Introduction

Human brains are now interpretable, at a rudimentary level. For example, fMRI scans can be reconstructed into images^[1] or text^[2], and EEGs can be used to play pong^[3]. However, these sensors do not have the resolution for fine-grained interpretation. Quantum magnetometers, such as ${NV}^{-}$ centers, seem like a viable alternative.

First, an overview of current sensors. The main advantages an EEG (electroencephalogram) has is it's cheap and fast. You can buy one for a few hundred dollars, and sample data every few milliseconds. However, the data is pretty bad. Connective tissue (such as the skull) surrounds the brain and distorts the electric field, so the spatial resolution is in the centimeter range.

Magnetic fields are not distorted as much, so an fMRI (functional magnetic resonance imager) has better resolution. However, they only track blood flow to the brain after the neurons fire, which means you can only get a useful image as fast as this response time—once every few seconds. They also weigh several tons and cost several hundred thousand dollars, which makes it expensive to generate a large dataset.

Another group of sensors, MEGs (magnetoencephalograms) solve the resolution problem with quantum sensors, getting to the millimeter and millisecond range. Currently SQUIDs (superconducting quantum interference devices) are most popular, as they can detect magnetic perturbations to $\sim {10}^{-14}T/\sqrt{Hz}$. In comparison, a neuron spikes^[4] at $\sim {10}^{-13}T$. However, unless we get better superconductors, they have to be cooled to around $80K$, so they end up costing several million dollars and again, weigh tons.

There has been some experimentation with SERFs^[5] (spin exchange relaxation free magnetometers) which work at room temperature, but they can't work in external magnetic fields—including the Earth's intrinsic one—so they require a room with magnetic shielding.

(Precision Magnetometers for Aerospace Applications: A Review, Fig 8)

On the figure's left are ${NV}^{-}$ sensors^[6], short for nitrogen-vacancy centers in diamond. They operate at room temperature, do not need magnetic shielding, and can potentially get to around $2.5\cdot {10}^{-13}T/\sqrt{Hz}$^[7] sensitivity, though current results are closer to ${10}^{-10}T/\sqrt{Hz}$.

Thus, a single ${NV}^{-}$ sensor could pick up on several hundred neurons firing in sync, and an array could do even better. I think we should build MEGs with ${NV}^{-}$ sensors, and apply them to brain interpretability.

${NV}^{-}$ Sensors

(Introduction to NV centers, adapted from quTools)

To summarize how they operate^[8]:

1. There are two electrons sitting in the vacancy (white) whose magnetic spins form a triplet (${}^{3}A$): $$\uparrow \uparrow ,\downarrow \downarrow ,\frac{\uparrow \downarrow +\downarrow \uparrow }{\sqrt{2}}$$
2. They occupy different orbitals so it doesn't break the Pauli exclusion principle. However, when their spins are parallel, they are "closer", giving them a higher energy. The energy difference is about $2.87GHz$.
3. To force them into the antiparallel state, you can excite the electrons (${}^{3}E$) with a $532nm$ laser and wait for them to decay. At room temperature the Boltzmann distribution gives $$1-e^{-\frac{h\times 2.87GHz}{k_b\times 298.15K}}\approx 99.95\%$$should end up in the $m_s=0$ state. Along the way, one electron may decay faster than the other, which is where the ${}^{1}A$ singlet state comes in. However, it's not really important for our purposes.
4. If you frequency sweep with a VNA, you'll find a dip around $2.87GHz$, as this frequency gets absorbed to promote $$\frac{\uparrow \downarrow +\downarrow \uparrow }{\sqrt{2}}⟶\uparrow \uparrow ,\downarrow \downarrow .$$
5. In the presence of a magnetic field (say, pointing in the $\uparrow$ direction), $\uparrow \uparrow$ will have a slightly lower energy than $\downarrow \downarrow$. This is the Zeeman effect, and will give you two dips in your frequency sweep.
6. The location of the dips can be used to calculate the magnetic field.

(Control of NV Centers, image by Ashish Kalakuntla)

There's a couple more tricks:

• Most diamonds have more than one ${NV}^{-}$ center (an ensemble), which can be aligned in four different orientations. There is also nuclear spin coupling^[9]. Altogether you may end up with many more dips, which can be used to recover the entire magnetic field:

(magnetic field strength is in gauss).

• To get a stronger signal, you can put the diamond in a cavity that resonates around $2.87GHz$^[10].
• You can replace the $532nm$ laser with an LED if it's bright enough (or close enough) to the diamond.

Production

A lab from Münster University built a $0.5{cm}^3$ ${NV}^{-}$ magnetometer, with sensitivity $2.8\cdot {10}^{-8}T/\sqrt{Hz}$^[11] by assembling (relatively) cheap parts.

Cost (per 1,000 sensors):

1. Diamonds with ${NV}^{-}$ centers—$150^[12],
2. Optical adhesive—$30,
3. LED—$400^[13],
4. Photodiode—$500^[14],
5. $622nm$ longpass filter—$500^[15],
6. PCB boards—$10,000? Unsure, I don't have a reference frame.

For readout you also need a waveform generator and power supply, which are around $20,000 for laboratory usage. Since you really only need microwaves around $2.87GHz$, I'm sure you can manufacture this for cheaper.

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1. https://www.nature.com/articles/s41598-023-42891-8 ↩︎

2. https://www.nature.com/articles/s41593-023-01304-9 ↩︎

3. https://monolithbci.com/ ↩︎

4. https://physics.stackexchange.com/a/11513/239251 ↩︎

5. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6063354/ ↩︎

6. https://en.wikipedia.org/wiki/Optically_detected_magnetic_resonance ↩︎

7. https://arxiv.org/pdf/1401.2438.pdf ↩︎

8. https://barosandu.github.io/quNV-Jupyter/T3E3-TEXT-Quantum-Sensing-with-Solid-State-Spins.html ↩︎

9. https://journals.aps.org/prb/pdf/10.1103/PhysRevB.103.L140102 ↩︎

10. https://www.nature.com/articles/s41467-021-21256-7 ↩︎

11. https://www.mdpi.com/1424-8220/24/3/743 ↩︎

12. https://www.adamasnano.com/fluorescent-agents/ ↩︎

13. https://www.mouser.com/ProductDetail/Wurth-Elektronik/150224GS73100?qs=5aG0NVq1C4wrwgedkfhj2Q%3D%3D ↩︎

14. https://www.lcsc.com/product-detail/Infrared-Receivers_Vishay-Intertech-VEMD1060X01_C144925.html ↩︎

15. https://www.meetoptics.com/filters/ ↩︎