Measuring the angular displacement of a mechanical oscillator is a ubiquitous task; however, the multimode nature of angular optomechanical coupling makes coherent signal enhancement challenging. Here we demonstrate coherently enhanced angular displacement readout with an integrated guided mode resonance (GMR) structure, applying it to precision readout of a nanomechanical oscillator. Specifically, we fabricate subwavelength gratings into 100-nm-thick Si$_3$N$_4$ membranes and record their vibration by direct transmission measurements. The narrow linewidth $\approx 2.5\;\text{mrad}$ of the GMR enables a shot-noise-limited displacement imprecision of $ 10^{-9}\;\text{rad}/\sqrt{\text{Hz}}$ with nanowatts of optical power, sufficient to resolve the thermal motion of a $Q\approx 10^6$ torsion mode with a signal-to-noise ratio of 47 dB. Control experiments based on polarization and wavelength detuning confirm that the measured signal arises from GMR-mediated transduction. These results establish guided-mode resonance as an on-chip approach to angular displacement readout in quantum optomechanical sensors.
Measuring the angular displacement of a mechanical oscillator is a ubiquitous task; however, the multimode nature of angular optomechanical coupling makes coherent signal enhancement challenging. Here we demonstrate coherently enhanced angular displacement readout with an integrated guided mode resonance (GMR) structure, applying it to precision readout of a nanomechanical oscillator. Specifically, we fabricate subwavelength gratings into 100-nm-thick Si3N4 membranes and record their vibration by direct transmission measurements. The narrow linewidth ≈2.5mrad of the GMR enables a shot-noise-limited displacement imprecision of 10−9rad/Hz with nanowatts of optical power, sufficient to resolve the thermal motion of a Q≈106 torsion mode with a signal-to-noise ratio of 47 dB. Control experiments based on polarization and wavelength detuning confirm that the measured signal arises from GMR-mediated transduction. These results establish guided-mode resonance as an on-chip approach to angular displacement readout in quantum optomechanical sensors.
The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. Full information of the state of light can only be gathered by a tomographic measurement. Here we demonstrate a tomographic interferometer readout by measuring arbitrary quadratures of the light field exiting a Michelson–Sagnac interferometer that contains a thermally excited high-quality silicon nitride membrane. A readout noise of 1.9 × 10 −16 m Hz −1/2 around the membrane's fundamental oscillation mode at 133 kHz has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.
Coupling mechanical motion to an optical resonator enables displacement measurements approaching the standard quantum limit (SQL). However, increasing the optomechanical coupling strength will inevitably lead to probing of the nonlinear response of the optical resonator. Thermal intermodulation noise (TIN) arising from the nonlinear mixing of thermomechanical motion can further increase the imprecision well above the SQL and has hitherto been canceled up to second order of nonlinearity via operation at the "magic detuning". In this work, we record the output of a membrane-in-the-middle microcavity system operating at room temperature and achieving high cooperativity, C>nth, and apply a nonlinear transform that removes all orders of TIN, improving the mechanical signal-to-noise ratio by nearly 10 dB. Our results can be applied to experiments affected by third-order TIN, which we expect to be the dominating intrinsic source of noise in high-cooperativity room-temperature cavity optomechanical systems.
In this work, we investigate a tool for hybrid quantum systems that implements a transducer to map small position changes of a micro-mechanical membrane onto the polarization of a laser beam. This is achieved with an interferometric setup that has reduced needs for stabilization. Specifically, an oscillating silicon nitride membrane placed in the middle of an asymmetric optical cavity causes phase shifts in the reflected, near-resonant light field. A beam displacer is used to combine the signal beam with a mode-matched, orthogonally polarized reference beam for polarization encoding. Subsequent balanced homodyne measurement is used to detect thermal membrane noise. Minor improvements in the design should achieve sufficiently high signal-to-noise ratio for the detection of motional quantum noise in the regime of high opto-mechanical coupling strength. This setup can provide a robust quantum link between a micro-mechanical oscillator and other systems such as atomic ensembles.
