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Frontiers in Optics

Quantum correlations in measurement-based control of a mechanical oscillator

Vivishek Sudhir, Dalziel Joseph Wilson, Sergey A. Fedorov, H. Schütz, Ryan Schilling, Andreas Nunnenkamp, Tobias Jan Kippenberg

Published Jan 1, 2016• 0 citations
Publisher

Abstract

Quantum measurements proceed by the establishment of correlations between the system being measured, and the meter performing the measurement. We use measurement-based feedback to distill such quantum correlations resulting from the interferometric position measurement of a nanomechanical oscillator. We also identify the role of “feedback back-action” in deteriorating the efficiency of this procedure. Finally, we use feedback to control another form of such correlations – optical squeezing.

DOI
10.1364/fio.2016.ff3d.6

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•Jan 1, 2017•0 citations
Quantum measurements proceed by the establishment of correlations between the system being measured, and the meter performing the measurement. We use measurement-based feedback to distill such quantum correlations resulting from the interferometric position measurement of a nanomechanical oscillator. We also identify the role of “feedback back-action” in deteriorating the efficiency of this procedure. Finally, we use feedback to control another form of such correlations – optical squeezing.
The motion of a macroscopic mechanical oscillator – a glass nanostring – has been measured, using a cavity-enhanced optical interferometer, with a sensitivity that is 40 dB below that at the standard quantum limit, forming the most precise measurement of the zero-point motion of a mechanical oscillator yet. The resulting back-action due to the measurement has been observed. A quantum feedback protocol is used to cancel 20 dB of back-action, in a first instance of quantum feedback applied on a mechanical oscillator. Quantum correlations developed between the oscillator and the measuring instrument – light – has been observed. The role of these correlations in quantum-enhanced metrology of weak forces is illustrated, and feedback is used to manipulate and enhance the same correlations.
Quantum correlations between imprecision and backaction are a hallmark of continuous linear measurements. Here, we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nanomechanical oscillator. Backaction imparted by the meter laser, due to radiation-pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e., feedback that suppresses measurement backaction, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to backaction arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits, of measurement-based feedback as a tool to manipulate quantum correlations.
Measurement-induced back-action, a direct consequence of the Heisenberg uncertainty principle, is the defining feature of quantum measurements. We use quantum measurement theory to analyze the recent experiment of Safavi-Naeini et al. [Phys. Rev. Lett. 108, 033602 (2012)], and show that the results of this experiment not only characterize the zero-point fluctuation of a near-ground-state nanomechanical oscillator, but also demonstrate the existence of quantum back-action noise---through correlations that exist between sensing noise and back-action noise. These correlations arise from the quantum coherence between the mechanical oscillator and the measuring device, which build up during the measurement process, and are key to improving sensitivities beyond the standard quantum limit.
The radiation pressure interaction of light with a mechanical oscillator leads to a fundamental disturbance on the oscillator. This disturbance - measurement backaction - is due to the quantum fluctuations in the amplitude of the light. When the phase of the light is detected to infer the mechanical position, quantum fluctuations in the phase - measurement imprecision - leads to a further uncertainty in the estimate of the position. In this conventional measurement strategy, these two noise sources impose a fundamental limit on the ability to estimate the position of the mechanical object - the so-called standard quantum limit [1]. However, the two noise contributions are in general correlated. The fluctuations in the amplitude quadrature drive the mechanical oscillator, and this backaction driven motion is transduced into the phase quadrature. Correlations thus established [2] form a valuable quantum mechanical resource that can be directly employed for back-action cancellation in the measurement record via “variational measurements” [3].
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.