🔬 optics

Anderson Localization with Single Photons from a Quantum Emitter

This paper experimentally demonstrates Anderson localization of single photons emitted by room-temperature quantum emitters in hexagonal boron nitride within disordered waveguide arrays, supported by a theoretical framework showing that configuration-averaged output intensity converges to a stationary distribution with a localization length scaling inversely with disorder strength.

Original authors: Simon J. U. White, Diego N. Bernal-García, Toan Trong Tran, Igor Aharonovich, Alexander S. Solntsev

Published 2026-05-06

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Simon J. U. White, Diego N. Bernal-García, Toan Trong Tran, Igor Aharonovich, Alexander S. Solntsev

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

The Big Idea: Getting Lost on Purpose

Imagine you are walking through a perfectly straight, empty hallway. If you start walking, you will naturally drift down the center, and your path will spread out evenly to the left and right. This is how light usually behaves in a perfect, orderly system.

Now, imagine that same hallway is filled with random, uneven obstacles—chairs, tables, and people standing in random spots. If you try to walk through this messy hallway, you won't get far. You'll bump into things, bounce back, and eventually get stuck right where you started. In physics, this phenomenon is called Anderson Localization. It's a way for waves (like light or sound) to get "trapped" in a messy environment instead of traveling through it.

The New Discovery: Trapping Single "Bullets" of Light

For a long time, scientists could only see this trapping effect using bright beams of light (like a flashlight) or pairs of light particles. But this new paper shows something new: You can trap single, individual particles of light (photons) using a messy system, even at room temperature.

The researchers used a special type of light source made from a tiny defect in a material called hexagonal boron nitride (think of it as a microscopic "glow-in-the-dark" speck in a hard crystal). This source emits one single photon at a time.

The Challenge:
Usually, scientists thought that for light to get trapped in this way, it needed to be very "coherent"—meaning the light waves had to be perfectly synchronized, like a marching band stepping in perfect unison. The light from their crystal source, however, is a bit "messy" in time (it's like a marching band where everyone is slightly out of step). The big question was: Can this "messy" single photon still get trapped?

The Answer:
Yes! The team proved that even though the light source is a bit "jittery" in time, the single photons still get stuck in the messy hallway. They don't spread out; they stay localized near where they entered.

How They Did It: The "Waveguide Highway"

To test this, they built a tiny chip with 101 parallel glass roads (called waveguides) running side-by-side.

The Ordered Road: In one set of roads, the gaps between them were perfectly equal. When they sent a photon in, it spread out nicely, like a ripple in a pond.
The Messy Road: In the second set, they randomly changed the distance between the roads. Some gaps were wide, some were narrow. This created the "disorder."

When they shot a single photon into the middle of the messy road, it didn't travel far. Instead, it stayed bunched up near the starting point, fading away exponentially as you moved further down the line.

The "Average" Trick

Here is a clever part of their experiment. Because the disorder was random, if you looked at just one specific messy road, the light might get stuck in a weird, jagged pattern. But the researchers didn't just look at one road; they looked at 30 different versions of the messy road (by shifting where they injected the light).

When they averaged the results of all 30 attempts, a clear pattern emerged: a smooth, exponential curve showing the light was trapped. This proved that the "messiness" of the road was the real cause of the trapping, not just a random fluke.

The "Recipe" for Trapping

The paper also provides a mathematical "recipe" (a theory) to predict exactly how well the light will be trapped based on how messy the roads are.

The Rule: The more random the gaps between the roads are (the higher the "variance" or disorder), the shorter the distance the light travels before getting stuck.
The Analogy: Think of it like a game of pinball. If the bumpers (obstacles) are placed in a very predictable pattern, the ball bounces far. If the bumpers are placed in a completely chaotic, random pattern, the ball gets stuck near the top. The researchers found a simple math rule that tells you exactly how "sticky" the trap will be based on how chaotic the bumpers are.

Why This Matters (According to the Paper)

The paper concludes that this works even with "imperfect" light sources that operate at room temperature. This is a big deal because:

It's Practical: You don't need expensive, super-cold equipment to see this effect.
It's Robust: The "jittery" nature of the light source didn't stop the trapping.
Future Uses: The authors suggest this makes these tiny crystal light sources very useful for building new types of computer chips that use light instead of electricity. Specifically, they mention these systems could be used for neuromorphic computing (mimicking how the brain works) and quantum photonic architectures (advanced quantum computers), because these fields actually need controlled disorder to function.

In short: The team proved that you can trap individual particles of light in a messy, room-temperature system, and they provided a simple rule to predict exactly how that trapping works. This opens the door for using these simple, robust light sources in advanced optical technologies.

Technical Summary: Anderson Localization with Single Photons from a Quantum Emitter

Problem Statement
Anderson localization, the suppression of wave transport due to multiple-scattering interference in disordered systems, is a fundamental phenomenon observed across optics, acoustics, and matter waves. While previously demonstrated in photonic systems using classical light or probabilistic photon pairs (e.g., from spontaneous parametric down-conversion), a robust experimental demonstration using deterministic single-photon sources (SPEs) has remained elusive. A primary concern is whether the limited temporal coherence of solid-state SPEs—often on the order of picoseconds at room temperature—prevents the formation of Anderson localization in coupled-mode systems, where temporal and spatial effects are linked. Furthermore, while the stationary intensity profiles of disordered lattices are well-known, a general theoretical framework connecting the configuration-averaged output intensity to the statistical properties of the disorder (specifically for off-diagonal disorder) has been needed to quantitatively interpret experimental data from single-photon sources.

