Laser cooling of a nanomechanical oscillator into its quantum ground state

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.

Investigation of genes involved in scent and color production in Rosa damascena Mill

Rosa damascena Mill., commonly known as the King Flower, is a fragrant and important species of the Rosaceae family. It is widely used in the perfumery and pharmaceutical industries. The scent and color of the flowers are significant characteristics of this ornamental plant. This study aimed to investigate the relative expression of MYB1, CCD1, FLS, PAL, CER1, GT1, ANS and PAR genes under two growth stages (S1 and S2) in two morphs. The CCD1 gene pathway is highly correlated with the biosynthesis of volatile compounds. The results showed that the overexpression of MYB1, one of the important transcription factors in the production of fragrance and color, in the Hot pink morph of sample S2 increased the expression of PAR, PAL, FLS, RhGT1, CCD1, ANS, CER1, and GGPPS. The methyl jasmonate (MeJA) stimulant had a positive and cumulative effect on gene expression in most genes, such as FLS in ACC.26 of the S2 sample, RhGT1, MYB1, CCD1, PAR, ANS, CER1, and PAL in ACC.1. To further study, a comprehensive analysis was performed to evaluate the relationship between the principal volatile compounds and colors. Our data suggest that the rose with pink flowers had a higher accumulation content of flavonoids and anthocyanin. To separate essential oil compounds, GC/MS analysis identified 26 compounds in four samples. The highest amount of geraniol, one of the main components of damask rose, was found in the Hot pink flower, 23.54%, under the influence of the MeJA hormone.

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.

Detecting single gravitons with quantum sensing

The quantization of gravity is widely believed to result in gravitons - particles of discrete energy that form gravitational waves. But their detection has so far been considered impossible. Here we show that signatures of single graviton exchange can be observed in laboratory experiments. We show that stimulated and spontaneous single-graviton processes can become relevant for massive quantum acoustic resonators and that stimulated absorption can be resolved through continuous sensing of quantum jumps. We analyze the feasibility of observing the exchange of single energy quanta between matter and gravitational waves. Our results show that single graviton signatures are within reach of experiments. In analogy to the discovery of the photo-electric effect for photons, such signatures can provide the first experimental clue of the quantization of gravity.

Tailoring Phonon Dispersion of a Genetically Designed Nanophononic Metasurface

Phonon engineering at the nanoscale holds immense promise for a myriad of applications. However, the design of phononic devices continues to rely on regular shapes chosen according to long-established simple rules. Here, we demonstrate an inverse design approach to create a two-dimensional phononic metasurface exhibiting a highly anisotropic phonon dispersion along the main axes of the Brillouin zone. A partial hypersonic bandgap of approximately 3.5 GHz is present along one axis, with gap closure along the orthogonal axis. Such a level of control is achieved through genetically optimized unit cells, with shapes exceeding conventional intuition. We experimentally validated our theoretical predictions using Brillouin light scattering, confirming the effectiveness of the inverse design method. Our approach unlocks the potential for automated engineering of phononic metasurfaces with on-demand functionalities, thus leading toward innovative phononic devices beyond the limitations of traditional design paradigms.

High Q-Factor Diamond Optomechanical Resonators with Silicon Vacancy Centers at Millikelvin Temperatures

Phonons are envisioned as coherent intermediaries between different types of quantum systems. Engineered nanoscale devices, such as optomechanical crystals (OMCs), provide a platform to utilize phonons as quantum information carriers. Here we demonstrate OMCs in diamond designed for strong for interactions between phonons and a silicon vacancy (SiV) spin. Using optical measurements at millikelvin temperatures, we measure a line width of 13 kHz (Q-factor of ∼4.4 × 105) for a 6 GHz acoustic mode, a record for diamond in the GHz frequency range and within an order of magnitude of state-of-the-art line widths for OMCs in silicon. We investigate SiV optical and spin properties in these devices and outline a path toward a coherent spin-phonon interface.

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.

