⚛️ quantum physics

Photon correlation Fourier spectroscopy of a B center in hBN

This study utilizes photon correlation Fourier spectroscopy to characterize the coherence and spectral diffusion of a blue-emitting B center in hexagonal boron nitride under non-resonant continuous wave excitation, revealing that while the emission approaches the Fourier limit at low power and short timescales, it broadens significantly to over a gigahertz at longer times due to spectral diffusion occurring on a 10–100 microsecond timescale.

Original authors: Aymeric Delteil, Stéphanie Buil, Jean-Pierre Hermier

Published 2026-03-27

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CC BY 4.0

Original authors: Aymeric Delteil, Stéphanie Buil, Jean-Pierre Hermier

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 have a tiny, magical light bulb embedded in a piece of blue crystal (hexagonal boron nitride). This light bulb is special because it emits single photons—particles of light one by one. Scientists love these because they are the "pixels" of the future quantum internet and ultra-sensitive sensors.

However, for these pixels to work perfectly, the light they emit needs to be pure and steady, like a laser beam. If the light flickers, changes color slightly, or loses its "rhythm," the quantum information gets scrambled.

This paper is like a high-tech detective story where the authors investigate why this specific "blue light bulb" (called a B center) isn't perfectly steady, and they use a clever new trick to catch the culprit in the act.

The Problem: The Fickle Light Bulb

Think of the light emitted by this bulb as a musical note.

The Ideal: A perfect note that holds its pitch forever.
The Reality: The note wavers. Sometimes it wavers so fast it's just a blur (pure dephasing). Sometimes, the whole note slowly drifts up and down the scale over time (spectral diffusion).

In the past, scientists tried to study this bulb by shining a very specific, matching laser on it (resonant excitation). It worked well, but it was like trying to listen to a whisper while standing next to a jet engine; the laser light was so bright it drowned out the bulb's natural voice, making it hard to see the bulb's true behavior.

The authors wanted to study the bulb under non-resonant excitation (just shining a regular blue flashlight on it). This is easier and more practical for real-world devices, but it usually makes the light bulb "squeakier" and less stable due to heat and electrical noise.

The Detective Tool: Photon Correlation Fourier Spectroscopy (PCFS)

Standard cameras or spectrometers are like taking a long-exposure photo of a spinning fan. You just see a blurry white circle. You can't tell how fast the blades are spinning or if they are wobbling.

The authors used a technique called Photon Correlation Fourier Spectroscopy (PCFS).

The Analogy: Imagine you are trying to figure out how fast a dancer is spinning, but you can only see them for a split second at a time.
The Trick: Instead of taking one long photo, you take millions of tiny snapshots of pairs of photons (light particles) arriving at your detector. You ask: "Did these two photons arrive at the same time? Did they interfere with each other?"
By looking at how these pairs behave over different time delays (from microseconds to seconds), the authors could reconstruct a "movie" of the light's stability. They could see the blur unfolding in real-time.

What They Discovered

Using this "super-microscope," they found two main things messing up the light bulb's rhythm:

The Heat Effect (Homogeneous Broadening):
- What it is: When they turned up the power of the flashlight (laser), the bulb got hotter.
- The Result: The light note got slightly "fuzzier" instantly. It's like a guitar string vibrating faster and less purely because the room got hot.
- The Good News: At low power, this fuzziness was very small. The light was almost as perfect as physics allows (close to the "Fourier limit").
The Drifting Environment (Spectral Diffusion):
- What it is: This is the big culprit. Imagine the light bulb is sitting in a room where the walls are made of jelly. Every few microseconds, the jelly shifts slightly, pushing the bulb and changing the pitch of its note.
- The Timescale: This happens on a timescale of 10 to 100 microseconds. That's incredibly fast for us, but slow enough for the bulb to "drift" before it settles.
- The Result: If you wait too long (milliseconds), the light note has wandered so far across the musical scale that it looks like a giant, messy smear (over 1 Gigahertz wide). But if you look at it very quickly (microseconds), the note is surprisingly stable.

The Big Picture

The authors realized that while the light bulb looks messy if you stare at it for a long time, it is actually very coherent if you look at it quickly.

Short time (microseconds): The light is nearly perfect.
Long time (milliseconds): The light is a mess because of the drifting environment.

Why This Matters

This is a huge win for quantum technology.

Practicality: You don't need the difficult, high-tech "resonant" setup to get good results. You can use a simple flashlight (non-resonant laser) and still get high-quality light, as long as you use the light quickly.
The Fix: The paper suggests that if we put this light bulb inside a tiny mirror box (a cavity), we can force it to emit its photons so fast that it doesn't have time to drift. This would make the light perfectly stable for quantum computers and sensors.

In summary: The authors built a special camera that can see the "heartbeat" of a quantum light source. They found that while the light wobbles over time due to its environment, it is actually very steady in the short term. This means we can use these easy-to-make light sources for future quantum tech, provided we catch the light before it has a chance to wander off.

1. Problem Statement

Solid-state single-photon emitters (SPEs) are critical for photonic quantum technologies, but their utility is often limited by decoherence mechanisms: pure dephasing (intrinsic, fast loss of coherence) and spectral diffusion (SD) (slow, environmental fluctuations causing frequency jumps).

