Mechanical Dissipation Below $1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{Hz}$ with a Cryogenic Diamagnetic Levitated Micro-Oscillator

Mechanical Dissipation Below $1 μ Hz$ with a Cryogenic Diamagnetic Levitated Micro-Oscillator

Yingchun Leng, Rui Li, Xi Kong, Han Xie, Di Zheng, Peiran Yin, Fang Xiong, Tong Wu, Chang-Kui Duan, Youwei Du, Zhang-qi Yin, Pu Huang, and Jiangfeng Du

Phys. Rev. Applied 15, 024061 – Published 24 February 2021

Abstract

Ultralow-dissipation mechanical systems play an important role in metrology and exploring macroscopic quantum phenomena. Here we report a diamagnetic levitated micromechanical oscillator operating at 3 K with measured dissipation down to $0.59 μ Hz$ and a quality factor up to $2 \times 10^{7}$ . This mechanical system achieves the lowest dissipation among the state-of-the-art microscale and nanoscale mechanical systems reported to date, with orders-of-magnitude reduction over other systems based on different principles. The cryogenic diamagnetic levitated oscillator is applicable on a wide range of mass, making it a good candidate system for ultrasensitive measurements of both force and acceleration. By virtue of the strong magnetic gradient, this system is potentially capable of studying quantum spin mechanics.

Received 21 August 2020
Revised 7 January 2021
Accepted 8 January 2021

DOI:https://doi.org/10.1103/PhysRevApplied.15.024061

Physics Subject Headings (PhySH)

Classical mechanics Cryogenics & vacuum technology Noise Quantum metrology Quantum sensing

Micromechanical & nanomechanical oscillators

Cryogenics Precision measurements

General PhysicsNonlinear Dynamics

Authors & Affiliations

Yingchun Leng ¹, Rui Li ^2,3,4, Xi Kong¹, Han Xie ¹, Di Zheng¹, Peiran Yin ¹, Fang Xiong¹, Tong Wu ¹, Chang-Kui Duan^2,3,4, Youwei Du ^1,5, Zhang-qi Yin ⁶, Pu Huang ^1,*, and Jiangfeng Du^2,3,4,†

¹National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
²Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
³CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, China
⁴Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
⁵Collaborative Innovation Center of Advanced Microstructures and Jiangsu Key Laboratory for Nano Technology, Nanjing 210093, China
⁶Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China

^*hp@nju.edu.cn
^†djf@ustc.edu.cn

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Vol. 15, Iss. 2 — February 2021

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Figure 1
Experimental setup. (a) The magnetogravitational trap (MGT) is placed on the three-stage spring-mass suspension system, which is used to isolate the external vibration. The whole structure is mounted inside the chamber of a cryostat. A 633-nm laser beam reaches the sample chamber through a fiber and is focused loosely on the microsphere. The piezoelectric positioners are used to control the position of the trap so that the scattered light can be collected via the lens. A CMOS camera is used to record the position of the microsphere, and an avalanche-photodiode detector (APD) is used to measure the real-time intensity of the scattered light, which is used as feedback to cool or excite the motion of the microsphere via the magnetic force of the magnetic field generated by a small coil near the MGT. (b) The spring-mass suspension structure and the MGT, where soft copper braids are used to realize thermal connection between different suspension stages. (c),(d) Snapshots of the excited motion of the microsphere corresponding to two oscillation modes of different resonant frequencies (mode 1, 11.7 Hz, mode 2, 8.4 Hz) in the $x$ - $y$ plane, where the exposure time is 200 ms, much longer than the oscillation period. The scale bar corresponds to $30 μ m$ . AWG, arbitrary-waveform generator; m1 mass 1; m2, mass 2; m3, mass 3.
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Figure 2
Measured mechanical dissipation. (a) Logarithmic plot of the free ring-down normalized oscillation energy $X (t)^{2} / X (0)^{2}$ versus time for the oscillation mode of resonant frequency 11.7 Hz. Green and blue dots are results with statistic errors measured in a helium-gas environment and a vacuum without helium gas, respectively. Solid curves are fitted to the exponential decay [Eq. (5)]. (b) Same as (a) but for the oscillation mode of resonant frequency 8.4 Hz, with yellow for the helium-gas environment and red for a vacuum without helium gas. (c) The mechanical dissipation $γ / 2 π$ and the corresponding oscillator's mass for mechanical systems based on different principles. The blue dashed line indicates that the mechanical dissipation is $1 μ Hz$ . The red star corresponds to the 11.7-Hz mode in this experiment, rhombuses correspond to a solid-state oscillator [20, 21, 22, 23, 24], squares correspond to an optical levitated oscillator [26, 27, 28], the pentagon corresponds to an electrical levitated oscillator [29], triangles correspond to a Meissner levitated oscillator [30, 31], and circles correspond to a milligram-scale pendulum oscillator [36, 37].
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Figure 3
Estimation for force and acceleration sensing. The force sensitivity (left axis) as a function of mass at an environmental temperature of 3 K (solid light-blue line) and 10 mK (dashed light-blue line). The force from a single electron spin (solid dark-blue line) and the force from a single proton spin (dashed dark-blue line) are shown for comparison. The right axis shows the acceleration sensitivity (red lines). Here we assume that dissipation is still dominated by gas. The experimentally measured dissipation $γ / 2 π = 0.59 μ Hz$ , diameter of the microsphere $7.8 μ m$ , and magnetic gradient $G = 10^{4} T / m$ are adopted.
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Physical Review Applied

Mechanical Dissipation Below 1μHz with a Cryogenic Diamagnetic Levitated Micro-Oscillator

Yingchun Leng, Rui Li, Xi Kong, Han Xie, Di Zheng, Peiran Yin, Fang Xiong, Tong Wu, Chang-Kui Duan, Youwei Du, Zhang-qi Yin, Pu Huang, and Jiangfeng Du

Phys. Rev. Applied 15, 024061 – Published 24 February 2021

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Mechanical Dissipation Below $1 μ Hz$ with a Cryogenic Diamagnetic Levitated Micro-Oscillator