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Spin mechanics with levitating ferromagnetic particles

MetadataDetails
Publication Date2020-04-13
JournalPhysical review. B./Physical review. B
AuthorsPaul Huillery, Tom Delord, L. Nicolas, Mathias van den Bossche, M. Perdriat
InstitutionsLaboratoire de Physique de l’ENS, École Normale SupĂ©rieure - PSL
Citations40
AnalysisFull AI Review Included

This research proposes and demonstrates initial steps toward coupling the librational (angular oscillation) mode of levitating ferromagnetic particles to the electronic spin of Nitrogen-Vacancy (NV) centers in diamond, aiming for quantum spin-mechanical experiments.

  • High-Frequency Mechanical Oscillators: Soft ferromagnets levitated in a Paul trap achieve librational frequencies up to 170 kHz under modest magnetic fields (0.1 T). This frequency significantly exceeds the decoherence rate of NV centers in typical CVD diamonds, enabling resolved sideband operation.
  • High Quality Factor: A mechanical quality factor (Q) close to 104 was achieved at a moderate vacuum level (4.5 x 10-2 mbar), crucial for maintaining coherent motion.
  • Hybrid Structures Demonstrated: Two types of composite particles were successfully levitated: (1) Nanodiamonds (FNDs) attached to iron magnets, and (2) Micro-diamonds coated with a 200 nm thick nickel layer.
  • Coherent Spin Control: Coherent manipulation (Rabi oscillations and Hahn-echoes) of NV center spins embedded in the hybrid structures was demonstrated, confirming the viability of the spin platform.
  • Spin Read-Out of Motion: The angular motion of the levitating particle was successfully read out using the NV electronic spin resonance (ESR) frequency shift, confirming the spin-mechanical coupling mechanism.
  • Quantum Prospects: The platform offers a path toward ultra-sensitive gyroscopy, torque balances, and realizing single-ion-like protocols for entangling distant spins using the magnet’s motional mode as a quantum bus.
ParameterValueUnitContext
Levitation Trap TypePaul Trap (Ring)N/A25 ”m thick tungsten wire, 200 ”m inner radius.
Ferromagnet MaterialIron (98% purity)N/ASoft ferromagnet, spherical particles.
Iron Particle Diameter0.5 to 3”mMost particles measured around 1 ”m.
Paul Trap Injection Voltage4000VacUsed for injection under ambient conditions.
External Magnetic Field (B)0.1TUsed for magnetic confinement of iron rods.
Librational Frequency (Iron Rod)170kHzMaximum measured frequency at 0.1 T B-field.
Mechanical Quality Factor (Q)9.3 x 103N/AMeasured at 4.5 x 10-2 mbar vacuum pressure.
NV Center Coherence Time (T2, echo)825nsMeasured in FNDs attached to levitating magnet.
Hybrid Structure 2 Diamond Size8 to 12”mMicro-diamond (MSY) with 103 to 104 NV centers.
Hybrid Structure 2 Coating Thickness200nmNickel coating applied to micro-diamond.
Hybrid Librational Frequency (Ni-coated Diamond)4.2kHzMeasured at 0.14 T B-field.
NV Spin Polarization Rate34”sMeasured in Ni-coated diamond hybrid structure.
Theoretical Coupling Rate (λφ/2π)100kHzEstimated for 80 nm x 40 nm ellipsoid hybrid structure at 30 mT.
Gas Damping Rate (Γgas)1HzEstimated heating rate at P = 10-3 mbar for 1 ”m sphere.

The core experimental challenge involved levitating and confining ferromagnetic particles and hybrid structures, followed by spin-mechanical coupling and readout.

