🔬 atomic physics

Generation of bright quantum high-order harmonic driven by combined coherent and bright squeezed vacuum light

This study demonstrates that combining strong coherent and weak bright squeezed vacuum lasers to drive high-order harmonic generation in atomic gas enables the creation of bright quantum high-order harmonics, where macroscopic propagation effects modulate the phase and quantum properties of the resulting attosecond bursts in a pressure-dependent manner, paving the way for attosecond quantum spectroscopy.

Original authors: Wentao Wang, Yaoshun Sun, Liyuan Wang, Lingrui Hu, Dajun Ding, Xiangyu Tang, Mingxuan Li, Jianmin Yuan, Sizuo Luo

Published 2026-07-24

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Wentao Wang, Yaoshun Sun, Liyuan Wang, Lingrui Hu, Dajun Ding, Xiangyu Tang, Mingxuan Li, Jianmin Yuan, Sizuo Luo

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 the universe is a giant, chaotic dance floor where tiny particles called electrons are constantly spinning and jumping. For a long time, scientists have been trying to take snapshots of these electrons to see exactly how they move. To do this, they use flashes of light so fast they are measured in "attoseconds"—a unit of time so short that an attosecond is to a second what a second is to the age of the universe. These super-fast flashes are created by smashing intense laser beams into gas, a process that forces the gas to spit out new, super-bright flashes of light. This is like hitting a drum so hard it rings with a sound so high-pitched you can't hear it, but can use it to see things.

However, most of these laser flashes are like a perfectly synchronized marching band: every member steps at the exact same time, creating a predictable, "classical" rhythm. But what if the light itself had a secret, jittery personality? What if the laser wasn't just a marching band, but a group of dancers who sometimes stumble, sometimes leap, and sometimes move in perfect, unpredictable sync? This is the world of "quantum light," where the light waves themselves have built-in fuzziness and randomness. Scientists are now asking: if we use this jittery, quantum light to drive the electron dance, will the resulting super-fast flashes of light also carry that same quantum "jitter"? If we can figure this out, we might be able to build a new kind of microscope that doesn't just see where electrons are, but also how they are quantum-mechanically connected to each other.

The Quantum DJ and the Jittery Crowd

In this study, a team of researchers decided to mix two very different types of light to see what kind of "music" the electrons would dance to. Imagine a DJ playing a track. Usually, the DJ uses one steady, powerful beat (a strong, standard laser). But for this experiment, the researchers added a second, quieter track that was "bright squeezed vacuum" (BSV) light. Think of the main laser as a steady, heavy bass drum, and the BSV light as a shaker that rattles with a very specific, jittery kind of randomness. When they mixed these two together and blasted them into a cloud of krypton gas, they didn't just get the usual rhythm; they got a whole new set of beats.

The main discovery is that this "quantum shaker" changed the game in a way that depends entirely on how crowded the dance floor is. The researchers found that the gas pressure (how many gas atoms are packed into the cell) acts like a volume knob for different types of light. When they cranked up the pressure, some of the new, weird light frequencies got louder, while others got quieter. Specifically, they saw three types of new flashes:

The Odd Ones: The usual, strong flashes (odd harmonics).
The Half-Step Ones: New flashes that appeared exactly halfway between the usual ones (half-integer harmonics). These happened when the electrons absorbed or released just one "jittery" photon from the BSV light.
The Even Ones: New flashes that appeared at even intervals (even harmonics). These happened when the electrons dealt with two "jittery" photons at once.

The most surprising part was that each of these three types of flashes had its own "sweet spot" for gas pressure. The usual flashes liked a pressure around 20 to 24 Torr. The "half-step" flashes liked a higher pressure (around 27 Torr), while the "even" flashes needed a much higher pressure (around 30 to 44 Torr) to shine brightly. It's as if the bass drum, the half-step shaker, and the even-step shaker all wanted to dance in rooms of different sizes to sound their best.

