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Tracking doublon-holon dynamics in high-harmonic generation from Mott insulators

This study investigates high-harmonic generation in laser-driven Mott insulators using exact diagonalization to reveal a filling-dependent crossover from intraband to interband-dominated dynamics, demonstrating how interaction strength and dephasing govern doublon-holon creation and quantum trajectory features.

Original authors: Tao-Yuan Du, Hui-Ru Li, Bo Li, Ruifeng Lu

Published 2026-05-05

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Tao-Yuan Du, Hui-Ru Li, Bo Li, Ruifeng Lu

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 crowded dance floor where the dancers are electrons. In a normal, easy-going crowd (like a standard semiconductor), the dancers move freely, and if you shine a bright light on them, they wiggle in a predictable way, creating a specific kind of "echo" of light called high-harmonic generation (HHG). Scientists have long understood this echo because they can treat each dancer as an individual.

But in a Mott insulator, the crowd is different. The dancers are so intensely annoyed by each other (due to strong repulsion) that they refuse to stand next to one another. They are stuck in a rigid pattern. This paper investigates what happens when you shine a powerful laser on this grumpy, crowded dance floor.

Here is the story of their findings, broken down into simple concepts:

1. The "Double-Occupancy" Problem (The Doublon)

In this crowded dance floor, the rule is usually "one dancer per spot." However, the laser is so strong it forces two dancers to squeeze onto the same spot. The scientists call this squeezed pair a "doublon."

The Metaphor: Think of the dance floor as a grid of chairs. Usually, one person sits in a chair. A "doublon" is like two people trying to sit in one chair at the same time. It's uncomfortable and rare, but the laser forces it to happen.
The Discovery: The researchers realized that counting how many of these "double-sitters" exist is the perfect way to understand what the electrons are doing. If there are no double-sitters, the electrons are just wiggling in their own seats (intraband motion). If there are many double-sitters, the electrons are jumping across the room to new seats (interband motion).

2. The Three Stages of the Dance (Filling Levels)

The paper looked at what happens when the dance floor is filled with different numbers of people (electrons):

The Empty Room (Dilute Filling): When there are very few dancers, they have plenty of space. They just wiggle back and forth in their seats like a pendulum. The light they emit is simple and low-energy. It's like a single person tapping their foot to a beat.
The Busy Room (Intermediate Filling): As you add more dancers, things get chaotic. Some dancers start squeezing together (creating doublons), while others jump to new seats. The light they emit becomes a mix of simple wiggles and complex jumps.
The Packed Room (Half-Filling): When the room is half-full (the "Mott insulator" state), the dancers are packed tight. The laser forces them to jump across the room constantly, creating a massive number of "double-sitters." This creates a strong, complex echo of light with a distinct "plateau" (a flat, strong signal) that scientists can measure.

3. The "Grumpiness" Factor (Interaction Strength)

The paper also tested what happens if the dancers get more grumpy (increasing the repulsion force, $U$ ).

The Metaphor: Imagine the dancers hate each other even more.
The Result: If they hate each other too much, they refuse to squeeze together or jump across the room. The "double-sitters" disappear, and the complex light echo vanishes. The strong repulsion acts like a wall, trapping the electrons in their original spots and stopping the high-energy light generation.

4. The "Noise" Factor (Dephasing)

In the real world, things aren't perfectly synchronized. There is noise, heat, or disorder that makes the dancers lose their rhythm. The scientists simulated this "noise" (called dephasing).

The Metaphor: Imagine the music suddenly gets a bit staticky, or the dancers start bumping into each other randomly.
The Result: Surprisingly, this "noise" actually helped trap the "double-sitters." When the dancers lose their perfect rhythm, they can't easily jump back to their original seats. They get stuck in the "double-sitter" state. This means that while the noise kills the high-energy "echo" (the plateau), it actually leaves behind more of these squeezed pairs. It's like a chaotic party where people get stuck in a corner because they can't find their way back to the dance floor.

5. The "Ghost Paths" (Quantum Trajectories)

Finally, the researchers looked at the "paths" the light takes.

In the empty room: The light behaves like a simple wave, following a smooth, predictable path (like a ball rolling on a flat floor).
In the packed room: The light behaves like a complex quantum particle. It leaves behind "ghost paths" or trajectories that look like a specific signature of the "double-sitters" recombining. The paper shows that you only see these complex, interesting paths when the dance floor is packed enough to force the "double-sitters" to exist.

The Bottom Line

This paper provides a new way to "see" what's happening inside these tricky materials. Instead of trying to track every single electron, the scientists found that simply counting the "double-sitters" (doublons) tells the whole story.

No doublons? The electrons are just wiggling in place.
Lots of doublons? The electrons are jumping across the room, creating a strong, complex light signal.
Too much grumpiness (repulsion)? The jumping stops.
Too much noise (dephasing)? The jumping gets messy, trapping the electrons in the "double-sitter" state.

By understanding this "doublon" count, scientists can better understand how these materials react to powerful lasers, bridging the gap between how they behave when they are calm (equilibrium) and how they behave when they are being blasted by light (nonequilibrium).

1. Problem Statement

High-harmonic generation (HHG) in solids has become a powerful tool for probing ultrafast quantum dynamics. In weakly correlated semiconductors, HHG is well-understood via a single-particle Bloch picture, distinguishing between intraband (carrier acceleration) and interband (tunneling and recombination) emissions. However, in strongly correlated Mott insulators, the independent quasiparticle picture breaks down due to strong electron-electron interactions.