Gradient-induced long-range optical pulling force based on photonic band gap

Optical pulling provides a new degree of freedom in optical manipulation. It is generally believed that long-range optical pulling forces cannot be generated by the gradient of the incident field. Here, we theoretically propose and numerically demonstrate the realization of a long-range optical pulling force stemming from a self-induced gradient field in the manipulated object. In analogy to potential barriers in quantum tunnelling, we use a photonic band gap design in order to obtain the intensity gradients inside a manipulated object placed in a photonic crystal waveguide, thereby achieving a pulling force. Unlike the usual scattering-type optical pulling forces, the proposed gradient-field approach does not require precise elimination of the reflection from the manipulated objects. In particular, the Einstein-Laub formalism is applied to design this unconventional gradient force. The magnitude of the force can be enhanced by a factor of up to 50 at the optical resonance of the manipulated object in the waveguide, making it insensitive to absorption. The developed approach helps to break the limitation of scattering forces to obtain long-range optical pulling for manipulation and sorting of nanoparticles and other nano-objects. The developed principle of using the band gap to obtain a pulling force may also be applied to other types of waves, such as acoustic or water waves, which are important for numerous applications.

Characteristics of coexisting attractors and ghost orbiting in an optomechanical microresonator

We explore the nonlinear interactions of an optomechanical microresonator driven by two external optical signals. Optical whispering-gallery waves are coupled to acoustic surface waves of a fused silica medium in the equatorial plane of a generic microresonator. The system exhibits coexisting attractors whose behaviors include limit cycles, steady states, tori, quasi-chaos, and fully developed chaos with ghost orbits of a known attractor. Bifurcation diagrams demonstrate the existence of self-similarity, periodic windows, and coexisting attractors and show high-density lines within chaos that suggests a potential ghost orbit. In addition, the Lyapunov spectral components as a function of control parameter illuminate the dynamic nature of attractors and periodic windows with symmetric and asymmetric formations, their domains of existence, their bifurcations, and other nonlinear effects. We show that the power-shift method can access accurately and efficiently attractors in the optomechanical system as it does in other nonlinear systems. To test whether the ghost orbit is the link between two attractors interrupted by chaos, we examine the elements of the bifurcation diagrams as a function of control parameter. We also use detuning as a second control parameter to avoid the chaotic region and clarify that the two attractors are one.

Room-temperature quantum optomechanics using an ultralow noise cavity

At room temperature, mechanical motion driven by the quantum backaction of light has been observed only in pioneering experiments in which an optical restoring force controls the oscillator stiffness1,2. For solid-state mechanical resonators in which oscillations are controlled by the material rigidity, the observation of these effects has been hindered by low mechanical quality factors, optical cavity frequency fluctuations3, thermal intermodulation noise4,5 and photothermal instabilities. Here we overcome these challenges with a phononic-engineered membrane-in-the-middle system. By using phononic-crystal-patterned cavity mirrors, we reduce the cavity frequency noise by more than 700-fold. In this ultralow noise cavity, we insert a membrane resonator with high thermal conductance and a quality factor (Q) of 180 million, engineered using recently developed soft-clamping techniques6,7. These advances enable the operation of the system within a factor of 2.5 of the Heisenberg limit for displacement sensing8, leading to the squeezing of the probe laser by 1.09(1) dB below the vacuum fluctuations. Moreover, the long thermal decoherence time of the membrane oscillator (30 vibrational periods) enables us to prepare conditional displaced thermal states of motion with an occupation of 0.97(2) phonons using a multimode Kalman filter. Our work extends the quantum control of solid-state macroscopic oscillators to room temperature.

Degeneracy and Photon Trapping in a Dissipationless Two-Mode Optomechanical Model

In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model by studying the behavior of some observables in the ground state. By controlling the coupling between membrane and modes, we find that the two lowest energy eigenstates become degenerate, as is indicated by the behavior of the mean value of some operators and by other quantifiers as a function of the coupling. Such degenerate states are characterized by a coherent superposition of eigenstates describing one of the two modes preferentially populated and the membrane dislocated from its equilibrium position due the radiation pressure (Schrödinger's cat states). The delocalization of the compound system photons+membrane results in an increase in fluctuations as measured by Robertson-Schrödinger uncertainty relations.

