Spin dynamical decoupling for generating macroscopic superpositions of a free-falling nanodiamond

At a Glance

Metadata	Details
Publication Date	2022-01-31
Journal	Physical review. A/Physical review, A
Authors	Benjamin D. Wood, Sougato Bose, Gavin W. Morley
Institutions	University College London, University of Warwick
Citations	22
Analysis	Full AI Review Included

Executive Summary

This research proposes a novel experimental scheme utilizing free-falling nanodiamonds to generate and maintain macroscopic spatial quantum superpositions, incorporating advanced spin control techniques.

Core Objective: To place a 250 nm diameter nanodiamond (containing 1.5 billion atoms) into a spatial superposition state with a separation exceeding 250 nm (estimated 276 nm).
Methodology: The diamond is dropped 2.4 m through a magnetic structure. The final 1.13 m contains magnetic teeth generating an alternating inhomogeneous magnetic field.
Spin Coherence Management: Spin dynamical decoupling (a modified XY8 sequence) is implemented via microwave π pulses synchronized with the diamond crossing the magnetic teeth. This is crucial for extending the Nitrogen-Vacancy (NV^-) spin coherence time (T₂) beyond the 190 ms drop duration.
Gravitational Phase Cancellation: The scheme uses a two-oscillation path inversion strategy, ensuring the two superposition components follow time-inverted paths in the second half of the drop. This cancels accumulated relative phase due to static potentials and significantly relaxes the required precision for external tilt stability.
Superposition Mechanism: The NV^- electron spin superposition, coupled with the inhomogeneous magnetic field (Stern-Gerlach effect), creates a superposition of forces, leading to spatial separation. Diamagnetic forces are used to recombine the superposition components.
Macroscopicity Probe: Successfully executing this experiment would probe the limits of quantum mechanics at an unprecedented macroscopic scale, contributing to tests of the quantum nature of gravity.

Technical Specifications

Parameter	Value	Unit	Context
Nanodiamond Diameter	250	nm	Mass (m) is 2.9 x 10^-17 kg.
Estimated Atom Count	1.5	Billion	Equivalent to the 250 nm diameter diamond.
Maximum Spatial Separation (s)	276	nm	Achieved separation distance.
Total Drop Distance	2.4	m	Composed of 1.27 m homogeneous field and 1.13 m inhomogeneous field.
Drop Time (Inhomogeneous Region)	190	ms	Required NV^- T₂ coherence time must exceed this duration.
Magnetic Field Gradient (B’)	940	T/m	Average magnitude used in the Hamiltonian.
Alternating Field Inhomogeneity	±1.45	T/mm	Gradient magnitude generated by magnetic teeth.
Bias Magnetic Field (B₀)	420	mT	Magnetic field at x = 0.
Diamagnetic Oscillation Frequency (ω)	10.56	Hz	Frequency of the superposition distance oscillation.
Number of Magnetic Teeth	~9800	N/A	Number of teeth crossed during the 1.13 m drop, corresponding to required π pulses.
Required Vacuum Pressure	< 10^-13	mbar	Necessary to prevent matter-wave decoherence from gas collisions.
Required Timing Precision	1	ns	For microwave pulse synchronization with tooth crossings.
Magnet Temperature Stability	< 1	mK	Required stability to suppress phase errors from thermal expansion.
Initial Diamond Temperature	5	K	Required for preparation and readout to enable single-shot spin readout fidelity (95%).

Key Methodologies

The proposed experiment follows an 11-step protocol focusing on preparation, quantum control during free fall, and readout:

Diamond Trapping and Characterization: Trap the nanodiamond (magnetic or Paul trap) and measure its mass by fitting the power-spectral density.
NV^- Confirmation: Confirm the presence of a single NV^- center using optical fluorescence spectroscopy and Hanbury Brown-Twiss measurement.
Alignment and Neutralization: Align the NV^- axis to the external magnetic field (x-axis) and electrically neutralize the diamond using a radioactive source or UV light.
Spin Initialization: Optically polarize the NV^- spin to the |0> state, then apply a pulse to transfer it to the |-1> state.
Free Fall Initiation: Drop the diamond. The initial 1.27 m drop occurs in a homogeneous magnetic field to build up speed for the subsequent dynamical decoupling phase.
Superposition Creation: After 1.27 m, apply a microwave π/2 pulse to create the initial spin superposition state: (|0> + |-1>)/√2.
Dynamical Decoupling (DD): The diamond falls through the 1.13 m magnetic tooth structure. Microwave π pulses (modified XY8 sequence) are applied, synchronized with the diamond crossing the alternating field gradient. This flips the spin states, driving spatial separation and refocusing spin decoherence.
Path Inversion and Recombination: The superposition components are allowed to recombine due to diamagnetic forces. An extra π pulse is applied at the first recombination point (95 ms into the inhomogeneous drop) for motional dynamical decoupling, inverting the paths for the second half of the drop.
Interferometry End: Apply a final π/2 pulse at the second recombination (190 ms total drop time in the inhomogeneous region) to end the interferometric sequence.
Readout: Catch the nanodiamond on a glass slide held at 5 K. Optically readout the final NV^- spin state using a confocal microscope setup.
Data Filtering: Measure the T₂ coherence time of the NV^- in each diamond used; only data from diamonds with T₂ times long enough for the 190 ms drop are included in the analysis.

Commercial Applications

The technology and techniques developed for this macroscopic superposition experiment are highly relevant to several emerging high-tech sectors:

Quantum Sensing and Metrology: The use of highly coherent NV^- centers in nanodiamonds is foundational for developing ultra-sensitive quantum sensors, including:
- High-resolution magnetometers.
- Inertial sensors (accelerometers and gyroscopes) capable of detecting minute gravitational changes or motion.
- Thermometry at the nanoscale (using NV^- spin properties).
Quantum Computing and Information: Nanodiamonds containing single NV^- centers serve as robust, solid-state qubits. The dynamical decoupling techniques (like modified XY8) are essential for maintaining coherence in quantum registers.
Advanced Materials Engineering: The requirement for isotopically pure ¹²C nanodiamonds with long T₂ times drives innovation in diamond synthesis, etching, and milling techniques for quantum applications.
High-Precision Control Systems: The need for nanosecond timing precision and sub-mK temperature stability in the magnetic structure necessitates the development of extremely stable and actively controlled experimental infrastructure (e.g., active optical table tilt stabilization).
Fundamental Physics Instrumentation: The experimental setup provides a platform for high-fidelity tests of quantum gravity models and wave-function collapse theories, requiring specialized, ultra-stable vacuum and magnetic field generation equipment.

View Original Abstract

Levitated nanodiamonds containing negatively charged nitrogen-vacancy centers\n(${\text{NV}}^{-}$) have been proposed as a platform to generate macroscopic\nspatial superpositions. Requirements for this include having a long\n${\text{NV}}^{-}$ spin coherence time, which necessitates formulating a\ndynamical decoupling strategy in which the regular spin flips do not cancel the\ngrowth of the superposition through the Stern-Gerlach effect in an\ninhomogeneous magnetic field. Here, we propose a scheme to place a\n$250$-nm-diameter diamond in a superposition with spatial separation of over\n$250$ nm, while incorporating dynamical decoupling. We achieve this by letting\na diamond fall for $2.4$ m through a magnetic structure, including $1.13$ m in\nan inhomogeneous region generated by magnetic teeth.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.105.012824