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arXiv:2303.17847 · Physical Review A

Stable magnetic levitation of soft ferromagnets for macroscopic quantum mechanics

Maria Fuwa

Published Aug 28, 2023• 6 citations
arXivHTMLPDF

Abstract

We propose a system for passive magnetic levitation and three-dimensional harmonic trapping of soft ferromagnets. Our protocol utilizes the magnetic-field gradient for vertical trapping, and the finite-size effect of the Meissner effect for horizontal trapping. We provide numerical and analytical estimations of possible mechanical dissipations to show that our system allows high mechanical Q factors above Q>108 , and quantum control of the levitated object is within reach of current technologies. The utilization of the soft ferromagnet's internal collective spin excitation may allow quantum mechanical phenomena with particles as large as the submillimeter scale.

DOI
10.1103/physreva.108.023523

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We propose a system for passive magnetic levitation and three-dimensional harmonic trapping of soft ferromagnets. Our protocol utilizes the magnetic-field gradient for vertical trapping, and the finite-size effect of the Meissner effect for horizontal trapping. We provide numerical and analytical estimations of possible mechanical dissipations to show that our system allows high mechanical Q factors above Q>108 , and quantum control of the levitated object is within reach of current technologies. The utilization of the soft ferromagnet's internal collective spin excitation may allow quantum mechanical phenomena with particles as large as the submillimeter scale.
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.
Magnetic levitation offer passive levitation of massive objects for use in advanced inertia sensors, for the generation of non-classical macroscopic motional states, and towards the table-top testing of low energy gravity with quantum mechanics. Magnons, a quanta of spin wave, couple to many physical quantities and strongly to electromagnetic fields, even at room temperature. In this work we demonstrate the stable trapping of a small YIG sphere using a magnetic Paul trap. We present a classical stability analysis of a magnetic Paul trap and show the stability diagram for all mechanical degrees of freedom. We show that coupling between librational and translational modes changes the stability region. We experimentally levitate the soft magnet yttrium iron garnet at room temperature obtaining Q-factors of ∼25\sim25∼25 and secular frequencies 15.815.815.8 Hz and 17.217.217.2 Hz. We provide numerical estimates of the achievable enhanced coupling between the center-of-mass motion and excited magnon modes, with a cooperativity above unity despite strong mechanical damping, indicating potential applications in quantum information processing, quantum interconnects and quantum memories.
Levitated systems have great potential in quantum sensing and exploring quantum effects at the macroscopic scale. Of particular interest are recent works suggesting that a levitated ferromagnet can beat the standard quantum limit of magnetometry. This work offers a theoretical model to analyze and understand critical features of the precessing dynamics of a levitated ferromagnetic needle, indeed much like a macrospin, in the presence of a weak magnetic field. The dynamics from the atomic scale reveals how the standard quantum limit is surpassed, thus verifying sensing advantages when compared with a collection of independent spins. Our theory further takes us to two additional experimental designs of immediate interest: measurement of the celebrated Berry phase with a precessing ferromagnetic needle and the use of its nutation motion to sense a low-frequency oscillating magnetic field. With a microscopic theory established for levitated ferromagnetic needles, future studies of macroscopic quantum effects and the associated quantum-classical transition also become possible.
Levitated systems have great potential in quantum sensing and exploring fundamental physics at the macroscopic scale. Of particular interest are recent works suggesting that a levitated ferromagnet can beat the standard quantum limit of magnetometry, a benchmark for quantum sensors. In this work, we show how a microscopic theory capturing atomic-scale spin-lattice interactions can be used to fully explain the emergence of collective precession dynamics of a levitated ferromagnet and the origin of its enhanced magnetometric sensitivity beyond that of independent spins. Our theory further takes us to two innovative experimental designs of immediate interest: measurement of the celebrated Berry phase with a precessing ferromagnetic needle and the use of its nutation motion to sense a low-frequency oscillating magnetic field. With a microscopic theory established for levitated ferromagnetic needles, future studies of macroscopic quantum effects and the associated quantum-classical transition also become possible.
The generation of macroscopic quantum states can drive both fundamental physics and quantum technologies. This work proposes a top-down approach to the generation of macroscopic spin GHZ states using a levitated ferromagnet, where a strong locking between the collective spin and the lattice rotation enables mechanical control of the collective spin. We quantify the metrological advantage of the resulting macrospin superposition state by showing that Heisenberg scaling of the quantum Fisher information is achievable. Roles of symmetry and geometry are analyzed in terms of decoherence due to gas collisions, identifying accessible conditions for experimental realization. The usefulness of a macrospin superposition state of a levitated cylindrical ferromagnet in testing spin-dependent wavefunction collapse models is also discussed.
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.