Optoacoustic Cooling of Traveling Hypersound Waves

We experimentally demonstrate optoacoustic cooling via stimulated Brillouin-Mandelstam scattering in a 50 cm long tapered photonic crystal fiber. For a 7.38 GHz acoustic mode, a cooling rate of 219 K from room temperature has been achieved. As anti-Stokes and Stokes Brillouin processes naturally break the symmetry of phonon cooling and heating, resolved sideband schemes are not necessary. The experiments pave the way to explore the classical to quantum transition for macroscopic objects and could enable new quantum technologies in terms of storage and repeater schemes.

Optical coupling control of isolated mechanical resonators

We present a Hamiltonian model describing two pairs of mechanical and optical modes under standard optomechanical interaction. The vibrational modes are mechanically isolated from each other and the optical modes couple evanescently. We recover the ranges for variables of interest, such as mechanical and optical resonant frequencies and naked coupling strengths, using a finite element model for a standard experimental realization. We show that the quantum model, under this parameter range and external optical driving, may be approximated into parametric interaction models for all involved modes. As an example, we study the effect of detuning in the optical resonant frequencies modes and optical driving resolved to mechanical sidebands and show an optical beam splitter with interaction strength dressed by the mechanical excitation number, a mechanical bidirectional coupler, and a two-mode mechanical squeezer where the optical state mediates the interaction strength between the mechanical modes.

Direct laser-written optomechanical membranes in fiber Fabry-Perot cavities

Integrated micro- and nanophotonic optomechanical experiments enable the manipulation of mechanical resonators on the single phonon level. Interfacing these structures requires elaborate techniques limited in tunability, flexibility, and scaling towards multi-mode systems. Here, we demonstrate a cavity optomechanical experiment using 3D-laser-written polymer membranes inside fiber Fabry-Perot cavities. Vacuum coupling rates of g0/2π ≈ 30 kHz to the fundamental megahertz mechanical mode are reached. We observe optomechanical spring tuning of the mechanical resonator frequency by tens of kilohertz exceeding its linewidth at cryogenic temperatures. The direct fiber coupling, its scaling capabilities to coupled resonator systems, and the potential implementation of dissipation dilution structures and integration of electrodes make it a promising platform for fiber-tip integrated accelerometers, optomechanically tunable multi-mode mechanical systems, and directly fiber-coupled systems for microwave to optics conversion.

High-sensitivity force sensing using a phonon laser in an active levitated optomechanical system

Force detection with high sensitivity is of paramount importance in many fields of study, from gravitational wave detection to investigations of surface forces. Here, we propose and demonstrate a force-sensing method based on gain-enhanced nonlinearity in a nonlinear phonon laser. Experimental and simulation results show that the input force leads to the frequency shift of phonon laser, due to nonlinearity. In addition, we further investigate the influences of the pumping power, numerical aperture, and microsphere's refractive index on the performance of this force-sensing system, regarding the sensitivity and the linear response range. Our work paves a new way towards the realization of precise metrology based on the nonlinearity of phonon laser.

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.

Dissipative optomechanics in high-frequency nanomechanical resonators

The coherent transduction of information between microwave and optical domains is a fundamental building block for future quantum networks. A promising way to bridge these widely different frequencies is using high-frequency nanomechanical resonators interacting with low-loss optical modes. State-of-the-art optomechanical devices rely on purely dispersive interactions that are enhanced by a large photon population in the cavity. Additionally, one could use dissipative optomechanics, where photons can be scattered directly from a waveguide into a resonator hence increasing the degree of control of the acousto-optic interplay. Hitherto, such dissipative optomechanical interaction was only demonstrated at low mechanical frequencies, precluding prominent applications such as the quantum state transfer between photonic and phononic domains. Here, we show the first dissipative optomechanical system operating in the sideband-resolved regime, where the mechanical frequency is larger than the optical linewidth. Exploring this unprecedented regime, we demonstrate the impact of dissipative optomechanical coupling in reshaping both mechanical and optical spectra. Our figures represent a two-order-of-magnitude leap in the mechanical frequency and a tenfold increase in the dissipative optomechanical coupling rate compared to previous works. Further advances could enable the individual addressing of mechanical modes and help mitigate optical nonlinearities and absorption in optomechanical devices.