The Secret of the "Action Phase"

Why did the pressure matter so much? The researchers used computer simulations to figure out that the jittery BSV light was messing with the "action phase" of the electrons. Imagine an electron as a surfer riding a wave. The "action phase" is like the surfer's internal clock, counting the seconds they've been riding. The weak, jittery BSV light didn't change the speed of the wave much, but it did tweak the surfer's internal clock by a tiny, random amount.

Because the gas pressure changes how the light waves travel through the room, it changes how much that "tweak" adds up. The computer models showed that this tiny tweak in the electron's clock caused the different types of flashes to get out of sync with each other at different pressures. When the pressure was just right for a specific type of flash, all the electrons in the gas cloud were "clapping" in perfect unison, making that flash super bright. When the pressure was wrong, they were clapping out of sync, and the flash died out. This explains why the "half-step" and "even" flashes needed different pressures than the usual ones.

The Jittery Light is Real

The team also looked at the "personality" of the light they created. In the world of light, you can measure how "bunched up" the photons are. A normal laser has photons that are spread out evenly. But the BSV light they used has photons that like to clump together (bunching). The researchers found that the new "half-step" and "even" flashes they created kept this clumpy, jittery personality.

When they simulated the experiment shot-by-shot (like taking a photo of the dance floor every single time the music started), they saw that the brightness of these new flashes jumped around wildly from one shot to the next. This "flickering" was a direct sign that the quantum jitter from the BSV light had been successfully transferred to the new, high-energy flashes. The usual flashes stayed steady, but the new ones were wild and unpredictable, just like their quantum parents.

What This Means

The paper doesn't claim to have solved all the mysteries of quantum mechanics, but it does show a clear path forward. By carefully tuning the gas pressure, scientists can now control not just how bright these super-fast flashes are, but also their quantum "personality." This is a big deal because it lays the groundwork for "attosecond quantum spectroscopy." In the future, this could allow scientists to use these jittery, quantum flashes to probe the deepest, most secret connections between electrons in matter, potentially revealing how quantum effects work on the tiniest scales of time and space. The researchers have essentially built a new kind of light switch that lets them turn the "quantumness" of light on and off, depending on how crowded the room is.

Technical Summary: Generation of Bright Quantum High-Order Harmonic Driven by Combined Coherent and Bright Squeezed Vacuum Light

Problem Statement
Attosecond pulses, typically generated via High-Harmonic Generation (HHG) driven by intense coherent lasers, have established a foundation for attosecond spectroscopy. Recent theoretical and experimental efforts have sought to extend this to the quantum regime by driving HHG with quantum light sources, such as Bright Squeezed Vacuum (BSV), to probe quantum-mechanical correlations in matter. While single-atom studies have demonstrated that quantum properties of BSV can be transferred to emitted XUV radiation through the absorption or emission of BSV photons, the macroscopic propagation of such quantum-driven harmonics in dense media remains largely unexplored. Unlike coherent fields, BSV fields exhibit large photon-number fluctuations, which may significantly alter coherence and quantum properties during propagation. Understanding these macroscopic effects is critical for generating bright, quantum-correlated XUV sources suitable for attosecond quantum spectroscopy.

Methodology
The study employs a combined experimental and theoretical approach to investigate macroscopic propagation effects in Quantum High-Harmonic Generation (QHHG).

Experimental Setup: A 35-fs, 800-nm Ti:sapphire laser pulse is split into two arms. One arm provides a strong coherent driving field (~1.7 × 10¹⁴ W/cm²). The other arm generates a weak 1600-nm BSV field via spontaneous parametric down-conversion (SPDC) in a 3-mm type-I BBO crystal, characterized by a second-order correlation function $g^{(2)}(0) = 2.324$ . These fields are recombined and focused into a 3-mm gas cell containing Krypton (Kr) atoms. The gas pressure is precisely controlled (5–60 Torr) to study phase-matching conditions. Emitted harmonics are recorded using a home-built XUV spectrometer.
Theoretical Modeling: The authors developed a comprehensive simulation model solving the one-dimensional time-dependent Schrödinger equation (1D-TDSE) coupled with Maxwell's equations for macroscopic propagation. The driving field is modeled as a superposition of a noiseless 800-nm fundamental component and a 1600-nm BSV field characterized by a Husimi distribution. To account for quantum fluctuations, 1000 single-shot realizations of the BSV field were randomly sampled. The macroscopic propagation accounts for dispersion, absorption, and phase modulation by neutral atoms and plasma.