  1. Ferromagnetic Rod Assembly (Soft Magnets):

    • Injection: Multiple spherical iron particles (0.5-3 ”m) were injected into the Paul trap using a metallic tip.
    • Particle Selection: The trap potential was lowered and air currents were used to eject excess particles, leaving 2 to 4 particles.
    • Binding: The trap frequency was reduced to bring the particles close (forming a Coulomb crystal due to electrostatic repulsion). A permanent magnet was then manually approached to apply a magnetic field (tens of Gauss). Attractive magnetic forces overcame repulsion, binding the particles into an elongated rod aligned with the B-field.
  2. Libration Excitation and Detection:

    • Confinement: A homogeneous magnetic field (up to 0.1 T) was applied using permanent magnets to confine the particle orientation.
    • Excitation: External Helmholtz coils generated a transverse magnetic field (Bexc) perpendicular to the confinement field. The coil current was switched ON/OFF three times at a frequency near the librational frequency to favor angular excitation over center-of-mass motion.
    • Optical Readout: A green laser was focused onto the particle. The reflected light was collected, and the resulting speckle pattern was monitored via an optical fiber and photodiode. Angular displacement caused changes in the speckle pattern intensity.
  3. Hybrid Structure Preparation (Scheme 2 Focus):

    • FND Attachment (Scheme 1): Fluorescent Nanodiamonds (FNDs, 100 nm) were nebulized onto iron particles cast on a coverslip. The resulting mixture was loaded into the Paul trap.
    • Nickel Coating (Scheme 2): Micro-diamonds (8-12 ”m) were coated with a 200 nm thick nickel layer via sputtering from an oven onto a quartz coverslip.
  4. Spin Read-Out of Motion (Ni-Coated Diamond):

    • ESR Tuning: The external magnetic field angle was tuned to maximize the photoluminescence (PL) signal from the NV centers.
    • Detection: A microwave field was applied, detuned to the side of an NV ESR transition (where the slope of the ESR signal is maximized).
    • Signal Processing: The PL signal was monitored during parametric excitation. The difference between signals obtained using positive and negative microwave detunings was calculated to remove the spin-independent optical signal component, isolating the spin-dependent angular motion signal.

The demonstrated technology enables the creation of high-performance mechanical oscillators coupled to quantum spins, opening doors for advanced sensing and quantum computing hardware.

  • Ultra-Sensitive Inertial Sensing:

    • Gyroscopy: The high librational frequency (up to 170 kHz) and high Q-factor (close to 104) make these levitating magnets superior mechanical oscillators for ultra-sensitive gyroscopy applications, exceeding current Paul trap limitations.
    • Torque Magnetometry: The platform can implement ultra-sensitive torque balances, leveraging the NV spin’s sensitivity to magnetic field gradients for precision measurements.
  • Quantum Information and Computing:

    • Quantum Transducers: The hybrid structures act as efficient spin-mechanical transducers, enabling coherent exchange between mechanical phonons and electronic spins.
    • Quantum Bus: The motional mode of the levitating magnet can serve as a quantum bus for entangling distant NV spins, a key requirement for distributed quantum networks.
    • Quantum State Engineering: The high coupling rate and resolved sideband regime allow for efficient preparation and cooling of the mechanical oscillator to its quantum ground state, necessary for quantum computation protocols.
  • Fundamental Physics Research:

    • Macroscopic Quantum Tests: The ability to control and measure the quantum state of a macroscopic object (micron-sized magnet) provides a platform for testing quantum mechanics on a large scale.
    • Magnetism Studies: Investigating fundamental effects like the Einstein-de Haas/Barnett effects by studying the interplay between magnetism and orbital angular momentum in levitating particles.
View Original Abstract

We propose and demonstrate first steps towards schemes where the librational\nmode of levitating ferromagnets is strongly coupled to the electronic spin of\nNitrogen-Vacancy (NV) centers in diamond. Experimentally, we levitate\nferromagnets in a Paul trap and employ magnetic fields to attain oscillation\nfrequencies in the hundreds of kHz range with Q factors close to $10^4$. These\nlibrational frequencies largely exceed the decoherence rate of NV centers in\ntypical CVD grown diamonds offering prospects for sideband resolved operation.\nWe also prepare and levitate composite diamond-ferromagnet particles and\ndemonstrate both coherent spin control of the NV centers and read-out of the\nparticle libration using the NV spin. Our results will find applications in\nultra-sensitive gyroscopy and bring levitating objects a step closer to\nspin-mechanical experiments at the quantum level.\n