Context: Hexagonal boron nitride (hBN) hosts "B centers" (blue-emitting color centers) which are bright and stable. While their coherence has been studied under resonant excitation (where high indistinguishability is restored at short timescales), their properties under non-resonant excitation (photoluminescence, PL) remain poorly characterized.
The Gap: Standard dispersive spectroscopy lacks the time resolution to distinguish between fast dephasing and rapid spectral diffusion. Conversely, standard Fourier-transform spectroscopy (FTS) requires long averaging times, masking fast dynamics.
Objective: To characterize the homogeneous and inhomogeneous broadening of a B center in hBN under continuous-wave (CW) non-resonant excitation, specifically quantifying the timescales and magnitudes of spectral diffusion and laser-induced dephasing.

2. Methodology

The authors employed Photon Correlation Fourier Spectroscopy (PCFS), a technique that combines interferometry with photon counting to access spectral dynamics on timescales shorter than the inverse photon count rate.

Experimental Setup:
- Sample: A single B center in hBN, excited by a 405 nm CW laser diode at 4 K.
- Interferometer: A Mach-Zehnder interferometer with a variable optical delay ( $\delta$ ) ranging from 0 to 1.3 ns.
- Detection: Avalanche photodiodes (APDs) at the output ports measure the second-order correlation function $g^{(2)}(\delta, \tau)$ , where $\tau$ is the time delay between photon detection events.
- Polarization Control: Measurements were taken in both parallel and orthogonal polarization configurations to isolate interference effects from intensity fluctuations (blinking).
Technique:
- PCFS Contrast: The contrast $C(\delta, \tau)$ is derived from the normalized antibunching in the cross-correlation signal. This contrast represents the squared modulus of the Fourier transform of an effective, time-dependent spectrum $S_{eff}(\omega, \tau)$ .
- Analysis: By varying $\tau$ (from microseconds to seconds), the authors could observe the evolution of the emission linewidth from the homogeneous limit (short $\tau$ ) to the inhomogeneous limit (long $\tau$ ).
- Models: The data was fitted using two models:
  1. Continuous Gaussian Diffusion (Ornstein-Uhlenbeck): Assumes continuous frequency wandering.
  2. Discrete Poissonian Jumps: Assumes random discrete jumps within a Gaussian envelope.

3. Key Contributions

Application of PCFS to hBN: This is one of the first comprehensive characterizations of B center coherence in the non-resonant regime using PCFS, bridging the gap between resonant and non-resonant studies.
Decoupling Mechanisms: The study successfully separates the power-dependent homogeneous broadening (pure dephasing) from the time-dependent inhomogeneous broadening (spectral diffusion).
Quantification of Timescales: The authors precisely determined the timescale of spectral diffusion ( $\sim 10-100$ $\mu$ s) and the magnitude of the linewidth broadening.

4. Key Results

Homogeneous Linewidth ( $\Delta\omega_{hom}$ ):
- The homogeneous linewidth is dominated by pure dephasing and is strongly dependent on laser power.
- At low power ( $\le 1$ mW), the coherence time $T_2$ is $\sim 2$ ns, corresponding to a linewidth only $\sim 2$ times the Fourier limit (lifetime-limited).
- As power increases to 4 mW, $T_2$ drops to 0.45 ns due to local heating and increased phonon interactions.
Spectral Diffusion (Inhomogeneous Broadening):
- Timescale: SD occurs on a timescale of 10 to 100 $\mu$ s.
- Magnitude: At short times ( $\tau < 10$ $\mu$ s), the total linewidth is close to the homogeneous limit. However, as $\tau$ increases, the linewidth broadens significantly, reaching > 1 GHz at long timescales.
- Power Dependence: The amplitude of the spectral diffusion is only weakly dependent on laser power, suggesting it is driven by the local charge environment rather than the excitation laser directly.
Model Fitting:
- Both the continuous Gaussian (Ornstein-Uhlenbeck) and discrete jump models provided consistent results regarding the extracted linewidths and timescales.
- The data shows a rapid increase in linewidth around $\tau \sim 10$ $\mu$ s, followed by a slower increase at millisecond scales, suggesting multiple diffusion mechanisms or a complex SD kernel.
Indistinguishability:
- At low power and short time delays, the emission is highly coherent (factor of $\sim 2$ above the Fourier limit), enabling high photon indistinguishability via post-selection or Purcell enhancement.

5. Significance and Implications

Validation of hBN for Quantum Tech: The results confirm that B centers in hBN are excellent candidates for quantum applications even under non-resonant excitation, provided the system is operated at low power and short time windows.
Application Potential:
- Quantum Sensing: The high coherence at short timescales makes these emitters suitable for single-photon interferometry-based sensing.
- Quantum Networking: The study suggests that inserting these emitters into a cavity (Purcell factor $\sim 20$ ) could restore high indistinguishability (90% Hong-Ou-Mandel visibility) even for photons separated by macroscopic time delays, overcoming the limitations of spectral diffusion.
Methodological Advancement: The paper demonstrates that PCFS is a robust, non-invasive tool for characterizing decoherence in solid-state emitters without requiring the complex stabilization needed for resonant fluorescence experiments. It provides a pathway to identify and mitigate specific decoherence channels (e.g., via electrical contacts to stabilize the charge environment).

In conclusion, this work provides a rigorous quantitative framework for understanding the decoherence dynamics of hBN quantum emitters, establishing that while spectral diffusion broadens the line to the GHz scale over time, the intrinsic coherence remains high enough for advanced quantum photonic applications when properly managed.