presence of large dissipations.

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.

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.

Nonreciprocal Transport Based on Cavity Floquet Modes in Optomechanics

Directional transport is obtained in various multimode systems by driving multiple, nonreciprocally interfering interactions between individual bosonic modes. However, systems sustaining the required number of modes become physically complex. In our microwave-optomechanical experiment, we show how to configure nonreciprocal transport between frequency components of a single superconducting cavity coupled to two drumhead oscillators. The frequency components are promoted to Floquet modes and generate the missing dimension to realize an isolator and a directional amplifier. A second cavity left free by this arrangement is used to cool the mechanical oscillators and bring the transduction noise close to the quantum limit. We furthermore uncover a new type of instability specific to nonreciprocal coupling. Our approach is generic and can greatly simplify quantum signal processing and the design of topological lattices from low-dimensional systems.

Parity-Time Symmetry in Non-Hermitian Complex Optical Media

The exploration of quantum-inspired symmetries in optical and photonic systems has witnessed immense research interest both fundamentally and technologically in a wide range of subject areas in physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory and recently ramified into a diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant application prospects and engineering of novel materials. In addition, there has been increasing research interest in many emerging directions beyond optics and photonics. Here, the state-of-the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings are brought together, and key concepts, a background, and a detailed perspective on new emerging directions are described. It can be anticipated that this trendy field of interest will be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, optoelectronics, and beyond, and will offer distinctive application prospects in novel functional materials.

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.

Large mechanical squeezing beyond 3dB of hybrid atom-optomechanical systems in a highly unresolved sideband regime

We propose a scheme for the generation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in the highly unresolved sideband (HURSB) regime where the decay rate of cavity is much larger than the frequency of the mechanical oscillator. The system is formed by two two-level atomic ensembles and an optomechanical system with cavity driven by two lasers with different amplitudes. In the HURSB regime, the squeezing of the movable mirror can not be larger than 3dB if no atomic ensemble or only one atomic ensemble is put into the optomechanical system. However, if two atomic ensembles are put into the optomechanical system, the strong mechanical squeezing beyond 3dB is achieved even in the HURSB regime. Our scheme paves the way toward the implementation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in experiments.

Cavity electromechanics with parametric mechanical driving

Microwave optomechanical circuits have been demonstrated to be powerful tools for both exploring fundamental physics of macroscopic mechanical oscillators, as well as being promising candidates for on-chip quantum-limited microwave devices. In most experiments so far, the mechanical oscillator is either used as a passive element and its displacement is detected using the superconducting cavity, or manipulated by intracavity fields. Here, we explore the possibility to directly and parametrically manipulate the mechanical nanobeam resonator of a cavity electromechanical system, which provides additional functionality to the toolbox of microwave optomechanics. In addition to using the cavity as an interferometer to detect parametrically modulated mechanical displacement and squeezed thermomechanical motion, we demonstrate that this approach can realize a phase-sensitive parametric amplifier for intracavity microwave photons. Future perspectives of optomechanical systems with a parametrically driven mechanical oscillator include exotic bath engineering with negative effective photon temperatures, or systems with enhanced optomechanical nonlinearities.

Microwave circuits are interesting tools for microwave optomechanics and quantum information processing. Here, the authors demonstrate a phase-sensitive microwave amplifier by using parametric frequency modulation of a MHz mechanical nanobeam integrated in a superconducting microwave cavity.

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.

Overcoming standard quantum limit using a momentum measuring interferometer

We show that back-action noise in the momentum measurement of a damped forced oscillator can be suppressed because of damping. Using this principle, we propose a back-action suppressed interferometer, in which the signal is a function of momentum of atoms in a harmonic trap. We show that the quantum noise limited sensitivity of this interferometer can overcome the standard quantum limit of force sensing, even at frequencies much smaller than the eigen frequency of the harmonic trap.