The small mass and high coherence of nanomechanical resonators render them the ultimate force probe, with applications ranging from biosensing and magnetic resonance force microscopy, to quantum optomechanics. A notorious challenge in these experiments is thermomechanical noise related to dissipation through internal or external loss channels. Here, we introduce a novel approach to defining nanomechanical modes, which simultaneously provides strong spatial confinement, full isolation from the substrate, and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localises the mode, without imposing the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables mechanical Q > 10 8 at 1 MHz, yielding the highest mechanical Qf -products (> 10 14 Hz) yet reported at room temperature. The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to 4.2 Kelvin predicts ∼quanta/ms heating rates, similar to trapped ions.

Controlling a quantum system based on the observation of its dynamics is inevitably complicated by the backaction of the measurement process. Efficient measurements, however, maximize the amount of information gained per disturbance incurred. Real-time feedback then enables both canceling the measurement's backaction and controlling the evolution of the quantum state. While such measurement-based quantum control has been demonstrated in the clean settings of cavity and circuit quantum electrodynamics, its application to motional degrees of freedom has remained elusive. Here we show measurement-based quantum control of the motion of a millimetre-sized membrane resonator. An optomechanical transducer resolves the zero-point motion of the soft-clamped resonator in a fraction of its millisecond coherence time, with an overall measurement efficiency close to unity. We use this position record to feedback-cool a resonator mode to its quantum ground state (residual thermal occupationn = 0.29 ± 0.03), 9 dB below the quantum backaction limit of sideband cooling, and six orders of magnitude below the equilibrium occupation of its thermal environment. This realizes a long-standing goal in the field, and adds position and momentum to the degrees of freedom amenable to measurement-based quantum control, with potential applications in quantum information processing and gravitational wave detectors. 1 arXiv:1805.05087v2 [quant-ph] 10 Sep 2018Controlling the state of a quantum system is a delicate task, since observation of the system will inevitably perturb it. 1, 2 Coherent quantum control avoids this issue, by coupling the system to another "controller" quantum system in such a way that the joint system converges to the target state without the need for measurement-at the expense of quantum resources in the controller. Measurement-based quantum control 3-5 is based on a different paradigm. It exerts control by measuring the quantum state, and applying feedback that depends on the measurement outcome, much alike classical control systems. In the quantum regime, however, the effect of the measurement's backaction must be taken into account, and effectively canceled. This requires an overall measurement efficiency η-in essence the amount of information gained per decoherence induced-close to unity, a challenging demand yet met only with the impeccable systems of cavity and circuit QED 6, 7 (e.g. η = 40 % in ref. 7 ).To prepare high-purity motional quantum states, researchers have traditionally relied on sideband cooling, a form of coherent quantum control. An engineered quantum optical bath acts as controller, to which the motional degree of freedom couples through optical forces. The motion thermalizes to this bath, at a temperature determined by the forces' quantum fluctuations. This temperature sets a fundamental limit to sideband cooling. In optomechanics, this limit requires that the cavity linewidth resolves the motional sidebands to enable ground state cooling with coherent light. 8 Systems operating in this regime have b...

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA puts a limitation-the so-called standard quantum limit-on the precision of sensing of position, velocity and acceleration. Here we show that QBA on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational 'drum' mode of a millimetre-sized dielectric membrane, and the spin oscillator is an atomic ensemble in a magnetic field. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by -1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

Quantum mechanics dictates that the precision of physical measurements must be subject to certain constraints. In the case of inteferometric displacement measurements, these restrictions impose a 'standard quantum limit' (SQL), which optimally balances the precision of a measurement with its unwanted backaction 1 . To go beyond this limit, one must devise more sophisticated measurement techniques, which either 'evade' the backaction of the measurement 2 , or achieve clever cancellation of the unwanted noise at the detector 3, 4 . In the half-century since the SQL was established, systems ranging from LIGO 5 to ultracold atoms 6 and nanomechanical devices 7, 8 have pushed displacement measurements towards this limit, and a variety of sub-SQL techniques have been tested in proof-of-principle experiments 9-13 . However, to-date, no experimental system has successfully demonstrated an interferometric displacement measurement with sensitivity (including all relevant noise sources: thermal, backaction, and imprecision) below the SQL. Here, we exploit strong quantum correlations in an ultracoherent optomechanical system to demonstrate off-resonant force and displacement sensitivity reaching 1.5dB below the SQL. This achieves an outstanding goal in mechanical quantum sensing, and further enhances the prospects of using such devices for state-of-the-art force sensing applications.

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10 7 ) mechanical modes in a phononicbandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to −2.4 dB (−3.6 dB if corrected for detection losses) and bandwidths 90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.optomechanics | quantum correlations | multimode W ithin the framework of quantum measurement theory (1, 2), quantum backaction (QBA) enforces Heisenberg's uncertainty principle: It implies that any "meter" measuring a system's physical variable induces random perturbations on the conjugate variable. Optomechanical transducers of mechanical motion (1-3) implement weak, linear measurements, whose QBA is typically small compared with thermal fluctuations in the device. Nonetheless, recent experiments have evidenced QBA in continuous position measurements of mesoscopic (mass m 200 ng) mechanical oscillators. Although QBA appears as a heating mechanism (4-7) from the point of view of the mechanics only, it correlates the fluctuations of mechanical position with the optical meter's quantum noise. These correlations are of fundamental, but also practical interest, e.g., as a source of entanglement and a means to achieve measurement sensitivities beyond standard quantum limits (8-11). Correspondingly, they have been intensely studied experimentally (5,(12)(13)(14)(15)(16)(17)(18)(19). Quantum correlations in multimode systems supporting many mechanical modes give rise to even richer physics and new measurement strategies (20-25). However, although quantum electromechanical coupling to several mechanical modes has been explored (26, 27), quantum fluctuations have so far been investigated only for a pair of collective motional modes of ∼900 cold atoms trapped in an optical resonator (28). In contrast, QBA cancellation and entanglement have been extensively studied with atomic spin oscillators (29-31).In our study, we use highly stressed, ∼60-nm-thick Si 3 N 4 membranes as nanomechanical resonators (32). They naturally constitute multimode systems, supporting mechanical modes at frequencies Ω (i,j ) m = Ω(1,1) m (i 2 + j 2 )/2 in the megahertz range, of which two examples are shown in Fig. 1C. The membrane is embedded in a 1.7-mm-long Fabry-Perot resonator held at a temperature T ≈ 10 K in a simple flow cryostat (Fig. 1A). The location zm of the membrane along the standing optical waves (wavelength 2π/k ) t...