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 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.

Continuous weak measurement allows localizing open quantum systems in state space, and tracing out their quantum trajectory as they evolve in time. Efficient quantum measurement schemes have previously enabled recording quantum trajectories of microwave photon and qubit states. We apply these concepts to a macroscopic mechanical resonator, and follow the quantum trajectory of its motional state conditioned on a continuous optical measurement record. Starting with a thermal mixture, we eventually obtain coherent states of 78% purity-comparable to a displaced thermal state of occupation 0.14. We introduce a retrodictive measurement protocol to directly verify state purity along the trajectory, and furthermore observe state collapse and decoherence. This opens the door to measurement-based creation of advanced quantum states, and potential tests of gravitational decoherence models.

Many applications of quantum information processing (QIP) require distribution of quantum states in networks, both within and between distant nodes [1]. Optical quantum states are uniquely suited for this purpose, as they propagate with ultralow attenuation and are resilient to ubiquitous thermal noise. Mechanical systems are then envisioned as versatile interfaces between photons and a variety of solid-state QIP platforms [2, 3]. Here, we demonstrate a key step towards this vision, and generate entanglement between two propagating optical modes, by coupling them to the same, cryogenic mechanical system. The entanglement persists at room temperature, where we verify the inseparability of the bipartite state and fully characterize its logarithmic negativity by homodyne tomography. We detect, without any corrections, correlations corresponding to a logarithmic negativity of E N = 0.35. Combined with quantum interfaces between mechanical systems and solid-state qubit processors already available [4, 5, 6, 7] or under development [8,9], this paves the way for mechanical systems enabling long-distance quantum information networking over optical fiber networks.Entanglement is a crucial resource for QIP [10]. As such, the ability to entangle fields of arbitrary wavelength will be important for linking nodes in heterogeneous QIP networks. Mechanical oscillators are uniquely poised in their ability to create such links, thanks to the frequency-independence of the radiation pressure interaction. The ability to entangle two radiation fields via a common mechanical interaction was outlined 20 years ago [11,12], and the intervening decades have seen the development of optomechanical devices [13] which are robustly quantum mechanical and routinely integrated into hybrid systems.Recently, mechanically-mediated entanglement has been reported between propagating microwave fields [14] as well as two superconducting qubits [15]. In both cases, the entanglement remained confined to the dilution refrigerator in which it was created. Here, we utilize an extremely coherent mechanical platform 1 arXiv:1911.05729v2 [quant-ph]