Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators

We realise a circular gray-field polariscope to image stress-induced birefringence in thin (submicron thick) silicon nitride (SiN) membranes and strings. This enables quantitative mapping of the orientation of principal stresses and stress anisotropy, complementary to, and in agreement with, finite element modeling (FEM). Furthermore, using a sample with a well known stress anisotropy, we extract a new value for the photoelastic (Brewster) coefficient of silicon nitride, $C \approx (3.4~\pm~0.1)\times~10^{-6}~\mathrm{MPa}^{-1}$. We explore possible applications of the method to analyse and quality-control stressed membranes with phononic crystal pattern

Phonon counting thermometry of an ultracoherent membrane resonator near its motional ground state

Generation of non-Gaussian quantum states of macroscopic mechanical objects is key to a number of challenges in quantum information science, ranging from fundamental tests of decoherence to quantum communication and sensing. Heralded generation of single-phonon states of mechanical motion is an attractive way towards this goal, as it is, in principle, not limited by the object size. Here we demonstrate a technique which allows for generation and detection of a quantum state of motion by phonon counting measurements near the ground state of a 1.5 MHz micromechanical oscillator. We detect scattered photons from a membrane-in-the-middle optomechanical system using an ultra-narrowband optical filter, and perform Raman-ratio thermometry and second-order intensity interferometry near the motional ground state ($\bar{n}=0.23\pm0.02$ phonons). With an effective mass in the nanogram range, our system lends itself for studies of long-lived non-Gaussian motional states with some of the heaviest objects to date.Comment: 11 pages, 10 figure

Measurement-based quantum control of mechanical motion

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 occupation n = 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.Comment: New version with corrected detection efficiency as determined with a NIST-calibrated photodiode, added references and revised structure. Main conclusions are identical. 41 pages, 18 figure

Continuous Force and Displacement Measurement Below 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. To go beyond this limit, one must devise more sophisticated measurement techniques, which either 'evade' the backaction of the measurement, or achieve clever cancellation of the unwanted noise at the detector. In the half-century since the SQL was established, systems ranging from LIGO to ultracold atoms and nanomechanical devices have pushed displacement measurements towards this limit, and a variety of sub-SQL techniques have been tested in proof-of-principle experiments. 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.Comment: 18 pages, 7 figure

Multimode optomechanical system in the quantum regime

We realise a simple and robust optomechanical system with a multitude of long-lived ($Q>10^7$) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate ($96~\mathrm{kHz}$) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures ($10\,\mathrm{K}$). Reaching this quantum regime entails, i.~a., quantum measurement backaction exceeding thermal forces, and thus detectable 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 $\lesssim 90\,\mathrm{ kHz}$. The multi-mode nature of the employed membrane and Fabry-Perot resonators lends itself to hybrid entanglement schemes involving multiple electromagnetic, mechanical, and spin degrees of freedom.Comment: 19 pages, 9 figure

Laser cooling a membrane-in-the-middle system close to the quantum ground state from room temperature

Many protocols in quantum science and technology require initializing a system in a pure quantum state. In the context of the motional state of massive resonators, this enables studying fundamental physics at the elusive quantum–classical transition, and measuring force and acceleration with enhanced sensitivity. Laser cooling has been a method of choice to prepare mechanical resonators in the quantum ground state, one of the simplest pure states. However, to overcome the heating and decoherence by the thermal bath, this usually has to be combined with cryogenic cooling. Here, we laser-cool an ultracoherent, soft-clamped mechanical resonator close to the quantum ground state directly from room temperature. To this end, we implement the versatile membrane-in-the-middle setup with one fiber mirror and one phononic crystal mirror, which reaches a quantum cooperativity close to unity already at room temperature. We furthermore introduce a powerful combination of coherent and measurement-based quantum control techniques, which allows us to mitigate thermal intermodulation noise. The lowest occupancy we reach is 30 phonons, limited by measurement imprecision. Doing away with the necessity for cryogenic cooling should further facilitate the spread of optomechanical quantum technologies

Phononically shielded photonic-crystal mirror membranes for cavity quantum optomechanics

We present a highly reflective, sub-wavelength-thick membrane resonator featuring high mechanical quality factor and discuss its applicability for cavity optomechanics. The $88.5~\text{nm}$ thin stoichiometric silicon-nitride membrane, designed and fabricated to combine 2D-photonic and phononic crystal patterns, reaches reflectivities up to $99.89~\%$ and a mechanical quality factor of $2.9 \times 10^7$ at room temperature. We construct a Fabry-Perot-type optical cavity, with the membrane forming one terminating mirror. The optical beam shape in cavity transmission shows a stark deviation from a simple Gaussian mode-shape, consistent with theoretical predictions. We demonstrate optomechanical sideband cooling to mK-mode temperatures, starting from room temperature. At higher intracavity powers we observe an optomechanically induced optical bistability. The demonstrated device has potential to reach high cooperativities at low light levels desirable for e.g. optomechanical sensing and squeezing applications or fundamental studies in cavity quantum optomechanics, and meets the requirements for cooling to the quantum ground state of mechanical motion from room temperature

Entanglement between Distant Macroscopic Mechanical and Spin Systems

Entanglement is a vital property of multipartite quantum systems, characterised by the inseparability of quantum states of objects regardless of their spatial separation. Generation of entanglement between increasingly macroscopic and disparate systems is an ongoing effort in quantum science which enables hybrid quantum networks, quantum-enhanced sensing, and probing the fundamental limits of quantum theory. The disparity of hybrid systems and the vulnerability of quantum correlations have thus far hampered the generation of macroscopic hybrid entanglement. Here we demonstrate, for the first time, generation of an entangled state between the motion of a macroscopic mechanical oscillator and a collective atomic spin oscillator, as witnessed by an Einstein-Podolsky-Rosen variance below the separability limit, $0.83 \pm 0.02<1$. The mechanical oscillator is a millimeter-size dielectric membrane and the spin oscillator is an ensemble of $10^9$ atoms in a magnetic field. Light propagating through the two spatially separated systems generates entanglement due to the collective spin playing the role of an effective negative-mass reference frame and providing, under ideal circumstances, a backaction-free subspace; in the experiment, quantum backaction is suppressed by 4.6 dB. Our results pave the road towards measurement of motion beyond the standard quantum limits of sensitivity with applications in force, acceleration,and gravitational wave detection, as well as towards teleportation-based protocols in hybrid quantum networks.Comment: 24 pages, 12 figure

Membrane-Based Scanning Force Microscopy

We report the development of a scanning force microscope based on an ultrasensitive silicon nitride membrane optomechanical transducer. Our development is made possible by inverting the standard microscope geometry - in our instrument, the substrate is vibrating and the scanning tip is at rest. We present topography images of samples placed on the membrane surface. Our measurements demonstrate that the membrane retains an excellent force sensitivity when loaded with samples and in the presence of a scanning tip. We discuss the prospects and limitations of our instrument as a quantum-limited force sensor and imaging tool.</p