Feedback cooling the fundamental torsional mechanical mode of a tapered optical fiber to 30 mK

Letter

Feedback cooling the fundamental torsional mechanical mode of a tapered optical fiber to 30 mK

Felix Tebbenjohanns, Jihao Jia, Michael Antesberger, Adarsh Shankar Prasad, Sebastian Pucher, Arno Rauschenbeutel, Jürgen Volz, and Philipp Schneeweiss

Phys. Rev. A 108, L031101 – Published 8 September 2023

Abstract

We experimentally study the fundamental torsional mechanical mode of the nanofiber waist of a tapered optical fiber. We find that this oscillator with a resonance frequency of $f = 161.7 kHz$ features a quality factor of up to $Q = 10^{7}$ and a $Q$ -frequency product of $Q f = 1 THz$ . The polarization fluctuations of a transmitted laser field serve as a probe for the torsional motion. We damp the oscillator's thermal motion from room temperature to 28(7) mK by means of active feedback. Our results might enable new types of fiber-based sensors and lay the foundation for a promising hybrid quantum optomechanical platform.

Received 31 May 2023
Accepted 21 August 2023

DOI:https://doi.org/10.1103/PhysRevA.108.L031101

Physics Subject Headings (PhySH)

Hybrid quantum systems

Optical fibers

Cooling & trapping

Atomic, Molecular & Optical

Authors & Affiliations

Felix Tebbenjohanns¹, Jihao Jia¹, Michael Antesberger^2,*, Adarsh Shankar Prasad², Sebastian Pucher ^1,†, Arno Rauschenbeutel ^1,2, Jürgen Volz ^1,2, and Philipp Schneeweiss ^1,2,‡

¹Department of Physics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany
²Vienna Center for Quantum Science and Technology, TU Wien-Atominstitut, Stadionallee 2, 1020 Vienna, Austria

^*Present address: University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology, Boltzmanngasse 5, 1090 Vienna, Austria.
^†Present address: Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany.
^‡philipp.schneeweiss@hu-berlin.de

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Issue

Vol. 108, Iss. 3 — September 2023

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Images

Figure 1
Schematic of the experimental setup. We launch a linearly polarized probe light field through an optical nanofiber that is placed inside a vacuum chamber. The mechanical torsional mode is illustrated in the bottom left. We split the transmitted probe light and perform an out-of-loop analysis of the polarization rotation $θ$ induced by the angular displacement of the nanofiber, $φ$ . We use a second, in-loop analysis setup and feedback to two electrodes below and above the nanofiber to cool its torsional motion. Balanced photodiode (BPD), half-wave plate (HWP), polarizing beamsplitter (PBS), 50:50 beamsplitter (BS), variable delay $d$ , and feedback gain $g$ .
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Figure 2
Characterization and cooling of the thermally excited torsional motion. (a) Power spectral density (PSD), $S_{V V} (f)$ , of the out-of-loop analyzer voltage with $100 Hz$ resolution. The prominent peaks at $f = 161.7 kHz$ and $f = 319.8 kHz$ correspond to the fundamental and second harmonic mode of the torsional motion, respectively. (b) PSD of the polarization rotation, $S_{θ θ} (f)$ , with $10 Hz$ resolution, zoomed in around the resonance frequency of the fundamental torsional mode in equilibrium with room temperature (red circles), and cooled with a moderate and strong feedback gain $g$ (black triangles and dark blue squares, respectively). The dashed lines are Lorentzian fits. The detection noise floor (black dashed) is estimated from the measured noise around the Lorentzian peaks. Inset: ring-down measurement of the fundamental mode at a vacuum pressure of $2 \times 10^{- 7} mbar$ , revealing a damping rate of $γ / (2 π) = 28 (1) mHz$ and a quality factor of $Q = 5.8 (1) \times 10^{6}$ . (c) Effective temperature $T_{fb}$ under feedback as a function of the feedback gain $g$ . By increasing the feedback gain from $g = 0$ to $g = 6.4 \times 10^{4}$ , we cool the motion by four orders of magnitude from room temperature to $28 (7) mK$ . The blue line is a model according to Eq. (2). Its thickness represents the statistical error of 26% of the motional energy measured at $g = 0$ . This error is because of a finite measurement time of $T = 160 s$ , as we detail in the main text.
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Figure 3
Pressure and power dependency of the motional energy. (a) Detected signal power $〈 θ^{2} 〉$ (left axis, blue dots) and damping rate $γ$ (right axis, red triangles) as a function of gas pressure $p$ in the vacuum chamber. The optical power in the fiber is $P = 0.5 mW$ . Due to a finite measurement time of $T = 50 s$ , the observed energy fluctuates, as indicated by error bars and discussed in the main text. The blue solid line indicates the average value of the data points, revealing that the motional energy is independent of the vacuum pressure. The red solid line is a fit of the form $γ = γ_{0} + a p$ . The extracted intrinsic damping rate of the torsional motion is $γ_{0} / (2 π) = 57 (5) mHz$ . (b) Signal power as a function of the optical power $P$ in the nanofiber at a fixed vacuum pressure of $2 \times 10^{- 7} mbar$ . The solid line indicates the average signal power of the data points, revealing that the motional energy is virtually independent of the optical power in the fiber.
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