Coherent multi-dimensional widefield microscopy

This paper introduces a widefield two-dimensional electronic spectroscopy microscope (2DESM) that combines femtosecond temporal and micrometer spatial resolution to simultaneously map spectral and spatial dynamics in heterogeneous systems, demonstrated by revealing distinct spatial variations in excitonic dynamics within bilayer WSe2.

The Gist

Imagine you are trying to understand how a crowd of people behaves at a massive concert.

The Old Way:
Previously, scientists had two main ways to study this crowd, but both had flaws:

1. The "Flashlight" Method: They would shine a bright light on a tiny spot and watch how that specific group reacted over time. This gave them great time details (like seeing a person jump), but they had to move the flashlight spot-by-spot to see the whole crowd. It took forever, and they missed how the whole group moved together.
2. The "Wide Shot" Method: They could take a photo of the whole crowd at once, but the camera was too slow to catch the fast movements. They could see where people were, but not how they were dancing or interacting in real-time.

The New Invention (2DESM):
The researchers in this paper built a "Super-Camera" called 2DESM (Widefield Two-Dimensional Electronic Spectroscopy Microscope). Think of it as a camera that can:

• See the entire crowd at once (widefield).
• Take ultra-fast snapshots (femtoseconds—quadrillionths of a second).
• Understand the complex relationships between the people (who is dancing with whom, who is out of sync).

How It Works: The "Echo Chamber" Analogy

To understand what this microscope actually does, imagine you are in a large, echoey hall (the material being studied) and you shout a specific note (a laser pulse).

1. The Setup: You shout a note, wait a tiny fraction of a second, and shout it again. Then you shout a third note to listen for the echo.
2. The Magic: In a normal room, you just hear the echo. But in this "Super-Camera," they don't just listen to the volume. They analyze how the echo changes based on the timing of your shouts.
   • If the echo is messy and fades quickly, it means the room is full of obstacles (disorder).
   • If the echo is clear and long-lasting, the room is very organized.
   • If the echo changes pitch, it means the people in the room are interacting with each other in complex ways.

The 2DESM does this with light and electrons instead of sound and people. It fires three ultra-fast laser pulses at a material and listens to the "echo" of light coming back. By doing this across the whole image at once, it creates a 3D map showing:

• Where the electrons are (Spatial).
• What energy they have (Spectral).
• How fast they lose their rhythm (Time/Coherence).

The Experiment: The "Glass House" vs. The "Open Field"

To test their new camera, the scientists looked at a tiny flake of a material called WSe2 (a type of 2D crystal). They set up two different environments for this flake:

1. The Glass House (Encapsulated): They sandwiched the crystal between layers of hexagonal boron nitride (hBN), like putting a delicate flower in a protective glass case.
2. The Open Field (Unprotected): They left another part of the crystal exposed to the air.

What They Discovered:

• The Glass House: The electrons inside the protected crystal were like a synchronized dance troupe. They moved together, held their rhythm longer, and showed a very clear, strong signal. The "dance" was chaotic only because of the material's own internal quirks, not because of outside noise.
• The Open Field: The exposed electrons were like a group of people trying to dance in a windy, noisy street. The signal was weaker, and the "dance" fell apart much faster. The air and environment disrupted their rhythm immediately.

Why This Matters

This isn't just about crystals; it's about the future of technology.

• Faster Computers: Understanding how electrons stay "in sync" (coherent) helps us build faster, more efficient quantum computers.
• Better Solar Cells: It helps us see how energy moves through materials, which is crucial for making better solar panels.
• Fixing the "Mess": The camera can pinpoint exactly where a material is "broken" or disordered, allowing engineers to fix specific spots rather than guessing.

In Summary:
The authors built a camera that acts like a high-speed, super-sensory detective. It doesn't just take a picture of a material; it listens to the "music" of the electrons, telling us exactly how they dance, how long they stay in rhythm, and how the environment around them changes their performance. This allows scientists to see the invisible quantum world in high definition, all at once.

Technical Summary

1. Problem Statement

The study of ultrafast electronic processes in low-dimensional quantum materials (such as transition metal dichalcogenides, TMDs) and van der Waals heterostructures requires techniques that offer simultaneous high spectral, temporal, and spatial resolution.

• Limitations of Current Methods:
  • Pump-Probe Microscopy: While effective for mapping population dynamics, it is inherently insensitive to quantum-coherent polarization evolution. It cannot resolve homogeneous vs. inhomogeneous broadening or coherent couplings between states.
  • Scanning 2DES: Traditional Two-Dimensional Electronic Spectroscopy (2DES) provides the necessary coherence information but relies on point-scanning approaches. This is slow, limits the field of view, and makes it difficult to correlate local structural heterogeneity with ultrafast dynamics across a sample.
• The Gap: There is a lack of a platform that can perform multidimensional coherent spectroscopy (to access decoherence and coupling) with widefield imaging capabilities (to capture spatial heterogeneity at the micrometer scale) without scanning.

