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

High photon-phonon pair generation rate in a two-dimensional optomechanical crystal

Integrated optomechanical systems are a leading platform for manipulating, sensing, and distributing quantum information, but are limited by residual optical heating. Here, we demonstrate a two-dimensional optomechanical crystal (OMC) geometry with increased thermal anchoring and a mechanical mode at 7.4 GHz, well aligned with the operation range of cryogenic microwave hardware and piezoelectric transducers. The eight times better thermalization than current one-dimensional OMCs, large optomechanical coupling rates, g0/2π  ≈  880 kHz, and high optical quality factors, Qopt = 2.4 × 105, allow ground-state cooling (nm = 0.32) of the acoustic mode from 3 K and entering the optomechanical strong-coupling regime. In pulsed sideband asymmetry measurements, we show ground-state operation (nm < 0.45) at temperatures below 10 mK, with repetition rates up to 3 MHz, generating photon-phonon pairs at  ≈ 147 kHz. Our results extend optomechanical system capabilities and establish a robust foundation for future microwave-to-optical transducers with entanglement rates exceeding state-of-the-art superconducting qubit decoherence rates.

Enhanced Laser Cooling of a Mechanical Resonator via Zero-Photon Detection

Throughout quantum science and technology, measurement is used as a powerful resource for nonlinear operations and quantum state engineering. In particular, single-photon detection is commonly employed for quantum-information applications and tests of fundamental physics. By contrast, and perhaps counterintuitively, measurement of the absence of photons also provides useful information, and offers significant potential for a wide range of new experimental directions. Here, we propose and experimentally demonstrate cooling of a mechanical resonator below its laser-cooled mechanical occupation via zero-photon detection on the anti-Stokes scattered optical field and verify this cooling through heterodyne measurements. Our measurements are well captured by a stochastic master equation and the techniques introduced here open new avenues for cooling, quantum thermodynamics, quantum state engineering, and quantum measurement and control.

Quantum collective motion of macroscopic mechanical oscillators

Collective phenomena arise from interactions within complex systems, leading to behaviors absent in individual components. Observing quantum collective phenomena with macroscopic mechanical oscillators has been impeded by the stringent requirement that oscillators be identical. We demonstrate the quantum regime for collective motion of N = 6 mechanical oscillators, a hexamer, in a superconducting circuit optomechanical platform. By increasing the optomechanical couplings, the system transitions from individual to collective motion, characterized by a [Formula: see text] enhancement of cavity-collective mode coupling, akin to superradiance of atomic ensembles. Using sideband cooling, we prepare the collective mode in the quantum ground state and measure its quantum sideband asymmetry, with zero-point motion distributed across distant oscillators. This regime of optomechanics opens avenues for studying multipartite entanglement, with potential advances in quantum metrology.

Nanocavities for Molecular Optomechanics: Their Fundamental Description and Applications

Vibrational Raman scattering-a process where light exchanges energy with a molecular vibration through inelastic scattering-is most fundamentally described in a quantum framework where both light and vibration are quantized. When the Raman scatterer is embedded inside a plasmonic nanocavity, as in some sufficiently controlled implementations of surface-enhanced Raman scattering (SERS), the coupled system realizes an optomechanical cavity where coherent and parametrically amplified light-vibration interaction becomes a resource for vibrational state engineering and nanoscale nonlinear optics. The purpose of this Perspective is to clarify the connection between the languages and parameters used in the fields of molecular cavity optomechanics (McOM) versus its conventional, "macroscopic" counterpart and to summarize the main results achieved so far in McOM and the most pressing experimental and theoretical challenges. We aim to make the theoretical framework of molecular cavity optomechanics practically usable for the SERS and nanoplasmonics community at large. While quality factors (Q) and mode volumes (V) essentially describe the performance of a nanocavity in enhancing light-matter interaction, we point to the light-cavity coupling efficiencies (η) and optomechanical cooperativities () as the key parameters for molecular optomechanics. As an illustration of the significance of these quantities, we investigate the feasibility of observing optomechanically induced transparency with a molecular vibration-a measurement that would allow for a direct estimate of the optomechanical cooperativity.

Optomechanical Microwave-to-Optical Photon Transducer Chips: Empowering the Quantum Internet Revolution

The first quantum revolution has brought us the classical Internet and information technology. Today, as technology advances rapidly, the second quantum revolution quietly arrives, with a crucial moment for quantum technology to establish large-scale quantum networks. However, solid-state quantum bits (such as superconducting and semiconductor qubits) typically operate in the microwave frequency range, making it challenging to transmit signals over long distances. Therefore, there is an urgent need to develop quantum transducer chips capable of converting microwaves into optical photons in the communication band, since the thermal noise of optical photons at room temperature is negligible, rendering them an ideal information carrier for large-scale spatial communication. Such devices are important for connecting different physical platforms and efficiently transmitting quantum information. This paper focuses on the fast-developing field of optomechanical quantum transducers, which has flourished over the past decade, yielding numerous advanced achievements. We categorize transducers based on various mechanical resonators and discuss their principles of operation and their achievements. Based on existing research on optomechanical transducers, we compare the parameters of several mechanical resonators and analyze their advantages and limitations, as well as provide prospects for the future development of quantum transducers.

