🔬 mesoscale physics

Real-time Amplitude and Phase Estimation of AC Fields with Diamond Spins

This paper demonstrates a real-time protocol for retrieving the amplitude and phase of AC magnetic fields using nitrogen-vacancy centers in diamond from single-shot measurements, achieving high sensitivity and temporal resolution while addressing challenges like frequency detuning and strong field regimes.

Original authors: Christopher T. -K. Lew, Samuel A. Wilkinson, Nicholas Gillespie, Brant C. Gibson, David A. Broadway, Jean-Philippe Tetienne

Published 2026-03-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Christopher T. -K. Lew, Samuel A. Wilkinson, Nicholas Gillespie, Brant C. Gibson, David A. Broadway, Jean-Philippe Tetienne

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to listen to a specific radio station in a noisy city. Usually, to hear the music clearly, you have to tune your radio, sit there for a long time, and average out all the static and background noise. You get a good idea of the song, but you can't hear it instantly as it changes.

This paper is about a new way to listen to "radio waves" (specifically, magnetic fields) that allows you to hear the song instantly, capturing both the volume (amplitude) and the timing (phase) of the signal in a single, split-second snapshot.

Here is the breakdown of how they did it, using simple analogies:

1. The Microphone: The Diamond "Spin"

Instead of a metal antenna, the scientists used a tiny defect inside a diamond called a Nitrogen-Vacancy (NV) center.

The Analogy: Think of the electron inside this diamond defect as a tiny, super-sensitive spinning top.
Normally, this top spins in a specific way. But if you shine a laser on it and zap it with microwave pulses, you can make it spin in a "superposition" (a mix of states), making it incredibly sensitive to outside magnetic fields.
When an AC (alternating current) magnetic field passes by, it pushes and pulls on this spinning top, changing how it spins.

2. The Problem: The "Blurry" Snapshot

In the past, scientists used these diamond tops to measure magnetic fields, but they had to take many measurements over a long time and average them together.

The Analogy: Imagine trying to take a photo of a hummingbird's wings. If you use a slow shutter speed and take 1,000 photos, then average them, you get a clear picture of the average position of the wings, but you miss the exact moment the wing was up or down. You lose the "real-time" motion.
Previous methods were great for steady signals but terrible for signals that change quickly or need to be measured in a single instant ("single-shot").

3. The Solution: The "Two-Step Dance"

The team at RMIT University developed a trick to get a perfect, real-time snapshot using just two quick measurements.

The Analogy: Imagine you are trying to figure out the speed and direction of a runner on a track.
- Measurement 1: You take a photo of the runner at a specific moment. You know where they are, but you don't know if they are speeding up or slowing down.
- Measurement 2: You wait a very specific amount of time (exactly one-quarter of the runner's stride cycle) and take a second photo.
- The Magic: By comparing these two photos, you can mathematically reconstruct exactly where the runner was, how fast they were going, and which way they were turning, all without waiting for them to finish the race.

In the paper, they used a microwave pulse sequence (called CPDD) to make the diamond spin "dance" in sync with the magnetic field. They took two measurements separated by a precise time delay. This allowed them to capture the In-Phase (I) and Quadrature (Q) components of the signal.

Think of I and Q as the "X and Y coordinates" on a map. If you know both coordinates, you know exactly where the signal is pointing and how strong it is.

4. The Results: Seeing the Invisible

They tested this with a 4 MHz signal (a very fast vibration).

Speed: They could update their measurement every 320 microseconds (that's 0.00032 seconds!).
Sensitivity: They could detect a magnetic field as weak as 78 nanotesla (about a million times weaker than a fridge magnet) and measure the phase (timing) with incredible precision.
Real-Time Tracking: They even showed that if the radio station suddenly changed its frequency, their "diamond microphone" could instantly retune itself and keep tracking the signal without losing the beat.

5. Why Does This Matter?

Why do we care about measuring magnetic fields instantly?

Medical Imaging: It could help create faster, sharper MRI scans.
Wireless Communication: It could act as a super-sensitive radio receiver that doesn't need big antennas.
Material Science: It can detect tiny electrical currents flowing inside materials (like eddy currents) in real-time, helping engineers find cracks or defects in metal structures instantly.
Fundamental Physics: It helps scientists study how materials behave when they are being "wiggled" by magnetic fields.

Summary

The authors took a quantum sensor (a diamond with a tiny defect) and taught it a new dance routine. Instead of waiting hours to get a clear picture of a magnetic field, they can now take a "snapshot" in a fraction of a second, telling them exactly how strong the field is and exactly what phase it is in. It's like upgrading from a slow, blurry security camera to a high-speed, 4K camera that never misses a beat.

1. Problem Statement

While Nitrogen-Vacancy (NV) centers in diamond are established as highly sensitive quantum sensors for AC magnetic fields, existing protocols primarily rely on time-averaged or time-correlated measurements (e.g., Quantum Heterodyne (Qdyne) or Coherently Averaged Synchronized Readout (CASR)). These methods require averaging thousands of measurements over seconds to achieve accurate phase and amplitude estimation. Consequently, they lack single-shot capability and cannot perform real-time tracking of rapidly changing signals on the microsecond ( $\mu$ s) to millisecond (ms) timescale. This limitation hinders applications requiring dynamic monitoring, such as eddy current imaging or studying fast material properties.

