Two-Tone Optomechanical Instability and Its Fundamental Implications for Backaction-Evading Measurements

While quantum mechanics imposes a fundamental limit on the precision of interferometric measurementsof mechanical motion due to measurement backaction, the nonlinear nature of the coupling also leads toparametric instabilities that place practical limits on the sensitivity by limiting the power in theinterferometer. Such instabilities have been extensively studied in the context of gravitational wavedetectors, and their presence has recently been reported in Advanced LIGO. Here, we observeexperimentally and describe theoretically a new type of optomechanical instability that arises in two-tone backaction-evading (BAE) measurements, a protocol designed to overcome the standard quantumlimit. We demonstrate the effect in the optical domain with a photonic crystal nanobeam cavity and in themicrowave domain with a micromechanical oscillator coupled to a microwave resonator. In contrast to thewell-known parametric oscillatory instability that occurs in single-tone, blue-detuned pumping, and resultsfrom a two-mode squeezing interaction between the optical and mechanical modes, the parametricinstability in balanced two-tone optomechanics results from single-mode squeezing of the mechanical modein the presence of small detuning errors in the two pump frequencies. Counterintuitively, the instabilityoccurs even in the presence of perfectly balanced intracavity fields and can occur for both signs of detuningerrors. We find excellent quantitative agreement with our theoretical predictions. Since the constraints ontuning accuracy become stricter with increasing probe power, the instability imposes a fundamentallimitation on BAE measurements as well as other two-tone schemes, such as dissipative squeezing of opticaland microwave fields or of mechanical motion. In addition to identifying a new limitation in two-tone BAEmeasurements, the results also introduce a new type of nonlinear dynamics in cavity optomechanics.

Quantum Measurement of Mechanical Motion close to the Standard Quantum Limit

Liu Qiu

In quantum mechanics, the Heisenberg uncertainty principle places a fundamental limit in the measurement precision for certain pairs of physical quantities, such as position and momentum, time and energy or amplitude and phase. Due to the Heisenberg uncertainty principle, any attempt to extract certain information from a quantum object would inevitably perturbitinanunpredictableway. This raises one question,"What is the precision limit in such quantum measurements?" The answer, standard quantum limit (SQL), has been obtained by Braginsky to figure out the fundamental quantum limits of displacement measurement in the context of gravitational wave detection. To circumvent the unavoidable quantum back-action from the priori measurement, quantum non-demolition measurement (QND) methods were introduced by Braginsky and Thorne. To surpass the SQL of the displacement measurement in an interferometer, one can measure only one quadrature of the mechanical motion while give up the information about the other canonically conjugated quadrature. Such measurements can be performed by periodic driving the mechanical oscillator, i.e. the back-action evading (BAE) measurement. Cavity optomechanics provides an ideal table-top platform for the testing of the quantum measurement theory. Mechanical oscillator is coupled to electromagnetic field via radiation pressure, which is enhanced by an optical micro-cavity. Over the last decade, laser cooling has enabled the preparation of mechanical oscillator in the ground state in both optical and microwave systems. BAE measurements of mechanical motion have been allowed in the microwave electromechanical systems, which led to the observations of mechanical squeezing and entanglement. However, despite the theoretical proposal almost 40 years ago, the sub-SQL measurements still remain elusive. This thesis reports our efforts approach the sub-SQL with a highly sideband-resolved silicon optomechanical crystal (OMC) in a 3He buffer gas environment at 2K. The OMC couples an optical mode at telecommunication wavelengths and a colocalized mechanical mode at GHz frequencies. The Helium3 buffer gas environment allows sufficient thermalization of the OMC despite the drastically decreased silicon thermal conductivity. We observe Floquet dynamics in motional sideband asymmetry measurement when employing multiple probe tones. The Floquet dynamics arises due to presence of Kerr-type nonlinearities and gives rise to an artificially modified motional sideband asymmetry, resulting from a synthetic gauge field among the Fourier modes. We demonstrate the first optical continuous two-tone backaction-evading measurement of a localized GHz frequency mechanical mode of silicon OMC close to the ground state by showing the transition from conventional sideband asymmetry to backaction-evading measurement. We discover a fundamental two-tone optomechanical instability and demonstrate its implications on the back-action evading measurement. Such instability imposes a fundamental limitation on other two-tone schemes, such as dissipative quantum mechanical squeezing. We demonstrate state-of-art laser sideband cooling of the mechanical motion to a mean thermal occupancy of 0.09 quantum, which is 7.4dB of the oscillator's zero-point energy and corresponds to 92% ground state probability. This also enables us to observe the dissipative mechanical squeezing below the zero-point motion for the first time with laser light.

