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arXiv:1903.10470 · Physical Review A

Measurement and feedback for cooling heavy levitated particles in low-frequency traps

L. S. Walker, Gordon R. M. Robb, Andrew J. Daley

Published Dec 12, 2019• 10 citations
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Abstract

We consider a possible route to ground-state cooling of a levitated nanoparticle, magnetically trapped by a strong permanent magnet, using a combination of measurement and feedback. The trap frequency of this system is much lower than those involving trapped ions or nanomechanical resonators. Minimization of environmental heating is therefore challenging as it requires control of the system on a timescale comparable to the inverse of the trap frequency. We show that these traps are an excellent platform for performing optimal feedback control via real-time state estimation, for the preparation of motional states with measurable quantum properties.

DOI
10.1103/physreva.100.063819

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Bulletin of the American Physical Society•Mar 16, 2021•1 citation
We consider a possible route to ground-state cooling of a levitated nanoparticle, magnetically trapped by a strong permanent magnet, using a combination of measurement and feedback. The trap frequency of this system is much lower than those involving trapped ions or nanomechanical resonators. Minimization of environmental heating is therefore challenging as it requires control of the system on a timescale comparable to the inverse of the trap frequency. We show that these traps are an excellent platform for performing optimal feedback control via real-time state estimation, for the preparation of motional states with measurable quantum properties.
Optically trapped nanoparticles have recently emerged as exciting candidates for tests of quantum mechanics at the macroscale and as versatile platforms for ultrasensitive metrology. Recent experiments have demonstrated parametric feedback cooling, nonequilibrium physics, and temperature detection, all in the classical regime. Here we provide the first quantum model for trapped nanoparticle cooling and force sensing. In contrast to existing theories, our work indicates that the nanomechanical ground state may be prepared without using an optical resonator; that the cooling mechanism corresponds to nonlinear friction; and that the energy loss during cooling is nonexponential in time. Our results show excellent agreement with experimental data in the classical limit, and constitute an underlying theoretical framework for experiments aiming at ground state preparation. Our theory also addresses the optimization of, and the fundamental quantum limit to, force sensing, thus providing theoretical direction to ongoing searches for ultra-weak forces using levitated nanoparticles.
Due to their exceptional isolation from the environment, magnetically levitated particles are explored as extremely sensitive mechanical sensors. For future gravity experiments on quantum superpositions, such systems need to be cooled close to their ground state. To demonstrate the combination of state of the art vibration isolation, milligram levitated high Q mechanical resonators and position detection with low noise, we present linear feedback cooling of a magnetically levitated gravity sensor to below 2 picometer amplitude and below 10 millikelvin mode temperature for two translational modes (the x- and y-mode) simultaneously. The sensor is a levitating permanent magnet in a type I superconducting trap, where its six resonance frequencies are measured with a superconducting coil coupled to a DC SQUID. This signal is measured with a lock-in amplifier and a feedback signal is sent to a piezoelectric actuator, allowing the cooling of resonant modes at 50.6 and 68.0 Hz simultaneously. These two translational modes have Q factors of 3.8⋅1063.8 \cdot 10^63.8⋅106 and 5.5⋅1065.5 \cdot 10^65.5⋅106 respectively. The experiment is mounted inside a dry dilution refrigerator where it is vibrationally attenuated with 110-130 dB at these frequencies. In this work, we discuss future improvements on the setup which may enable quantum ground state cooling on a magnetically levitated particle, that has previously been shown to be a gravitational sensor.
Abstract The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering1. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems2, 3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback4. Successful implementations thus far include experiments on the level of optical and atomic systems5–7. Here we demonstrate real-time optimal control of the quantum trajectory8 of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.
We develop the theory describing the quantum coupled dynamics of the center-of-mass motion of a nanoparticle and an ensemble of ions co-trapped in a dual-frequency linear Paul trap. We first derive analytical expressions for the motional frequencies and classical trajectories of both nanoparticle and ions. We then derive a quantum master equation for the ion-nanoparticle system and quantify the sympathetic cooling of the nanoparticle motion enabled by its Coulomb coupling to a continuously Doppler-cooled ion. We predict that motional cooling down to sub-kelvin temperatures is achievable in state-of-the-art experiments even in the absence of motional feedback and in the presence of micromotion. We then extend our analysis to an ensemble of NNN ions, predicting a linear increase of the cooling rate as a function of NNN and motional cooling of the nanoparticle down to tenths of millikelvin in current experimental platforms. Our work establishes the theoretical toolbox needed to explore the ion-assisted preparation of non-Gaussian motional states of levitated nanoparticles.
We set out to create a mechanical system with a size scale generally considered to reside in the classical regime and make it behave quantum mechanically. Our system consists of a silica microsphere diamagnetically levitated in an ultra-high vacuum environment. The combination of a strong magnetic field gradient, generated by ferromagnetic pole pieces and permanent magnets, and the gravitational interaction create a 3-dimensional trap for the particle. We measure the particle's motion in the trap by scattering laser light off of the particle, and use that measurement to provide negative feedback to the particle, removing mechanical energy via a radiation pressure damping force from a second laser. In the ideal case, the energy of the particle will near that of its quantum mechanical ground state. It is in this regime that we aim to create non-classical states of the particle's mechanical motion. By measuring the decoherence rate or the evolution of quantum uncertainty of non-classical states of the trapped particle, we may be able to observe deviations from quantum mechanical predictions that can be attributed to the gravitational interaction.
Quantum control of complex objects in the regime of large size and mass provides opportunities for sensing applications and tests of fundamental physics. The realization of such extreme quantum states of matter remains a major challenge. We demonstrate a quantum interface that combines optical trapping of solids with cavity-mediated light-matter interaction. Precise control over the frequency and position of the trap laser with respect to the optical cavity allowed us to laser-cool an optically trapped nanoparticle into its quantum ground state of motion from room temperature. The particle comprises 108 atoms, similar to current Bose-Einstein condensates, with the density of a solid object. Our cooling technique, in combination with optical trap manipulation, may enable otherwise unachievable superposition states involving large masses.