🔬 optics

Superluminal Correlations in Ensembles of Optical Phase Singularities

Using ultrafast electron microscopy with unprecedented spatial and temporal resolution, researchers directly observed optical phase singularities in hexagonal boron nitride membranes accelerating to superluminal velocities before annihilation, revealing new insights into topological defect dynamics and ultrafast information flow in polaritonic media.

Original authors: Tomer Bucher, Alexey Gorlach, Arthur Niedermayr, Qinghui Yan, Harel Nahari, Kangpeng Wang, Ron Ruimy, Yuval Adiv, Michael Yannai, Tom Lenkiewicz Abudi, Eli Janzen, Christina Spaegele, Charles Roques-C

Published 2026-03-27

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Tomer Bucher, Alexey Gorlach, Arthur Niedermayr, Qinghui Yan, Harel Nahari, Kangpeng Wang, Ron Ruimy, Yuval Adiv, Michael Yannai, Tom Lenkiewicz Abudi, Eli Janzen, Christina Spaegele, Charles Roques-Carmes, James Edgar, Frank Koppens, Giovanni Vanacore, Hanan Herzig Sheinfux, Shai Tsesses, Ido Kaminer

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 a calm pond. If you drop two stones in it, ripples spread out, cross each other, and create a complex, dancing pattern of peaks and valleys. Now, imagine that in this dancing pattern, there are tiny, invisible "whirlpools" where the water seems to stop moving entirely, but the direction of the spin around them is perfectly defined. In physics, we call these phase singularities. They are like the eye of a storm in a wave field.

For decades, scientists have known that these singularities behave a bit like tiny particles. They can bump into each other, pair up, and even destroy one another (annihilate) when a "clockwise" whirlpool meets a "counter-clockwise" one.

The Big Discovery: The "Ghost" Speeding Past Light

This new paper is like a high-speed camera that finally caught these singularities in the act of doing something impossible: moving faster than the speed of light.

Here is the twist: They aren't breaking the laws of physics (like Einstein's rule that nothing with mass can go faster than light). Instead, they are "ghosts." Because a singularity is a point of zero energy (a perfect calm spot in the storm), it can "jump" or "slide" across the wave pattern at incredible speeds without actually carrying any energy or information. It's like a shadow moving across a wall faster than light; the shadow isn't a physical object, so it doesn't break the rules.

The Secret Ingredient: The "Slow-Motion" Material

How did they see this? They used a special material called hexagonal boron nitride (hBN).

Think of this material as a "traffic jam" for light. Usually, light zips through things at full speed. But in this material, the light waves (specifically a type called phonon-polaritons) move incredibly slowly, like a snail on a hot sidewalk.

Here is the magic trick:

The singularities are trying to move at their natural, super-fast speed.
Because the "road" (the light wave) they are riding on is moving so slowly, the singularities look like they are zooming past the speed of light relative to the material.
It's like a race car driving at 200 mph on a treadmill that is moving backward at 190 mph. To an observer standing on the treadmill, the car looks like it's moving at 390 mph!

The "Particle" Analogy That Breaks

Scientists used to think of these singularities exactly like tiny billiard balls bouncing around in a liquid.

The Good News: They do act like billiard balls when it comes to how far apart they sit from each other. They avoid each other or clump together just like particles in a liquid.
The Bad News: They don't act like billiard balls when it comes to speed. Real billiard balls can't suddenly accelerate to infinite speeds. But these singularities? As they get ready to crash into each other and vanish, they accelerate wildly, reaching speeds that seem to defy logic.

How They Did It: The Ultimate Slow-Motion Camera

To see this, the researchers needed a camera that could take pictures faster than a blink of an eye and zoom in closer than a virus.

They used an Ultrafast Electron Microscope. Instead of using light to take a picture, they fired a beam of electrons (tiny particles) at the material.
They used a "strobe light" technique with lasers to freeze the motion.
The result? They captured a movie of these singularities being born, dancing, and dying, with a resolution so fine they could see details 30 times smaller than the light wave itself, and time steps as short as 3 femtoseconds (that's 0.000000000000003 seconds!).

Why Does This Matter?

New Physics: It proves that these "ghost" speeds are a universal rule for waves, not just a fluke.
Super-Fast Data: It suggests that in certain materials, information could theoretically flow in strange, ultra-fast ways, even if the light itself is moving slowly.
Better Microscopes: The techniques they developed to track these "ghosts" could help us build better electron microscopes to see atoms and molecules more clearly in the future.

In a Nutshell:
The scientists used a super-slow material and a super-fast electron camera to catch optical "whirlpools" accelerating to speeds that look faster than light. They found that while these whirlpools act like particles in a crowd, they have a wild, super-fast side that particles don't have, revealing a hidden, chaotic dance in the fabric of light.

1. Problem Statement

Phase singularities (points of zero intensity carrying quantized topological charge) are universal features in wave systems, from superfluids to optics. While the spatial correlations of singularity ensembles (resembling particles in liquids) are well-studied, their full phase-space correlations (joint position and velocity distributions) governing system evolution have remained experimentally inaccessible.

Theoretical models (specifically Gaussian random wave interference) predict that optical singularities can exhibit unbounded velocities approaching or exceeding the speed of light ( $c$ ) during creation and annihilation events. However, observing these dynamics requires sub-cycle temporal resolution (femtoseconds) and sub-wavelength spatial resolution (nanometers), which has historically been a significant technical barrier. Furthermore, it is unclear how material properties (specifically group velocity) influence the observability of these superluminal phenomena.

