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Appearance and Disappearance of Quantum Correlations in Measurement-Based Feedback Control of a Mechanical Oscillator

Vivishek Sudhir, Dalziel Joseph Wilson, Ryan Schilling, Schuetz, H, Sergey A. Fedorov, Amir Hossein Ghadimi, Andreas Nunnenkamp, Tobias Jan Kippenberg

Published Jan 6, 2017• 66 citations

Abstract

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.

DOI: 10.17863/cam.7737

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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].

Abstract We study synchronization of a quantum van der Pol oscillator with a harmonic drive and demonstrate that quantum synchronization can be enhanced by performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying feedback control to the oscillator. The phase coherence of the oscillator is increased by reducing quantum fluctuations via the continuous measurement, whereas the measurement backaction inevitably induces fluctuations around the phase-locking point. We propose a simple feedback policy for suppressing measurement-induced fluctuations by adjusting the frequency of the harmonic drive, which results in enhancement of quantum synchronization. We further demonstrate that the maximum enhancement of quantum synchronization is achieved by performing quantum measurement on the quadrature angle at which the phase diffusion of the oscillator is the largest and the maximal information on the oscillator phase is extracted.

We study synchronization of a quantum van der Pol oscillator with a harmonic drive and demonstrate that quantum synchronization can be enhanced by performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying feedback control to the oscillator.The phase coherence of the oscillator is increased by reducing quantum fluctuations via the continuous measurement, whereas the measurement backaction inevitably induces fluctuations around the phase-locking point.We propose a simple feedback policy for suppressing measurement-induced fluctuations by adjusting the frequency of the harmonic drive, which results in enhancement of quantum synchronization.We further demonstrate that the maximum enhancement of quantum synchronization is achieved by performing quantum measurement on the quadrature angle at which the phase diffusion of the oscillator is the largest and the maximal information on the oscillator phase is extracted.

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We analyze synchronization of a quantum van der Pol (vdP) oscillator driven by a harmonic signal and demonstrate that performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying a feedback control to the oscillator can enhance quantum synchronization. We show that the phase coherence of the oscillator is increased by the reduction of quantum fluctuations due to the continuous measurement, but also that the measurement backaction inevitably induces fluctuations around the phase-locking point. We propose a simple feedback policy that can suppress the measurement-induced fluctuations by adjusting the frequency detuning between the oscillator and the driving signal, which leads to enhancement of quantum synchronization. We further demonstrate that the maximum phase coherence can be achieved by performing the quantum measurement on the quadrature angle at which the phase diffusion of the oscillator takes the largest value and the maximum information of the oscillator phase is attained.

We report on the observation of quantum correlations developed in a light beam that has interacted with a room-temperature nanomechanical oscillator. The vacuum fluctuations of the light drive the mechanical oscillator via the radiation pressure interaction, so that the phase of the transmitted light carries imprints of its own amplitude. We detect these subtle correlations, at the 5% level, using broadband measurements of the transmitted light in a homodyne detector tuned close to the amplitude quadrature. We also show how such correlations can be used for quantum-enhanced force metrology at room-temperature.