Integrated microcavity optomechanics with a suspended photonic crystal mirror above a distributed Bragg reflector

Increasing the interaction between light and mechanical resonators is an ongoing endeavor in the field of cavity optomechanics. Optical microcavities allow for boosting the interaction strength through their strong spatial confinement of the optical field. In this work, we follow this approach by realizing a sub-wavelength-long, free-space optomechanical microcavity on-chip fabricated from an (Al,Ga)As heterostructure. A suspended GaAs photonic crystal mirror is acting as a highly reflective mechanical resonator, which together with a distributed Bragg (DBR) reflector forms an optomechanical microcavity. We demonstrate precise control over the microcavity resonance by change of the photonic crystal parameters. We find that the microcavity mode can strongly couple to the transmissive modes of the DBR. The interplay between the microcavity mode and a guided resonance of the photonic crystal modifies the cavity response and results in a stronger dynamical backaction on the mechanical resonator compared to conventional optomechanical dynamics.

Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory

The quality factor, Q, of photonic resonators permeates most figures of merit in applications that rely on cavity-enhanced light-matter interaction such as all-optical information processing, high-resolution sensing, or ultralow-threshold lasing. As a consequence, large-scale efforts have been devoted to understanding and efficiently computing and optimizing the Q of optical resonators in the design stage. This has generated large know-how on the relation between physical quantities of the cavity, e.g., Q, and controllable parameters, e.g., hole positions, for engineered cavities in gaped photonic crystals. However, such a correspondence is much less intuitive in the case of modes in disordered photonic media, e.g., Anderson-localized modes. Here, we demonstrate that the theoretical framework of quasinormal modes (QNMs), a non-Hermitian perturbation theory for shifting material boundaries, and a finite-element complex eigensolver provide an ideal toolbox for the automated shape optimization of Q of a single photonic mode in both ordered and disordered environments. We benchmark the non-Hermitian perturbation formula and employ it to optimize the Q-factor of a photonic mode relative to the position of vertically etched holes in a dielectric slab for two different settings: first, for the fundamental mode of L3 cavities with various footprints, demonstrating that the approach simultaneously takes in-plane and out-of-plane losses into account and leads to minor modal structure modifications; and second, for an Anderson-localized mode with an initial Q of 200, which evolves into a completely different mode, displaying a threefold reduction in the mode volume, a different overall spatial location, and, notably, a 3 order of magnitude increase in Q.

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.

Active-feedback quantum control of an integrated low-frequency mechanical resonator

Preparing a massive mechanical resonator in a state with quantum limited motional energy provides a promising platform for studying fundamental physics with macroscopic systems and allows to realize a variety of applications, including precise sensing. While several demonstrations of such ground-state cooled systems have been achieved, in particular in sideband-resolved cavity optomechanics, for many systems overcoming the heating from the thermal bath remains a major challenge. In contrast, optomechanical systems in the sideband-unresolved limit are much easier to realize due to the relaxed requirements on their optical properties, and the possibility to use a feedback control schemes to reduce the motional energy. The achievable thermal occupation is ultimately limited by the correlation between the measurement precision and the back-action from the measurement. Here, we demonstrate measurement-based feedback cooling on a fully integrated optomechanical device fabricated using a pick-and-place method, operating in the deep sideband-unresolved limit. With the large optomechanical interaction and a low thermal decoherence rate, we achieve a minimal average phonon occupation of 0.76 when pre-cooled with liquid helium and 3.5 with liquid nitrogen. Significant sideband asymmetry for both bath temperatures verifies the quantum character of the mechanical motion. Our method and device are ideally suited for sensing applications directly operating at the quantum limit, greatly simplifying the operation of an optomechanical system in this regime.