2. Methodology

The authors propose and demonstrate a real-time, phase-sensitive AC sensing protocol using an ensemble of NV centers. The core innovation lies in retrieving amplitude and phase from a single pair of consecutive measurements rather than long-term averaging.

Sensing Scheme:
- The protocol utilizes a generalized spin qubit (TLS) driven by a microwave (MW) field and an AC probe field.
- Sequential Measurements: Two measurements are performed with a specific time delay, $\Delta t = (n + \frac{1}{4})T_{AC}$ , where $T_{AC}$ is the period of the AC field. This delay ensures the second measurement captures the signal in quadrature (90° phase shift) relative to the first.
- I/Q Extraction: The first measurement yields the in-phase component ( $I$ ), and the second yields the quadrature component ( $Q$ ).
- Real-time Retrieval: Amplitude ( $R$ ) and Phase ( $\phi$ ) are calculated instantaneously using standard trigonometric relations:
  $R(t) = \sqrt{I(t)^2 + Q(t)^2}, \quad \phi(t) = \text{atan}(Q(t)/I(t))$
Control Sequence:
- The experiment employs Continuous Phased Dynamical Decoupling (CPDD) based on the XY8 sequence. This sequence suppresses environmental noise and amplitude errors while maintaining robustness against spatial inhomogeneities in the MW driving field.
- The qubit is initialized optically, evolved, and read out via a $(\pi/2)_y$ pulse orthogonal to the initial $(\pi/2)_x$ pulse to operate in a phase-sensitive slope detection mode.
Experimental Setup:
- A 100 $\mu$ m thick NV-doped diamond sample is placed on a coplanar waveguide (CPW) for MW control.
- An 8-turn planar coil generates the AC test field (4 MHz).
- Photoluminescence (PL) is collected to read out the spin state.

3. Key Contributions

Single-Shot Protocol: Demonstrated the first protocol to retrieve both amplitude and phase of an AC field from a single pair of measurements, eliminating the need for long integration times.
Real-Time Tracking: Showed the ability to dynamically change the probe frequency in real-time to track time-varying AC signals.
Error Characterization: Systematically mapped and quantified errors arising from:
- Frequency Detuning: Analyzed how deviations between the probe frequency and the AC signal affect the IQ diagram (causing ellipticity and phase rotation).
- Strong Field Regime: Investigated non-linear effects and phase wrapping at high field amplitudes ( $>5 \mu$ T).
Dynamic Adaptation: Proved the system can adjust the CPDD parameters and time delays on the fly to maintain resonance with a changing signal frequency.

4. Results

Performance Metrics:
- Temporal Resolution: 320 $\mu$ s per shot.
- Sensitivity: Achieved a per-shot amplitude sensitivity of 78 nT and phase sensitivity of 63 mrad.
- Normalized Sensitivity: Approximately $1.7 \text{ nT}/\sqrt{\text{Hz}}$ and $1.2 \text{ mrad}/\sqrt{\text{Hz}}$ .
Dynamic Signal Tracking:
- Successfully tracked a test signal where amplitude, phase, and frequency were varied every 320 ms (for amplitude/phase) and 1.28 s (for frequency).
- When the probe frequency was dynamically adjusted to match the test signal, the measured amplitude and phase remained in excellent agreement with the set values.
Error Analysis:
- Frequency Detuning: Observed that detuning causes the IQ circle to compress into an ellipse and introduces a phase rotation. The ellipticity and rotation angle were quantitatively matched to an idealized theoretical model.
- Strong Fields: At high amplitudes, the IQ diagram distorted due to phase wrapping (population limits between 0 and 1), consistent with theoretical predictions.
Allan Deviation: Showed $\tau^{-1/2}$ behavior (white noise) up to ~100 ms, with minimum deviations of 4.2 nT and 1.9 mrad at longer integration times ( $\tau \approx 160-390$ ms).

5. Significance

This work represents a paradigm shift in quantum sensing, moving from static, averaged measurements to dynamic, real-time sensing.

Applications: The ability to resolve AC fields on the $\mu$ $μ$ s timescale opens new avenues for:
- Eddy Current Imaging: Probing conductive material properties in real-time.
- Dynamic Material Science: Studying fast magnetic AC susceptibility changes.
- Wireless Communication: Potential for real-time signal demodulation and localization.
Scalability: The protocol is compatible with ensemble sensing, making it robust for practical applications where single-spin sensitivity is not required but spatial resolution and speed are critical.
Future Outlook: The authors note that temporal resolution could be further improved (by a factor of 4) by optimizing laser pulse durations and photon collection efficiency, suggesting a path toward even faster quantum sensing.

In conclusion, this paper establishes a foundational framework for real-time quantum magnetometry, demonstrating that NV centers can function as high-speed, phase-sensitive receivers for AC fields without the latency of traditional averaging techniques.