RESUMEN
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 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 × 107 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 example, for 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.
RESUMEN
Controlling a quantum system by using observations of its dynamics is complicated by the backaction of the measurement process-that is, the unavoidable quantum disturbance caused by coupling the system to a measurement apparatus. An efficient measurement is one that maximizes the amount of information gained per disturbance incurred. Real-time feedback can then be used to cancel the backaction of the measurement and to control the evolution of the quantum state. Such measurement-based quantum control has been demonstrated in the clean settings of cavity and circuit quantum electrodynamics, but its application to motional degrees of freedom has remained elusive. Here we demonstrate measurement-based quantum control of the motion of a millimetre-sized membrane resonator. An optomechanical transducer resolves the zero-point motion of the resonator in a fraction of its millisecond-scale coherence time, with an overall measurement efficiency close to unity. An electronic feedback loop converts this position record to a force that cools the resonator mode to its quantum ground state (residual thermal occupation of about 0.29). This occupation is nine decibels below the quantum-backaction limit of sideband cooling and six orders of magnitude below the equilibrium occupation of the thermal environment. We thus realize a long-standing goal in the field, adding position and momentum to the degrees of freedom that are amenable to measurement-based quantum control, with potential applications in quantum information processing and gravitational-wave detectors.
RESUMEN
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.
RESUMEN
We discuss several techniques based on laser-driven interferometers and cavities to measure nanomechanical motion. With increasing complexity, they achieve sensitivities reaching from thermal displacement amplitudes, typically at the picometer scale, all the way to the quantum regime, in which radiation pressure induces motion correlated with the quantum fluctuations of the probing light. We show that an imaging modality is readily provided by scanning laser interferometry, reaching a sensitivity on the order of 10 fm / Hz 1 / 2 , and a transverse resolution down to 2 µ m . We compare this approach with a less versatile, but faster (single-shot) dark-field imaging technique.
RESUMEN
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) 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 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 â²90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
RESUMEN
Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how their frame is clamped to the sample mount, which in practice usually necessitates delicate, and difficult-to-reproduce mounting solutions. Here, we demonstrate that a phononic bandgap shield integrated in the membrane's silicon frame eliminates this dependence, by suppressing dissipation through phonon tunneling. We dry-etch the membrane's frame so that it assumes the form of a cm-sized bridge featuring a 1-dimensional periodic pattern, whose phononic density of states is tailored to exhibit one, or several, full band gaps around the membrane's high-Q modes in the MHz-range. We quantify the effectiveness of this phononic bandgap shield by optical interferometry measuring both the suppressed transmission of vibrations, as well as the influence of frame clamping conditions on the membrane modes. We find suppressions up to 40 dB and, for three different realized phononic structures, consistently observe significant suppression of the dependence of the membrane's modes on sample clamping-if the mode's frequency lies in the bandgap. As a result, we achieve membrane mode quality factors of 5 × 10(6) with samples that are tightly bolted to the 8 K-cold finger of a cryostat. Q × f -products of 6 × 10(12) Hz at 300 K and 14 × 10(12) Hz at 8 K are observed, satisfying one of the main requirements for optical cooling of mechanical vibrations to their quantum ground-state.