Rigorous full-wave calculation of optical forces on microparticles immersed in vector Pearcey beams

We present the electromagnetic fields of vector Pearcey beams by employing the vector angular spectrum representation. The beams maintain the inherent properties of autofocusing performance and inversion effect. Based on the generalized Lorenz-Mie theory and Maxwell stress tensor approach, we derive the partial-wave expansion coefficients of arbitrary beams with different polarization and the rigorous solution to evaluate the optical forces. Furthermore, we investigate the optical forces experienced by a microsphere placed in vector Pearcey beams. We study the effects on the longitudinal optical force arising from the particle size, permittivity and permeability. This exotic curved trajectory transport of particles by vector Pearcey beams may find applications in the case where the transport path is partly blocked.

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.

Engineered entropic forces allow ultrastrong dynamical backaction

When confined within an optical cavity light can exert strong radiation pressure forces. Combined with dynamical backaction, this enables important processes, such as laser cooling, and applications ranging from precision sensors to quantum memories and interfaces. However, the magnitude of radiation pressure forces is constrained by the energy mismatch between photons and phonons. Here, we overcome this barrier using entropic forces arising from the absorption of light. We show that entropic forces can exceed the radiation pressure force by eight orders of magnitude and demonstrate this using a superfluid helium third-sound resonator. We develop a framework to engineer the dynamical backaction from entropic forces, applying it to achieve phonon lasing with a threshold three orders of magnitude lower than previous work. Our results present a pathway to exploit entropic forces in quantum devices and to study nonlinear fluid phenomena such as turbulence and solitons.

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.

Enhanced nonlinear optomechanics in a coupled-mode photonic crystal device

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

Enhancement of magnon-photon-phonon entanglement in a cavity magnomechanics with coherent feedback loop

In this paper, we present a coherent feedback loop scheme to enhance the magnon-photon-phonon entanglement in cavity magnomechanics. We provide a proof that the steady state and dynamical state of the system form a genuine tripartite entanglement state. To quantify the entanglement in the bipartite subsystem and the genuine tripartite entanglement, we use the logarithmic negativity and the minimum residual contangle, respectively, in both the steady and dynamical regimes. We demonstrate the feasibility of our proposal by implementing it with experimentally realizable parameters to achieve the tripartite entanglement. We also show that the entanglement can be significantly improved with coherent feedback by appropriately tuning the reflective parameter of the beam splitter and that it is resistant to environmental thermalization. Our findings pave the way for enhancing entanglement in magnon-photon-phonon systems and may have potential applications in quantum information.

Optimal Cooling of Multiple Levitated Particles through Far-Field Wavefront Shaping

Light forces can be harnessed to levitate mesoscopic objects and cool them down toward their motional quantum ground state. Roadblocks on the way to scale up levitation from a single to multiple particles in close proximity are the requirements to constantly monitor the particles' positions as well as to engineer light fields that react fast and appropriately to their movements. Here, we present an approach that solves both problems at once. By exploiting the information stored in a time-dependent scattering matrix, we introduce a formalism enabling the identification of spatially modulated wavefronts, which simultaneously cool down multiple objects of arbitrary shapes. An experimental implementation is suggested based on stroboscopic scattering-matrix measurements and time-adaptive injections of modulated light fields.

Laser Cooling of Nuclear Magnons

The initialization of nuclear spin to its ground state is challenging due to its small energy scale compared with thermal energy, even at cryogenic temperature. In this Letter, we propose an optonuclear quadrupolar effect, whereby two-color optical photons can efficiently interact with nuclear spins. Leveraging such an optical interface, we demonstrate that nuclear magnons, the collective excitations of nuclear spin ensemble, can be cooled down optically. Under feasible experimental conditions, laser cooling can suppress the population and entropy of nuclear magnons by more than 2 orders of magnitude, which could facilitate the application of nuclear spins in quantum information science.

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.

Kerr Enhanced Backaction Cooling in Magnetomechanics

Optomechanics is a prime example of light matter interaction, where photons directly couple to phonons, allowing the precise control and measurement of the state of a mechanical object. This makes it a very appealing platform for testing fundamental physics or for sensing applications. Usually, such mechanical oscillators are in highly excited thermal states and require cooling to the mechanical ground state for quantum applications, which is often accomplished by using optomechanical backaction. However, while massive mechanical oscillators are desirable for many tasks, their frequency usually decreases below the cavity linewidth, significantly limiting the methods that can be used to efficiently cool. Here, we demonstrate a novel approach relying on an intrinsically nonlinear cavity to backaction-cool a low frequency mechanical oscillator. We experimentally demonstrate outperforming an identical, but linear, system by more than 1 order of magnitude. Furthermore, our theory predicts that with this approach we can also surpass the standard cooling limit of a linear system. By exploiting a nonlinear cavity, our approach enables efficient cooling of a wider range of optomechanical systems, opening new opportunities for fundamental tests and sensing.