The application of quantum mechanics to macroscopic motion suggests many counterintuitive phenomena. While the quantum nature of the motion of individual atoms and molecules has long been successfully studied, an equivalent demonstration of the motion of a near-macroscopic structure remains a challenge in experimental physics. A nanomechanical resonator is an excellent system for such a study. It typically contains > 10 10 atoms, and it may be modeled in terms of macroscopic parameters such as bulk density and elasticity. Yet it behaves like a simple harmonic oscillator, with mass low enough and resonant frequency high enough for its quantum zero-point motion and single energy quanta to be experimentally accessible. In pursuit of quantum phenomena in a mechanical oscillator, two important goals are to prepare the oscillator in its quantum ground state, and to measure its position with a precision limited by the Heisenberg uncertainty principle. In this work we have demonstrated techniques that advance towards both of these goals. Our system comprises a 30 micron × 170 nm, 2.2 pg, 5.57 MHz nanomechanical resonator capacitively coupled to a 5 GHz superconducting microwave resonator. The microwave resonator and nanomechanical resonator are fabricated together onto a single silicon chip and measured in a dilution refrigerator at temperatures below 150 mK. At these temperatures the coupling of the motion to the thermal environment is very small, resulting in a very high mechanical Q, approaching ∼ 10 6 . By driving with a microwave pump signal, we observed sidebands generated by the mechanical motion and used these to measure the thermal motion of the resonator. Applying a pump tone red-detuned from the microwave resonance, we used the microwave field to damp the mechanical resonator, extracting energy and "cooling" the motion in a manner similar to optical cooling of trapped atoms. Starting from a mode temperature of ∼ 150 mK, we reached ∼ 40 mK by this "backaction cooling" technique, corresponding to an occupation factor only ∼ 150 times above the ground state of motion. We also determined the precision of our device in measurement of position. Quantum mechanics dictates that, in a continuous position measurement, the precision may be no better than the zero-point motion of the resonator. Increasing the coupling of the resonator to detector will eventually result in back-action driving of the motion, adding imprecision and enforcing this limit. We demonstrated that our system is capable of precisions approaching this limit, and identified the primary experimental factors preventing us from reaching it: noise added to the measurement by our amplifier, and excess dissipation appearing in our microwave resonator at high pump powers. Furthermore, by applying both red- and blue-detuned phase-coherent microwave pump signals, we demonstrated back-action evading (BAE) measurement sensitive to only a single quadrature of the motion. By avoiding the back-action driving in the measured quadrature, such a technique has the potential for precisions surpassing the limit of the zero-point motion. With this method, we achieved a measurement precision of ∼ 100 fm, or 4 times the quantum zero-point motion of the mechanical resonator. We found that the measured quadrature is insensitive to back-action driving by at least a factor of 82 relative to the unmeasured quadrature. We also identified a mechanical parametric amplification effect which arises during the BAE measurement. This effect sets limits on the BAE performance but also mechanically preamplifies the motion, resulting in a position resolution 1.3 times the zero-point motion. We discuss how to overcome the experimental limits set by amplifier noise, pump power and parametric amplification. These results serve to define the path forward for demonstrating truly quantum-limited measurement and non-classical states of motion in a nearly-macroscopic object.