An integrated microwave-to-optics interface for scalable quantum computing

Microwave-to-optics transduction is emerging as a vital technology for scaling quantum computers and quantum networks. To establish useful entanglement links between qubit processing units, several key conditions must be simultaneously met: the transducer must add less than a single quantum of input-referred noise and operate with high efficiency, as well as large bandwidth and high repetition rate. Here we present a design for an integrated transducer based on a planar superconducting resonator coupled to a silicon photonic cavity through a mechanical oscillator made of lithium niobate on silicon. We experimentally demonstrate its performance with a transduction efficiency of 0.9% with 1 μW of continuous optical power and a spectral bandwidth of 14.8 MHz. With short optical pulses, we measure the added noise that is limited to a few photons, with a repetition rate of up to 100 kHz. Our device directly couples to a 50 Ω transmission line and can be scaled to a large number of transducers on a single chip, laying the foundations for distributed quantum computing.

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.

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.

Magnon squeezing enhanced ground-state cooling in cavity magnomechanics

Cavity magnomechanics has recently become a new platform for studying macroscopic quantum phenomena. The magnetostriction induced vibration mode of a large-size ferromagnet or ferrimagnet reaching its ground state represents a genuine macroscopic quantum state. Here we study the ground-state cooling of the mechanical vibration mode in a cavity magnomechanical system, and focus on the role of magnon squeezing in improving the cooling efficiency. The magnon squeezing is obtained by exploiting the magnon self-Kerr nonlinearity. We find that the magnon squeezing can significantly and even completely suppress the magnomechanical Stokes scattering. It thus becomes particularly useful in realizing ground-state cooling in the unresolved-sideband regime, where the conventional sideband cooling protocols become inefficient. We also find that the coupling to the microwave cavity plays only an adverse effect in mechanical cooling. This makes essentially the two-mode magnomechanical system (without involving the microwave cavity) a preferred system for cooling the mechanical motion, in which the magnon mode is established by a uniform bias magnetic field and a microwave drive field.

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.

Cryogenic and hermetically sealed packaging of photonic chips for optomechanics

We demonstrate a hermetically sealed packaging system for integrated photonic devices at cryogenic temperatures with plug-and-play functionality. This approach provides the ability to encapsulate a controlled amount of gas into the optical package allowing helium to be used as a heat-exchange gas to thermalize photonic devices, or condensed into a superfluid covering the device. This packaging system was tested using a silicon-on-insulator slot waveguide resonator which fills with superfluid ⁴He below the transition temperature. To optimize the fiber-to-chip optical integration 690 tests were performed by thermally cycling optical fibers bonded to various common photonic chip substrates (silicon, silicon oxide and HSQ) with a range of glues (NOA 61, NOA 68, NOA 88, NOA 86H and superglue). This showed that NOA 86H (a UV curing optical adhesive with a latent heat catalyst) provided the best performance under cryogenic conditions for all the substrates tested. The technique is relevant to superfluid optomechanics experiments, as well as quantum photonics and quantum optomechanics applications.

All-Optical Synchronization of Remote Optomechanical Systems

Synchronization and frequency locking between remote mechanical oscillators are of scientific and technological importance. The key challenges are to align the oscillation frequencies and realize strong nonlinear interaction of both oscillators to a common carrier capable of long-distance transmission. Here, we experimentally realize the all-optical synchronization between two different optomechanical systems, a microsphere and a microdisk. The mechanical oscillation of the microsphere induced by the radiation pressure is loaded onto the pump laser via the optomechanical interaction, which is directly transmitted through a 5-km-long single-mode fiber to excite the mechanical oscillation of the microdisk. By finely tuning both the optical and mechanical frequencies of the two microresonators, the oscillation of the microdisk is injection locked to the microsphere, resulting in a synchronized phase relation of the two systems. Our results push a step forward the long-distance synchronization network using optomechanical microresonators.

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.

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.

Intensive Cavity-Magnomechanical Cooling of a Levitated Macromagnet

We describe microwave cavity-magnomechanical center-of-mass cooling of a levitated magnetic sphere. The standing magnetic component of the electromagnetic wave within a microwave cavity exerts a dynamical force on a magnonic crystalline sphere and dissipates the mechanical energy through scattering into the magnon mode. The coupling is established by the magnetic dipole interaction and enriched by the collective spin motion. We find that the final cooled phonon occupation achieved is an intensive property independent of the mass and size of the sphere, in contrast to standard optomechanical couplings. This is of particular importance for testing quantum mechanics with macroscopic objects.

Quantum control of a nanoparticle optically levitated in cryogenic free space

Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence^1-3. Quantum control of mechanical motion has been achieved by engineering the radiation-pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator^4-7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states⁸. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects^9,10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10^-15 grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales¹¹.

Two-dimensional optomechanical crystal cavity with high quantum cooperativity

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

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