Key Contributions and Results

Generation of Quantum Harmonic Components: The experiment successfully generated a spectrum comprising:
- Odd harmonics ( $H_{2N+1}$ ): Driven by the coherent field.
- Half-integer harmonics ( $H_{(2N+1)\pm 1/2}$ ): Resulting from the absorption or emission of a single BSV photon.
- Even harmonics ( $H_{2N}$ ): Resulting from the absorption or emission of two BSV photons.
  The introduction of the BSV field, while remaining in a perturbative regime regarding ionization, successfully imprinted quantum features onto the XUV spectrum.
Distinct Pressure-Dependent Yields: A primary finding is that different harmonic components exhibit significantly different optimal gas pressures for maximum yield.
- Odd harmonics ( $H_{2N+1}$ ) peak around 20–24 Torr.
- Half-integer harmonics show split optima: $H_{2N+1/2}$ peaks at higher pressures (e.g., ~27 Torr), while $H_{2N+3/2}$ peaks at lower pressures (e.g., ~13 Torr).
- Even harmonics ( $H_{2N}$ ) require the highest pressures, peaking around 30–44 Torr.
  This contrasts with the behavior of harmonics driven solely by coherent light, where pressure dependence is uniform across orders.
Phase-Matching Mechanism: Theoretical analysis based on a wave-mixing model reveals that the BSV field perturbs the action phase ( $\phi_{act}$ ) of the electron wave packet. While the BSV field is too weak to significantly alter the degree of ionization (and thus refractive index changes due to plasma), it introduces a phase term $\sigma$ to the action phase.
- The total phase mismatch is given by $\Delta k = \Delta k_{coh} + \nabla \sigma$ .
- The perturbation $\sigma$ depends on the relative phase and amplitude of the BSV field.
- This perturbation modifies the phase-matching conditions for sub-cycle emission bursts (labeled P1–P4), causing their optimal pressures to shift in opposite directions depending on the sign of the perturbation phase.
- Macroscopic integration of these shifted bursts results in the observed distinct pressure dependencies for different harmonic orders.
Quantum Fluctuations and Statistics: Numerical simulations of shot-to-shot harmonic spectra confirm the preservation of quantum properties after macroscopic propagation.
- Photon Statistics: Odd harmonics ( $H_{2N+1}$ ) exhibit Gaussian-like distributions ( $g^{(2)}(0) \approx 1.1$ ), similar to coherent light. In contrast, half-integer and even harmonics show slow-decaying probability distributions indicative of photon bunching and super-bunching, with $g^{(2)}(0)$ values around 2 and exceeding 4, respectively.
- Pressure Sensitivity: The second-order correlation function $g^{(2)}(0)$ is highly sensitive to gas pressure. In phase-mismatched regimes, intensity fluctuations are amplified by macroscopic propagation effects, yet the quantum nature (bunching) of the non-odd harmonics is maintained near optimal phase-matching pressures.

Significance
The paper demonstrates the successful generation and macroscopic manipulation of bright quantum XUV sources. By combining a strong coherent field with a weak BSV field, the authors show that the quantum properties of the driving field (specifically photon-number fluctuations) are transferred to the emitted high-order harmonics even after propagation through a dense gas medium.

The work establishes that macroscopic phase-matching conditions can be tuned to control the relative intensity and quantum statistics of different harmonic components (odd, even, and half-integer). This capability lays a foundational basis for attosecond quantum spectroscopy, offering a pathway to probe quantum electron dynamics in matter using XUV photons with tailored quantum correlations. The study confirms that despite the complexity of macroscopic propagation in dense media, the quantum signatures of the driving field can be preserved and utilized to generate bright, quantum-correlated attosecond bursts.

The Quantum DJ and the Jittery Crowd

The Secret of the "Action Phase"

The Jittery Light is Real

What This Means

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