The Challenge: Existing interpretations of HHG in Mott systems are often ambiguous. While previous studies have highlighted the role of doublon-holon (double occupancy and hole) excitations, particularly near half-filling, there is a lack of systematic understanding regarding how the HHG mechanism evolves as the electron filling factor changes from dilute to half-filled regimes.
The Gap: There is a need for a microscopic diagnostic that links equilibrium spin-charge separation to nonequilibrium strong-field responses, specifically tracking how the transition from single-particle-like behavior to many-body doublon-dominated behavior occurs.

2. Methodology

The authors employ a rigorous theoretical framework based on the one-dimensional Hubbard model driven by a strong laser field.

Model System: A 1D Hubbard chain with periodic boundary conditions. The Hamiltonian includes nearest-neighbor hopping ( $t_0$ ) and on-site Coulomb repulsion ( $U$ ).
Simulation Techniques:
- Exact Diagonalization (ED): Used to solve the field-free Hamiltonian and establish the equilibrium eigenstates and Hubbard bands.
- Time-Dependent Density-Matrix Propagation: The system's evolution under a laser pulse is simulated using a Lindblad-type master equation. This allows for the inclusion of pure dephasing (phenomenological $T_2$ ) to model coherence loss.
- Current Decomposition: The total electric current is exactly decomposed into intraband and interband components using projection operators defined on the many-body eigenbasis.
Diagnostic Tool: The authors use the time-dependent doublon population ( $D(t)$ ) as the primary diagnostic. They project eigenstates onto equilibrium Hubbard bands to distinguish between spin-wave-like motion (conserving doublon number) and doublon-holon creation (changing doublon number).
Parameters: Simulations cover three filling regimes (5%, 25%, and 50%), two interaction strengths ( $U/t_0 = 5$ and $10$), and laser fields in the mid-infrared regime (9.11 $\mu$ m).

3. Key Contributions

Doublon-Based Diagnostic: The paper establishes the doublon population as a transparent microscopic indicator to distinguish between intraband (spin-wave) and interband (charge excitation) dynamics in correlated systems.
Filling-Dependent Crossover: It identifies and characterizes a continuous crossover in HHG mechanisms driven by electron filling:
1. Dilute Filling (5%): Dominated by intraband Bloch-like motion (spin-wave precession).
2. Intermediate Filling (25%): A mixed regime where both intraband and interband dynamics coexist.
3. Half-Filling (50%): Dominated by interband doublon-holon creation, leading to a distinct HHG plateau and cutoff.
Role of Dephasing: The study elucidates how dephasing selectively suppresses interband coherence while paradoxically enhancing net doublon accumulation by inhibiting coherent Rabi oscillations that would otherwise return population to the ground state.
Quantum Trajectory Analysis: Time-frequency analysis reveals that clear quantum trajectories in the sub-gap region emerge only when many-body eigenstates possess non-zero doublon numbers (characteristic of half-filling), distinguishing them from single-electron Bloch oscillations.

4. Key Results

Filling Dependence:
- At 5% filling, the current follows the laser envelope with sinusoidal oscillations, and the HHG spectrum decays rapidly with no plateau. The doublon population remains near zero.
- At 25% filling, interband excitation begins, evidenced by higher-frequency components in the current and enhanced harmonic yield.
- At 50% filling, the system exhibits a robust HHG plateau and cutoff. The doublon population increases rapidly and saturates, confirming that interband transitions across the Mott gap are the dominant mechanism.
Interaction Strength ( $U$ ):
- Increasing $U$ enlarges the Mott gap ( $\Delta_{\text{Mott}}$ ) and enhances correlation-induced localization.
- This leads to a systematic suppression of interband contributions and HHG yield across all filling levels, as the energy threshold for doublon-holon creation becomes harder to reach.
Current Decomposition & Dephasing:
- Below the Mott gap, intraband and interband currents flow in opposite directions, leading to destructive interference.
- Introducing dephasing suppresses interband coherence, reducing the destructive interference and smoothing the sub-gap spectrum.
- Crucially, dephasing prevents the recombination of doublon-holon pairs, leading to a higher residual doublon population at the end of the pulse compared to the coherent case.
Quantum Trajectories: Time-frequency analysis shows that distinct quantum trajectories in the below- $\Delta_{\text{Mott}}$ region appear only at half-filling. This is attributed to the presence of doublon occupation within the lower Hubbard band eigenstates, which is absent in dilute regimes.

5. Significance

Theoretical Bridge: The work provides a transparent link between equilibrium many-body physics (spin-charge separation, Hubbard bands) and nonequilibrium strong-field phenomena. It moves beyond the single-particle approximation to explain HHG in correlated materials.
Experimental Guidance: The findings suggest that by tuning electron filling (via doping) or environmental parameters (temperature, disorder affecting $T_2$ ), experimentalists can control the balance between coherent and incoherent dynamics in Mott insulators.
Control Mechanism: The identification of dephasing as a mechanism to enhance doublon accumulation offers a potential route to control nonlinear optical responses and potentially manipulate charge states in quantum materials using strong laser fields.
New Perspective: It redefines the understanding of "intraband" motion in Mott systems, showing that even within the lower Hubbard band, dynamics can involve non-negligible doublon motion, challenging the strict separation of spin and charge dynamics in driven systems.