The coupling of nanomechanical resonators to controllable quantum systems represents a growing and promising area of research. Recent advances in this field have brought to astonishing results, such as the initialization of a mechanical resonator into its quantum ground state and even the preparation of non-classical coherent states of motion. These achievements open up appealing scenarios to quantum information technologies and to the exploration of the quantum-classical boundary. From an application perspective, such quantum-mechanical hybrid systems provide a versatile and attractive tool for a variety of precision measurements, like ultra-sensitive detection of force, mass, and displacement. \n \nQuantum control over a mechanical resonator, or, conversely, the prospect of using resonator's motion for probing quantum states, both involve some tight requirements. First of all, the interaction between the mechanics and its quantum partner has to be large on the scale of the decoherence rates of the coupled systems. In most cases, the coupling mechanism has to be activated by engineering the resonator with electrodes, magnets, or mirrors, or by using tailored laser fields. For this reason, the search for a strong coupling typically competes with the requirement of overcoming decoherence effects. In addition, for quantum effects to be observable, strong coupling has to be accompanied by the preparation of zero entropy initial states, for instance by cooling the resonator into its ground state of motion. \n \nThe motivation pursued by this thesis is to contribute to the inspiring field of hybrid systems by walking through each of the aforementioned directions. We in fact demonstrate a promising system in which optically active quantum dots, embedded in fully self-assembled core-shell nanowires, are coupled to the nanowire motion. Mechanical vibrations of the nanowire modulate the quantum dot emission energy over a broad range exceeding 14 meV, by means of deformation potential coupling. In our system, therefore, both the coupling mechanism and the quantum states themselves are intrinsic to the resonator's structure. Besides revealing unusually strong, such a built-in opto-mechanical interaction produces a hybrid system whose inherent coherence is unspoiled by any functionalization or external field and whose fabrication is simpler than top-down techniques. \n \nWe further demonstrate the use of a quantum point contact as a displacement transducer to measure and control the low-temperature thermal motion of a nearby micromechanical cantilever. We show that by including the QPC in a suitable feedback loop, we are able to cool the cantilever's fundamental mechanical mode down to the level of the measurement noise, achieving a squashing of the QPC noise at high gain. Due to its off-board design, our system is particularly versatile and suitable to force-sensing applications. Since the QPC transducer is sensitive to local modifications of the nearby electric field, our approach is in principle compatible with any nanoscale resonator, without requiring any functionalization to activate the coupling. By improving the performance of the QPC as a one-dimensional conductor and the cantilever-QPC capacitive coupling, our system has the potential to achieve quantum-limited displacement resolution and ground state cooling. We then report on some ongoing attempts to overcome the current limitations of our system and couple mechanical motion to different mesoscopic transport devices. \n \nWe remark that our demonstration of an as-grown quantum-dot-in-nanowire hybrid system opens up bright prospects on future experiments, as also testified by the very recent ferment of the scientific community around this topic. We find that the opto-mechanical coupling rate is not far from the nanowire mechanical frequency. This fact makes our system particularly promising for the quantum non-demolition readout of a quantum dot state through a measurement of the nanowire position. On the other hand, we show that the coupling can be further optimized, and the nanowire mechanical heating rate reduced, thus disclosing the captivating perspective of using quantum dots to probe and control the mechanical state of a nanowire. In this context, it would be important to investigate a possible spin-oscillator coupling in our system, given the long coherence time offered by a spin state in a quantum dot. The wide range of control over the quantum dots emission energy and the ability to tune two neighboring dots into resonance pave the way to mechanically induced emitter-emitter coupling. In addition, our monolithic opto-mechanical system constitutes a good candidate for recent proposals of a tripartite hybrid system, which would integrate an optical cavity, a quantum two-level system and a mechanical resonator. The intrinsically strong coupling between the quantum dots and the nanowire motion would enhance the interaction between the mechanics and the cavity field, leading for instance to efficient cooling of the resonator to the ground state. Finally, the quantum dot sensitivity to the nanowire resonant vibration could also support the use of our system as an integrated force probe or as a nanomechanical mass sensor. In other words, the results reported in this dissertation constitute not only a relevant proof-of-principle, moreover they open up intriguing challenges for future research.
We present an optomechanical displacement transducer that relies on three cavity modes parametrically coupled to a mechanical oscillator and whose frequency spacing matches the mechanical resonance frequency. The additional resonances allow reaching the standard quantum limit at a substantially lower input power (compared to the case of a single cavity mode), as both sensitivity and quantum backaction are enhanced. Furthermore, it is shown that in the case of multiple cavity modes, coupling between the modes is induced via reservoir interaction, e.g., enabling quantum backaction noise cancellation. Experimental implementation of the schemes is discussed in both the optical and microwave domain.