Methodology
The authors employed a combined experimental, numerical, and theoretical approach:

Experimental Setup:
- Source: A single-photon emitter (SPE) based on a defect in hexagonal boron nitride (hBN), operated at room temperature. The emitter was characterized via Hanbury Brown and Twiss interferometry, confirming single-photon emission with a second-order correlation $g^{(2)}(0) = 0.29$ and an excited-state lifetime of $\tau_1 \approx 2.7$ ns.
- Photonic Platform: Integrated waveguide arrays were fabricated in fused silica using femtosecond direct laser writing. Two arrays were created: a periodic array (ordered) and a disordered array. In the disordered array, off-diagonal disorder was introduced by randomly varying the inter-waveguide spacing, resulting in coupling coefficients $\kappa_n$ drawn from a uniform distribution $U(\kappa_0 - \Delta, \kappa_0 + \Delta)$ with a disorder strength $\Delta/\kappa_0 = 0.8$ .
- Measurement: Single photons were coupled into either the central (bulk) or edge waveguide of the arrays. The output intensity profiles at the end-facet were imaged using an electron-multiplying charge-coupled device (EMCCD). To observe the stationary profile, the experiment averaged over 30 (bulk) and 4 (edge) different disorder realizations by shifting the excitation site.
Numerical Modeling:
- Simulations modeled the propagation of light in both ordered and disordered arrays using the tight-binding approximation, where the propagation distance $z$ acts as time.
- The authors simulated ensembles of $10^4$ disorder realizations to compute the configuration-averaged intensity evolution and end-facet profiles.
- Theoretical predictions for localization lengths were derived using exact diagonalization, the inverse participation ratio (IPR), and the transfer-matrix method (TMM).
Theoretical Framework:
- The authors developed a general theory for wave propagation in disordered tight-binding lattices. They demonstrated that for systems with a non-degenerate spectrum, the configuration-averaged intensity converges to a stationary spatial distribution at large propagation distances. This limit corresponds to the "dephased" (diagonal-ensemble) state where interference between distinct eigenmodes vanishes.
- For purely off-diagonal disorder, they derived that the effective localization length $\xi$ of this stationary profile is a weighted harmonic mean of the individual eigenmode localization lengths.
- Crucially, they established an analytical scaling relation: $\xi \sim 1/\sigma^2$ , where $\sigma^2$ is the variance of the random logarithmic couplings.

Key Results

Experimental Observation: The experiment successfully demonstrated Anderson localization of single photons from an hBN SPE. In the ordered array, photons exhibited discrete diffraction. In the disordered array, the configuration-averaged output intensity showed pronounced exponential localization near the injection site.
Localization Lengths:
- Bulk Excitation: The experiment yielded an effective localization length of $\xi = 7.11 \pm 0.55$ , compared to a simulation value of $\xi = 5.15 \pm 0.41$ .
- Edge Excitation: Localization was observed at the boundary, with an experimental $\xi = 10.08 \pm 2.66$ (averaged over 4 realizations) versus a simulation of $\xi = 7.52 \pm 0.73$ . The larger length at the edge is attributed to reduced scattering pathways.
Coherence Independence: The study confirmed that the limited temporal coherence of the hBN SPE (picosecond scale) does not preclude Anderson localization. The characteristic time difference between interfering paths in the waveguide array is in the femtosecond range, well within the coherence time of the source. Furthermore, scanning the excitation wavelength over a 20 nm range showed no significant change in the localization length, confirming the robustness of the effect against spectral variations.
Theoretical Validation: The experimental data aligns with the derived theoretical framework. The observed stationary profiles confirm that disorder averaging drives the system toward a propagation-invariant state determined solely by the eigenmode intensities. The measured localization lengths are consistent with the predicted inverse-variance scaling ( $\xi \sim 1/\sigma^2$ ).

Significance and Claims
The paper claims to provide the first experimental demonstration of Anderson localization using single photons emitted by a solid-state defect at room temperature. This establishes defect-based hBN emitters as practical, room-temperature platforms for studying Anderson localization in integrated photonics.

The work's primary theoretical contribution is the derivation of a general framework showing that the configuration-averaged output intensity converges to a stationary profile characterized by an effective localization length. This framework provides a direct, quantitative link between the statistical properties of engineered disorder (specifically the variance of coupling coefficients) and the measurable localization length.

The authors assert that these results support the use of controlled disorder in integrated photonic architectures for applications such as neuromorphic computing, reservoir computing, and quantum information processing, where the robustness of localization against source imperfections (like limited temporal coherence) is a critical design factor. The study confirms that the stationary nature of the localization effect makes it accessible even with realistic, non-ideal quantum sources.