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Feedback Cooling the Mechanical Motion of a Diamagnetic Particle in a Magneto-Gravitational Trap

Bradley R. Slezak

Published Sep 27, 2018• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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 Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence [1-4]. Quantum control of mechanical motion has been achieved by engineering the radiation pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator [5-8]. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states [9]. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects [10,11], since their trapping potential is fully controllable. In this work, we optically levitate a femto-gram dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its center-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 43%. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales [12,13].
Levitation of microscopic objects in vacuum combines exceptional environmental isolation with precise control of their dynamics, pushing the limits of sensing and macroscopic quantum physics. In particular, magnetic levitation allows a large range of particle sizes, while avoiding detrimental effects from high-intensity optical trapping beams and electric field noise. However, existing diamagnetic and Meissner levitation approaches are typically constrained by low mechanical eigenfrequencies, limited integrability with other systems due to bulky coils or magnets, and, for Meissner levitation, the need for cryogenic operation. Here, we demonstrate a room-temperature on-chip magnetic levitation platform capable of stably levitating a nanogram (6.5 micrometer radius) ferromagnetic microsphere. The platform is scalable and tunable, and supports librational modes with eigenfrequencies exceeding 10 kHz. Further miniaturization and coupling to solid-state spin qubits could enable cooling to the quantum ground state. Beyond quantum experiments, this architecture enables integrated precision sensing and studies of isolated ferromagnet thermodynamics.
Abstract Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence1–3. Quantum control of mechanical motion has been achieved by engineering the radiation–pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator4–7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states8. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects9, 10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10−15 grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales11.
We show that by magnetically trapping a superconducting microsphere close to a quantum circuit, it is possible to perform ground-state cooling and prepare quantum superpositions of the center-of-mass motion of the microsphere. Due to the absence of clamping losses and time-dependent electromagnetic fields, the mechanical motion of micrometer-sized metallic spheres in the Meissner state is predicted to be very well isolated from the environment. Hence, we propose to combine the technology of magnetic microtraps and superconducting qubits to bring relatively large objects to the quantum regime.