On-chip mechanical exceptional points based on an optomechanical zipper cavity

Exceptional points (EPs) represent a distinct type of spectral singularity in non-Hermitian systems, and intriguing physics concepts have been studied with optical EPs recently. As a system beyond photonics, the mechanical oscillators coupling with many physical systems are expected to be further exploited EPs for mechanical sensing, topology energy transfer, nonreciprocal dynamics, etc. In this study, we demonstrated on-chip mechanical EPs with a silicon optomechanical zipper cavity, wherein two near-degenerate mechanical breathing modes are coupled via a single colocalized optical mode. By tailoring the dissipative and coherent couplings between two mechanical oscillators, the spectral splitting with 1/2 order response, a distinctive feature of EP, was observed successfully. Our work provides an integrated platform for investigating the physics related to mechanical EPs on silicon chips and suggests their possible applications for ultrasensitive measurements.

Macroscopic laser pulling based on the Knudsen force in rarefied gas

Optical pulling is an attractive concept due to the counterintuitive feature, the profound mechanism underneath and promising applications. In recent ten years, optical pulling of micro-nano objects have been fully demonstrated. However, optical pulling of a macroscopic object is challenging. Herein, laser pulling of a macroscopic object is presented in rarefied gas. The pulling force is originated from the Kundsen force when a gauss laser beam irradiates a macroscopic structure composed of the absorptive bulk cross-linked graphene material and a SiO₂ layer. A torsional pendulum device qualitatively presents the laser pulling phenomenon. A gravity pendulum device was used to further measure the pulling force that is more than three orders of magnitudes larger than the radiation pressure. This work expands the scope of optical pulling from microscale to macroscale and provides an effective technique approach for macroscopic optical manipulations.

Improving mechanical cooling by using magnetic thermal noise in a cavity-magnomechanical system

The cavity-magnomechanical system is a significant platform for studying quantum information. In this paper, a scheme to realize the ground-state cooling of the mechanical phonon mode in a cavity-magnomechanical system is proposed. In the general cooling method, the system is usually driven by a strong pumping field, and the Hamiltonian of the system needs to be linearized. Different from this cooling method, in a cavity-magnomechanical tripartite interaction system, we consider the magnetic thermal noise as an incoherent drive to facilitate cooling, where the thermal magnon number can enhance the effective coupling between the photon and phonon modes. The mechanical mode can be cooled to its ground state when the magnon thermal number is increased.

Modulation depth and bandwidth analysis of planar thermo-optic diamond actuators

Thermo-optic actuators based on bulk materials are considered too slow in applications such as laser frequency control. The availability of high-quality optical materials that have extremely fast thermal response times, such as diamond, present an opportunity for increasing performance. Here, diamond thermal actuators are investigated for configurations that use a planar thermal resistive layer applied to a heat-sinked rectangular prism. A general analytical formulation is obtained which simplifies substantially for high thermal conductivity such as diamond. Expressions for modulation depth, bandwidth and power requirements are obtained as functions of modulator dimensions and heat-transfer coefficients. For a 1 mm × 1 mm cross-section diamond at wavelength of 1 μm, around 450 W of applied heat power is needed to achieve a π phase shift at a modulation frequency of 2 kHz.

Enhancing the force sensitivity of a squeezed light optomechanical interferometer

Application of frequency-dependent squeezed vacuum improves the force sensitivity of an optomechanical interferometer beyond the standard quantum limit by a factor of e^-r, where r is the squeezing parameter. In this work, we show that the application of squeezed light along with quantum back-action nullifying meter in an optomechanical cavity with mechanical mirror in middle configuration can enhance the sensitivity beyond the standard quantum limit by a factor of e^-reff, where r_eff = r + ln(4Δ/ζ)/2, for 0 < ζ/Δ < 1, with ζ as the optomechanical cavity decay rate and Δ as the detuning between cavity eigenfrequency and driving field. The technique described in this work is restricted to frequencies much smaller than the resonance frequency of the mechanical mirror. We further studied the sensitivity as a function of temperature, mechanical mirror reflectivity, and input laser power.

