High-cooperativity quantum transduction predicted between solid-state spin centers and magnon modes

Spin center defects in insulating materials, such as nitrogen-vacancy (NV) centers in diamond, have emerged as potential stationary qubits within a solid-state platform for quantum sensing, communication and information processing. Efficiently creating entanglement between NV centers, or between NV centers and traveling excitations (flying qubits) remains a key goal for this system. The underlying challenge is the intrinsically weak coupling between NV centers separated by more than a few nanometers, due to the rapid falloff of exchange or magnetic dipolar couplings. If the NV centers are to be optically read out independently and simultaneously then at those micron-scale separations the coupling between these centers is negligible.

In our recent paper, Candido et al 2021 Mater. Quantum. Technol. 1 01100, we predict a realistic scheme for “quantum transduction” between an NV center and a quantized excitation of a magnetic disk called a magnon. The magnon is the quantum of excitation of a “spin wave” of a magnetic material; these spin waves describe excitations of the magnetic moments of the material and have similarities to elastic waves in ordinary solids (whose quantum of excitation is the phonon). We describe how the quantum information encoded in the NV center spin can be transduced into the occupation of a single magnon mode. This could be used in sequence to entangle multiple NV centers. The desired mediating magnon mode is a highly localized mode concentrated at the edge of a magnetic disk, magnetized along the disk axis. We evaluated the efficiency of this quantum transduction for a ferrimagnetic disk made of the organic low-damping, low-moment vanadium tetracyanoethylene. The efficiency is measured by the value of the cooperativity, which enumerates the number of times quantum information can be transferred between the NV center and the magnon mode before it is lost to decoherence.

We derived an analytical expression for the spin-magnon cooperativity as a function of NV position under a micron-scale disk, and showed that, surprisingly, the cooperativity will be higher using this magnetic material than in more conventional materials with larger magnetic moments, due to in part to the reduced demagnetization field. For reasonable experimental parameters, we predicted that the spin-magnon-mode coupling strength is g~2π10 kHz. For isotopically pure 12C diamond we predicted strong coupling of an NV spin to the unoccupied magnon mode, with cooperativity Cλ=15 for a wide range of NV spin locations within the diamond, well within the spatial precision of  NV center implantation. Thus our proposal describes a practical pathway for single-spin-state-to-single-magnon-occupancy transduction and for entangling NV centers over micron length scales.

 This work appears as the very first paper in the new “Materials for Quantum Technology” journal, published by the Institute of Physics (which was founded in London in 1874).

Predicted strong coupling of solid-state spins via a single magnon mode Denis R Candido, Gregory D Fuchs, Ezekiel Johnston-Halperin and Michael E Flatté, Materials for Quantum Technology, Volume 1, Number 1, article 011001 (2021).https://iopscience.iop.org/article/10.1088/2633-4356/ab9a55

 

Figure 1

Schematic view of the strong quantum-coherent coupling between NV-center spin and magnon mode. The green disk represents the normally magnetized V[TCNE]x ferrimagnetic material placed on top of a diamond [111] substrate possessing NV centers.

Schematic view of the strong quantum-coherent coupling between NV-center spin and magnon mode. The green disk represents the normally magnetized V[TCNE]xferrimagnetic material placed on top of a diamond [111] substrate possessing NV centers.

Figure 3

Frequencies of NV center levels |±1 (blue and red solid lines), FMR and magnons (black solid lines) as a function of external dc magnetic field B dc parallel to the [111] diamond crystallographic direction and NV center axis. Inset shows a zoom-in of the crossing region between |−1> level with both magnonic m = 1, 2, 3, 4, 5, 6 and FMR frequencies.

Frequencies of NV center levels |±1 (blue and red solid lines), FMR and magnons (black solid lines) as a function of external dc magnetic field B dc parallel to the [111] diamond crystallographic direction and NV center axis. Inset shows a zoom-in of the crossing region between |−1> level with both magnonic m = 1, 2, 3, 4, 5, 6 and FMR frequencies.

Figure 2

(a) In plane fringe fields h(r) at z = −50 nm (orange plane) for the modes (4, 1, 1), (5, 1, 1), (6, 1, 1). (b) In plane fringe fields h(r) for the mode (6, 1, 1) at depth z = −65 nm, z = −80 nm and z = −95 nm (blue, red and yellow planes, respectively). (c) Fringe fields h(r) for cross section view θ = 0 (blue plane) for modes (4, 1, 1), (5, 1, 1), (6, 1, 1). The white lines delimit the disk dimensions R = 500 nm and d = 100 nm.

(a) In plane fringe fields h(r) at z = −50 nm (orange plane) for the modes (4, 1, 1), (5, 1, 1), (6, 1, 1). (b) In plane fringe fields h(r) for the mode (6, 1, 1) at depth z = −65 nm, z = −80 nm and z = −95 nm (blue, red and yellow planes, respectively). (c) Fringe fields h(r) for cross section view θ = 0 (blue plane) for modes (4, 1, 1), (5, 1, 1), (6, 1, 1). The white lines delimit the disk dimensions R = 500 nm and d = 100 nm.

Figure 4

Spatial plot of the cooperativity of the λ = (6, 1, 1) magnon mode (a) at 30 nm below the disk (z = −80 nm), (b) within cross-section plane, (c) along the teal line within (a), (d) along the teal line within (b). The dashed white border shows the strong-coupling regime stability region where Cλ ≥ 1, where the white rectangle indicates a tolerance for spatial implantation imprecision for the NV centers while still achieving high cooperativity. The green lines delimit the disk dimension d = 100 nm and R = 500

Spatial plot of the cooperativity of the λ = (6, 1, 1) magnon mode (a) at 30 nm below the disk (z = −80 nm), (b) within cross-section plane, (c) along the teal line within (a), (d) along the teal line within (b). The dashed white border shows the strong-coupling regime stability region where Cλ ≥ 1, where the white rectangle indicates a tolerance for spatial implantation imprecision for the NV centers while still achieving high cooperativity. The green lines delimit the disk dimension d = 100 nm and R = 500 nm.

The material is based on work supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Award Number DE-SC0019250.
Flatté Research Group member Dr. Denis Candido contributed to this work.