2. Methodology

The authors utilized a combination of advanced hardware and algorithmic techniques to map the ultrafast dynamics of optical singularities:

Experimental Platform:
- Material: Thin flakes of hexagonal boron nitride (hBN), chosen for its support of hyperbolic phonon-polaritons (PhPs). These polaritons possess a slow group velocity ( $v_g \ll c$ ) and low optical losses, confined to sub-wavelength dimensions ( $\sim 630$ nm).
- Microscopy: An Ultrafast Transmission Electron Microscope (UTEM) operating at 200 kV.
- Technique: Photon-Induced Near-field Electron Microscopy (PINEM) combined with Free-Electron Ramsey Imaging (FERI). This allows for the reconstruction of both the amplitude and phase of the near-field.
Experimental Scheme:
- A mid-infrared femtosecond laser pulse ( $\lambda \approx 7 \mu$ $λ \approx 7 μ$ m) is split into three paths:
  1. Upconverted to UV to generate electron probe pulses.
  2. Used to pre-modulate electrons at a reference sample (Si $_3$ N $_4$ membrane with Al coating).
  3. Used to excite PhP wavepackets in the hBN sample.
- Timing Control: Two independent delay stages control the group delay (pump-probe delay for dynamics) and the sub-cycle phase delay (for phase retrieval).
Data Acquisition & Processing:
- Resolution: Achieved 20 nm spatial resolution ( $\sim \lambda_{PhP}/30$ ) and 3 fs temporal resolution ( $\sim T_{cycle}/8$ ).
- Dataset: Recorded 285 phase-resolved frames over an 800 ps window, covering a $21 \times 21 \mu$ m $^2$ field of view.
- Analysis: Automated algorithms identified singularity centroids, assigned topological charges ( $\pm 1$ ), tracked trajectories, and computed joint distance-velocity distributions. Drift correction was applied using affine transforms based on feature extraction.

3. Key Contributions

First Direct Measurement of Singularity Phase-Space Correlations: The study provides the first experimental measurement of the joint distance-velocity distribution for ensembles of optical singularities, moving beyond simple spatial correlations.
Observation of Superluminal Dynamics: The authors experimentally confirmed that phase singularities accelerate to unbounded velocities exceeding the speed of light ( $v > c$ ) immediately prior to annihilation or after creation.
Role of Slow Group Velocity: The paper demonstrates that the slow group velocity of hyperbolic phonon-polaritons in hBN is a critical factor that amplifies the average singularity velocity, making superluminal events statistically common (29% of events) rather than rare.
Validation of Universal Wave Theory: The experimental data aligns perfectly with the Gaussian random wave model, confirming that the acceleration of singularities is a universal feature of wave interference, independent of the specific physical medium.

4. Key Results

Superluminal Velocities:
- The measured average singularity velocity was $\langle v \rangle \approx 1.04c$ .
- 29% of the tracked singularities exhibited velocities exceeding $c$ .
- In contrast, theoretical modeling suggests that in free space (where phase velocity equals group velocity), only ~0.4% of singularities would exceed $c$ , with an average velocity of $\sim 0.1c$ .
- The enhancement is attributed to the ratio of phase velocity to group velocity in hBN ( $v_{ph}/v_g \approx 12$ ).
Annihilation Dynamics:
- Trajectories of opposite-charged singularities form continuous curves in space-time. As they approach annihilation, they must accelerate to infinite velocity to satisfy phase continuity, resulting in a "parabolic" space-time trajectory where the tangent (velocity) exceeds $c$ .
- This is a geometric consequence of phase continuity, not a violation of relativity, as singularities carry zero intensity and transmit no energy/information.
Correlation Functions:
- Distance Correlations: Matched the theoretical prediction for interacting particles in a liquid (short-range order), confirming the "particle-like" nature of singularities in terms of spatial distribution.
- Velocity Distributions: Showed a heavy tail significantly deviating from the Maxwell-Jüttner distribution of relativistic particles, confirming the "breakdown" of the particle analogy due to superluminal speeds.
- Joint Distance-Velocity Distribution: Revealed that opposite-charge pairs at small distances exhibit high relative velocities (acceleration toward annihilation), while same-charge pairs are rare at small distances.

5. Significance

Fundamental Physics: This work resolves a long-standing theoretical prediction regarding the unbounded velocities of topological defects, demonstrating that "superluminal" motion is a generic feature of wave singularities, not an anomaly.
Material Science: It highlights the unique utility of hyperbolic materials (hBN) for studying ultrafast wave dynamics. The slow group velocity of PhPs acts as a "magnifying glass" for singularity dynamics, making them observable with current technology.
Information Flow: The findings suggest new paradigms for ultrafast information flow in polaritonic media, where topological defects can evolve and interact on femtosecond timescales.
Technological Advancement: The combination of UTEM, PINEM, and FERI sets a new standard for deep sub-wavelength and deep sub-cycle imaging, enabling the study of quantum and classical wave phenomena previously inaccessible.
Future Applications: The methodology opens avenues for studying exotic topological phases in 2D heterostructures, higher-order singularities, and the interaction of singularities with free electrons for electron holography. It also offers potential strategies to mitigate "granularity" effects in electron microscopy by mapping fluctuation dynamics.

1. Problem Statement

2. Methodology

3. Key Contributions

4. Key Results

5. Significance

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