EPFL2020

Ultra low quantum decoherence nano-optomechanical systems

Mohammadjafar Bereyhi

Thermal motion of a room-temperature mechanical resonator typically dominates the quantum backaction of its position measurement. This is a longstanding barrier for exploring cavity optomechanics at room temperature. In order to enter the quantum regime of the optomechanical interaction, we need to be in the "backaction-dominated" regime, where we can study the limits of quantum measurement and how to circumvent them. To create a system which can enter the quantum regime, the optomechanical transducer has to satisfy certain criteria. A quantum-enabled optomechanical system consists of an optical cavity and a mechanical resonator with ultra low quantum decoherence, which are strongly coupled to each other via the optomechanical interaction.High stress silicon nitride has enabled nanomechanical resonators with exceptionally low dissipation at room temperature via several soft-clamping techniques. Achieving high optomechanical coupling to these coherent nanobeams results in high optomechanical cooperativities, thus alleviating the thermal motion barrier for room temperature quantum optomechanics. Monolithic integration of high-Q nanobeam resonators with optical cavities has been limited to doubly-clamped nanobeams due to the complexity of the device fabrication and long device sizes required for conventional soft-clamping using phononic crystals. In addition, the previous demonstrations of such systems showed limited optomechanical couplings thus a limited single photon cooperativity.I present the design, fabrication and characterization of three different classes of nanomechanical resonators clamp-tapered, fractal-like, and polygon resonators, which support perimeter modes, with Q factors exceeding 3 billion at room temperature and their optical readout using an integrated nearfield nano-optomechanical transducer using high stress silicon nitride. Our transducer features a one-dimensional Fabry-Perot optical cavity integrated with a high-Q nanomechanical resonator. The Fabry-Perot optical cavity is formed by patterning two photonic crystal reflectors on a silicon nitride waveguide designed for high-Q optical modes. Our approach allows individual optimization of optical and mechanical resonators, while maintaining a high optomechanical coupling rate due to large optomechanical mode overlap. Our best performing devices show on-chip optomechanical transducers with single photon cooperativities as high as 123 with mechanical quality factor of 120 million at room temperature. The developed system is of great interest to the optomechanics and sensing community. In quantum optomechanics, it will serve as a platform for quantum feedback control of the nanomechanical resonators to achieve motional ground state of a macroscopic resonator and generation of squeezed light at room temperature. Owing to their record value mechanical quality factors, the room temperature force sensitivity of our highest Q perimeter modes is on par with atomic force microscopy cantilevers at millikelvin temperature.Complete documentation of a nanofabrication process is the key to its reproducibility. Process-specific details of the fabrication techniques are usually missing in journal publications. To bridge this gap, I developed NanoFab-net.org. An online open-access tool that allows sharing process-specific fabrication reports, extracting the metadata and obtaining a unique digital object identifier (DOI) for each report.

EPFL2022

A hybrid on-chip optomechanical transducer for ultrasensitive force measurements

Emanuel Gavartin, Tobias Kippenberg

Nanoscale mechanical oscillators(1) are used as ultrasensitive detectors of force(2), mass(3) and charge(4). Nanomechanical oscillators have also been coupled with optical and electronic resonators to explore the quantum properties of mechanical systems(5). Here, we report an optomechanical transducer in which a Si3N4 nanomechanical beam(6,7) is coupled to a disk-shaped optical resonator made of silica on a single chip. We demonstrate a force sensitivity of 74 aN Hz(-1/2) at room temperature with a readout stability better than 1% at the minute scale. Our system is particularly suited for the detection of very weak incoherent forces, which is difficult with existing approaches because the force resolution scales with the fourth root of the averaging time(8). By applying dissipative feedback(9) based on radiation pressure, we significantly relax this constraint and are able to detect an incoherent force with a force spectral density of just 15 aN Hz(-1/2) (which is 25 times less than the thermal noise) within 35 s of averaging time (which is 30 times less than the averaging time that would be needed in the absence of feedback). It is envisaged that our hybrid on-chip transducer could improve the performance of various forms of force microscopy(8,10-12).