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Concept# Measurement in quantum mechanics

Summary

In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule. For example, a quantum particle like an electron can be described by a quantum state that associates to each point in space a complex number called a probability amplitude. Applying the Born rule to these amplitudes gives the probabilities that the electron will be found in one region or another when an experiment is performed to locate it. This is the best the theory can do; it cannot say for certain where the electron will be found. The same quantum state can also be used to make a prediction of how the electron w

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Here we describe how, utilizing a time-dependent optomechanical interaction, a mechanical probe can provide an amplified measurement of the virtual photons dressing the quantum ground state of an ultrastrongly coupled light-matter system. We calculate the thermal noise tolerated by this measurement scheme and discuss an experimental setup in which it could be realized.

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.

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We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end products it produces, which is generated according to a given probability distribution. We formulate the problem in the context of hypothesis testing and consider the specific case in which the objects can be modeled as pure loss channels. We demonstrate theoretically that a simple quantum strategy, using readily available resources and measurement schemes in the form of two-mode squeezed vacuum and photon counting, can outperform any classical strategy. We experimentally implement this protocol, exploiting optical twin beams, validating our theoretical results, and demonstrating that, in this task, there is a quantum advantage in a realistic setting.