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arXiv:1003.3752 · Physical Review A

Measuring nanomechanical motion with an imprecision below the standard quantum limit

G. Anetsberger, E. Gavartin, O. Arcizet, Quirin P. Unterreithmeier, Eva Maria Weig, M. L. Gorodetsky, J. P. Kotthaus, Tobias Jan Kippenberg

Published Dec 29, 2010• 154 citations
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Abstract

We report a room-temperature measurement of nanomechanical motion with an imprecision below the standard quantum limit (SQL), using cavity-enhanced optical near fields. Fundamental thermodynamical cavity frequency fluctuation limits the total imprecision to $3 \mathrm{dB}$ below the SQL at room temperature [corresponding to $(530 \mathrm{am}/\sqrt{\mathrm{Hz}}){}^{2}$ in absolute units] and is expected to reduce to negligible values at moderate cryogenic temperatures. Coupling strengths exceeding those required to reach the SQL by more than two orders of magnitude are achieved, allowing a shot-noise limited imprecision more than $10 \mathrm{dB}$ below the SQL. The transducer, thus, in principle, allows access to the quantum backaction dominated regime, a prerequisite for exploring quantum backaction, measurement-induced squeezing, and obtaining sub-SQL sensitivity using backaction evading techniques.

DOI
10.1103/physreva.82.061804

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arXiv:2210.12222•Oct 21, 2022•1 citation
We report a room-temperature measurement of nanomechanical motion with an imprecision below the standard quantum limit (SQL), using cavity-enhanced optical near fields. Fundamental thermodynamical cavity frequency fluctuation limits the total imprecision to 3dB3 \mathrm{dB}3dB below the SQL at room temperature [corresponding to (530am/Hz)2(530 \mathrm{am}/\sqrt{\mathrm{Hz}}){}^{2}(530am/Hz​)2 in absolute units] and is expected to reduce to negligible values at moderate cryogenic temperatures. Coupling strengths exceeding those required to reach the SQL by more than two orders of magnitude are achieved, allowing a shot-noise limited imprecision more than 10dB10 \mathrm{dB}10dB below the SQL. The transducer, thus, in principle, allows access to the quantum backaction dominated regime, a prerequisite for exploring quantum backaction, measurement-induced squeezing, and obtaining sub-SQL sensitivity using backaction evading techniques.
When measuring the position of a mechanical oscillator, quantum mechanics imposes a strict limit on the attainable precision: Any reduction of imprecision leads to increased quantum backaction of the measuring probe on the oscillator. This quantum limit can be circumvented, in principle allowing to indefinitely reduce imprecision, by monitoring only a single quadrature of the oscillator. Such backaction-evading measurement has been recently demonstrated in electromechanical oscillators coupled to microwave resonant circuits. Here we demonstrate this technique in a photonic crystal nanomechanical oscillator, cryogenically and optomechanically cooled to a few quanta.
Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, due to backaction arising from quantum fluctuations in the measurement field. This standard quantum limit can be surpassed by monitoring only one of the two non-commuting quadratures of the motion, known as backaction-evading measurement. This technique has not been implemented using optical interferometers to date. Here we demonstrate, in a cavity optomechanical system operating in the optical domain, a continuous two-tone backaction-evading measurement of a localized gigahertz-frequency mechanical mode of a photonic-crystal nanobeam cryogenically and optomechanically cooled close to the ground state. Employing quantum-limited optical heterodyne detection, we explicitly show the transition from conventional to backaction-evading measurement. We observe up to 0.67 dB (14%) reduction of total measurement noise, thereby demonstrating the viability of backaction-evading measurements in nanomechanical resonators for optical ultrasensitive measurements of motion and force.
Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved problem in modern physics. Position measurements of small objects allow us to probe the area where the classical approximation breaks down. In quantum mechanics, Heisenbergâ s uncertainty principle dictates that any measurement of the position must be accompanied by measurement induced back-action---in this case manifested as an uncertainty in the momentum. In recent years, cavity optomechanics has become a powerful tool to perform precise position measurements and investigate their fundamental limitations. The utilization of optical micro-cavities greatly enhances the interaction between light and state-of-the-art nanomechanical oscillators. Therefore, quantum mechanical phenomena have been successfully observed in systems far beyond the microscopic world. In such a cavity optomechanical system, the fluctuations in the position of the oscillator are transduced onto the phase of the light, while fluctuations in the amplitude of the light disturb the momentum of the oscillator during the measurement. As a consequence, correlations are established between the amplitude and phase quadrature of the probe light. However, so far, observation of quantum effects has been limited exclusively to cryogenic experiments, and access to the quantum regime at room temperature has remained an elusive goal because the overwhelming amount of thermal motion masks the weak quantum effects. This thesis describes the engineering of a high-performance cavity optomechanical device and presents experimental results showing, for the first time, the broadband effects of quantum back-action at room temperature. The device strongly couples mechanical and optical modes of exceptionally high quality factors to provide a measurement sensitivity ∼ ⁣104\sim\!10^4∼104 times below the requirement to resolve the zero-point fluctuations of the mechanical oscillator. The quantum back-action is then observed through the correlations created between the probe light and the motion of the nanomechanical oscillator. A so-called â variational measurementâ , which detects the transmitted light in a homodyne detector tuned close to the amplitude quadrature, resolves the quantum noise due to these correlations at the level of 10\% of the thermal noise over more than an octave of Fourier frequencies around mechanical resonance. Moreover, building on this result, an additional experiment demonstrates the ability to achieve quantum enhanced metrology. In this case, the generated quantum correlations are used to cancel quantum noise in the measurement record, which then leads to an improved relative signal-to-noise ratio in measurements of an external force. In conclusion, the successful observation of broadband quantum behavior on a macroscopic object at room temperature is an important milestone in the field of cavity optomechanics. Specifically, this result heralds the rise of optomechanical systems as a platform for quantum physics at room temperature and shows promise for generation of ponderomotive squeezing in room-temperature interferometers.
Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements imposes a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a backaction evading measurement technique, reduce thermal noise to below the level of backaction, and exploit cancellations of any excess noise contributions at the detector. Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL sensitivity nearly two times better than previous measurements, and with an architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. We measure a total sensitivity below the SQL by 2.8 dB, corresponding to a reduction in the noise power by 72±5.1% below the quantum limit. Through the use of a detuned cavity and the optical spring effect, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the Universe.
Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements impose a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a back-action evading measurement technique, or else exploit cancellations of any excess noise contributions at the detector. %Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL measurement sensitivity nearly two times better than previous measurements, and with architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. By exploiting quantum correlations created by an optical spring, we measure a total sensitivity below the SQL by 2.8\textbf{2.8}2.8 dB, corresponding to a reduction in the noise power by 72±5.1\textbf{72}\pm\textbf{5.1}72±5.1 \% below the quantum limit. Through the use of a detuned optical spring, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies ranges applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the universe.