Nonequilibrium thermodynamics in cavity optomechanics

Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium. As an emerging field, nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes, particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations. Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability, excellent mechanical performance, and ability to operate deep in the quantum regime. Here, we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems. The experimental results in entropy production assessment, fluctuation theorems, heat transfer, and heat engines are highlighted.

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.

From cavity optomechanics to cavity-less exciton optomechanics: a review

Cavity optomechanical coupling based on radiation pressure, photothermal forces and the photoelastic effect has been investigated widely over the past few decades, including optical measurements of mechanical vibration, dynamic backaction damping and amplification, nonlinear dynamics, quantum state transfer and so on. However, the delicate cavity operation, including cavity stabilization, fine detuning, tapered fibre access etc., limits the integration of cavity optomechanical devices. Dynamic backaction damping and amplification based on cavity-less exciton optomechanical coupling in III-V semiconductor nanomechanical systems, semiconductor nanoribbons and monolayer transition metal dichalcogenides have been demonstrated in recent years. The cavity-less exciton optomechanical systems interconnect photons, phonons and excitons in a highly integrable platform, opening up the development of integrable optomechanics. Furthermore, the highly tunable exciton resonance enables the exciton optomechanical coupling strength to be tuned. In this review, the mechanisms of cavity optomechanical coupling, the principles of exciton optomechanical coupling and the recent progress of cavity-less exciton optomechanics are reviewed. Moreover, the perspectives for exciton optomechanical devices are described.

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.

Photothermal effect in macroscopic optomechanical systems with an intracavity nonlinear optical crystal

Intracavity squeezing is a promising technique that may improve the sensitivity of gravitational wave detectors and cool optomechanical oscillators to the ground state. However, the photothermal effect may modify the occurrence of optomechanical coupling due to the presence of a nonlinear optical crystal in an optical cavity. We propose a novel method to predict the influence of the photothermal effect by measuring the susceptibility of the optomechanical oscillator and identifying the net optical spring constant and photothermal absorption rate. Using this method, we succeeded in precisely estimating parameters related to even minor photothermal effects, which could not be measured using a previously developed method.

Millimeter-scale ultrathin suspended metasurface integrated high-finesse optomechanical cavity

A typical optomechanical system is a cavity with one movable mirror and one fixed mirror. However, this configuration has been considered incapable of integrating sensitive mechanical elements while maintaining high cavity finesse. Although the membrane-in-the-middle solution seems to be able to overcome this contradiction, it introduces additional components that will lead to unexpected insertion loss, resulting in reduced cavity quality. Here we propose a Fabry-Perot optomechanical cavity composed of an ultrathin suspended Si₃N₄ metasurface and a fixed Bragg grating mirror, with a measured finesse up to 1100. Transmission loss of this cavity is very low as the reflectivity of this suspended metasurface tends to unity around 1550 nm. Meanwhile, the metasurface has a millimeter-scale transverse dimension and a thickness of only 110 nm, which guarantees a sensitive mechanical response and low cavity diffraction loss. Our metasurface-based high-finesse optomechanical cavity has a compact structure, which facilitates the development of quantum and integrated optomechanical devices.

Design of GHz Mechanical Nanoresonator with High Q-Factor Based on Optomechanical System

Micro-electromechanical systems (MEMS) have dominated the interests of the industry due to its microminiaturization and high frequency for the past few decades. With the rapid development of various radio frequency (RF) systems, such as 5G mobile telecommunications, satellite, and other wireless communication, this research has focused on a high frequency resonator with high quality. However, the resonator based on an inverse piezoelectric effect has met with a bottleneck in high frequency because of the low quality factor. Here, we propose a resonator based on optomechanical interaction (i.e., acoustic-optic coupling). A picosecond laser can excite resonance by radiation pressure. The design idea and the optimization of the resonator are given. Finally, with comprehensive consideration of mechanical losses at room temperature, the resonator can reach a high Q-factor of 1.17 × 104 when operating at 5.69 GHz. This work provides a new concept in the design of NEMS mechanical resonators with a large frequency and high Q-factor.