2. Methodology: 2DESM (Widefield 2D Electronic Spectroscopy Microscope)

The authors developed 2DESM, a system that integrates conventional 2DES with optical widefield imaging.

• Optical Setup:
  • Source: A home-built non-collinear optical parametric amplifier (NOPA) pumped by a Yb:KGW laser, generating broadband pulses (1.4–2.1 eV).
  • Pulse Generation:
    • Pump: An Interferometric Collinear Pulse Generator (ICPG) based on the TWINS scheme (birefringent wedges) creates two phase-locked pump pulses with a controllable delay ($t_{pu}$).
    • Probe: A mechanical delay stage controls the pump-probe delay ($t_{del}$).
    • Detection: An Interferometric Collinear Spectrometer (ICS), similar to the ICPG, is placed in the probe path to introduce a delay ($t_{pr}$) between probe replicas for spectral resolution.
  • Imaging: A widefield objective (20X, NA 0.40) and tube lens image the transmitted probe light onto a high-speed scientific camera (Thorlabs CS135MUN).
• Data Acquisition Strategy:
  • Synchronization: A chopper wheel modulates the pump beam, triggering the camera to acquire pairs of frames (pump-on and pump-off) for high signal-to-noise ratio (SNR) via differential imaging.
  • Hyperspectral Hypercube: The system scans $t_{pu}$ and $t_{pr}$ to build a time-domain hypercube $S(x, y; t_{pu}, t_{pr}, t_{del})$.
  • Fourier Transform: A 2D Fourier Transform is applied to the time delays to convert the data into the frequency domain, yielding the 2D spectrum $S(x, y; \omega_{pu}, \omega_{pr}, t_{del})$ for every pixel in the field of view.
• Performance Metrics:
  • Temporal Resolution: ~38 fs (pulse duration) / 55 fs (cross-correlation FWHM).
  • Spatial Resolution: ~1.05 µm (diffraction-limited).
  • Spectral Resolution: ~50 meV at 1.5 eV.

3. Key Contributions

• Novel Instrumentation: The first demonstration of a widefield 2DES microscope that captures spatially resolved 2D maps simultaneously, eliminating the need for point-by-point scanning.
• Simultaneous Resolution: Achieves femtosecond temporal, micrometer spatial, and broadband spectral resolution in a single acquisition.
• Direct Access to Coherence: Enables the direct observation of decoherence dynamics, inhomogeneous broadening, and coherent coupling in heterogeneous systems, which are invisible to standard pump-probe microscopy.

4. Results: Application to Bilayer WSe$_2$

The technique was validated on a bilayer WSe$_2$ flake encapsulated in hexagonal boron nitride (hBN), comparing a fully encapsulated region against an unprotected region.

• Spatial Heterogeneity:
  • The fully encapsulated region showed a signal amplitude 5 times larger than the unprotected region.
  • The unprotected region exhibited a quasi-stationary signal plateau, while the encapsulated region showed a double-exponential decay.
• Exciton Dynamics:
  • Encapsulated Region:
    • Decoherence Time: Extracted from the intrinsic linewidth ($\gamma = 23 \pm 2$ meV), yielding a decoherence time of $\hbar/\gamma \approx 29$ fs.
    • Broadening: Significant inhomogeneous broadening ($\sigma = 40 \pm 1$ meV) was observed, indicating disorder-driven effects.
    • Relaxation: A fast decay followed by a slower relaxation ($\tau_2 \approx 0.5$ ps) attributed to the decay of bright K-K excitons into momentum-forbidden dark K-Q excitons.
  • Unprotected Region:
    • Showed a redshift of ~13 meV in the exciton energy due to different dielectric screening.
    • Similar intrinsic linewidth ($\gamma \approx 22$ meV), suggesting that at room temperature, dephasing is dominated by thermally activated phonon scattering, which is unaffected by the hBN capping.
• 2DES Maps: The 2D maps clearly distinguished between diagonal (inhomogeneous broadening) and anti-diagonal (homogeneous broadening) features, allowing for the separation of disorder effects from intrinsic lifetime limits.

5. Significance and Future Impact

• Platform for Quantum Materials: 2DESM establishes a versatile platform for probing quantum coherence, many-body interactions (biexcitons, trions), and non-local energy transfer in 2D materials and heterostructures.
• Correlating Structure and Dynamics: It uniquely links local structural environments (e.g., strain, defects, encapsulation quality) with ultrafast coherent processes, which is critical for optimizing optoelectronic devices.
• Future Directions: The authors highlight the potential to extend this technique to cryogenic temperatures (to access long-lived coherent states), higher-order multidimensional spectroscopy, and integration with tip-enhanced imaging or electrically driven devices for local control of quantum coupling.

In summary, this work bridges the gap between high-resolution spectroscopy and imaging, providing a powerful new tool to visualize and quantify the complex interplay between disorder, coherence, and energy transfer in nanoscale quantum systems.