Nanomechanical Resonators: Toward Atomic Scale

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

Cooling of mechanical resonator in a hybrid intracavity squeezing optomechanical system

A hybrid intracavity squeezing optomechanical cooling system, in which an auxiliary cavity couples to an optomechanical cavity with a nonlinear medium inside it, is proposed to realize the ground state cooling of the mechanical resonator in the highly unresolved sideband regime. We demonstrate that the quantum backaction heating can be suppressed perfectly by the intracavity squeezing, and the cooling process can be further promoted by adjusting the tunnel coupling between the coupled cavities. The scheme has good performance in resisting the environmental thermal noise and better tolerance for the auxiliary cavity quality factor and provides the possibility for the quantum manipulation of the mechanical resonator with large mass and low frequency.

High-precision multiparameter estimation of mechanical force by quantum optomechanics

A nanomechanical oscillator can be used as a sensitive probe of a small linearized mechanical force. We propose a simple quantum optomechanical scheme using a coherent light mode in the cavity and weak short-pulsed light-matter interactions. Our main result is that if we transfer some displacement to the mechanical mode in an initialization phase, then a much weaker optomechanical interaction is enough to obtain a high-precision multiparameter estimation of the unknown force. This approach includes not only estimating the displacement caused by the force but also simultaneously observing the phase shift and squeezing of the mechanical mode. We show that the proposed scheme is robust against typical experimental imperfections and demonstrate the feasibility of our scheme using orders of magnitude weaker optomechanical interactions than in previous related works. Thus, we present a simple, robust estimation scheme requiring only very weak light-matter interactions, which could open the way to new nanomechanical sensors.

Floquet Control of Optomechanical Bistability in Multimode Systems

Cavity optomechanical systems make possible the fine manipulation of mechanical degrees of freedom with light, adding functionality and having broad appeal in photonic technologies. We show that distinct mechanical modes can be exploited with a temporally modulated Floquet drive to steer between distinct steady states induced by changes of cavity radiation pressure. We investigate the additional influence of the thermo-optic nonlinearity on these dynamics and find that it can suppress or amplify the control mechanism in contrast to its often performance-limiting character. Our results provide new techniques for the characterization of thermal properties of optomechanical systems and their control, sensing and computational applications.

Recent Advances in Nanomechanical Membrane-Type Surface Stress Sensors towards Artificial Olfaction

Nanomechanical sensors have gained significant attention as powerful tools for detecting, distinguishing, and identifying target analytes, especially odors that are composed of a complex mixture of gaseous molecules. Nanomechanical sensors and their arrays are a promising platform for artificial olfaction in combination with data processing technologies, including machine learning techniques. This paper reviews the background of nanomechanical sensors, especially conventional cantilever-type sensors. Then, we focus on one of the optimized structures for static mode operation, a nanomechanical Membrane-type Surface stress Sensor (MSS), and discuss recent advances in MSS and their applications towards artificial olfaction.

Engineering nanoscale hypersonic phonon transport

Controlling vibrations in solids is crucial to tailor their elastic properties and interaction with light. Thermal vibrations represent a source of noise and dephasing for many physical processes at the quantum level. One strategy to avoid these vibrations is to structure a solid such that it possesses a phononic stop band, that is, a frequency range over which there are no available elastic waves. Here we demonstrate the complete absence of thermal vibrations in a nanostructured silicon membrane at room temperature over a broad spectral window, with a 5.3-GHz-wide bandgap centred at 8.4 GHz. By constructing a line-defect waveguide, we directly measure gigahertz guided modes without any external excitation using Brillouin light scattering spectroscopy. Our experimental results show that the shamrock crystal geometry can be used as an efficient platform for phonon manipulation with possible applications in optomechanics and signal processing transduction.