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Attosecond correlation interferometry

This paper demonstrates the generation and characterization of correlated attosecond extreme-ultraviolet emissions by transferring infrared quantum correlations from two-mode bright squeezed vacuum to high-harmonic generation, enabling the sub-cycle resolution of amplitude and phase correlations through even-harmonic interferometry and revealing a transition to near-silence in joint fluctuations within 30 attoseconds.

Original authors: Chen Mor, Assaf Shonfeld, Keren Deutsch, Noa Yaffe, Michael Birk, Matan Even Tzur, Barak Dayan, Oren Cohen, Nirit Dudovich

Published 2026-10-21

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CC BY 4.0

Original authors: Chen Mor, Assaf Shonfeld, Keren Deutsch, Noa Yaffe, Michael Birk, Matan Even Tzur, Barak Dayan, Oren Cohen, Nirit Dudovich

Original paper licensed under CC BY 4.0 (https://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

Light is more than just a beam that illuminates a room; it is a stream of particles called photons that can be linked together in ways that defy our everyday intuition. When these photons are generated together, they share a secret connection, meaning that a change in one instantly affects the other, regardless of the distance between them. Scientists have long used these linked pairs to build ultra-precise sensors and secure communication systems, but they have mostly studied them using light that oscillates relatively slowly, on timescales of femtoseconds. This is still incredibly fast, yet it is too slow to capture the frantic, sub-cycle motion of electrons as they jump around inside atoms. Electrons move on an attosecond timescale, a unit of time so brief that a billion billion of them fit into a single second. For decades, the challenge has been to create and measure these quantum connections at such extreme speeds, a task that requires tools capable of seeing the invisible dance of electrons without blurring the picture.

A team of researchers at the Weizmann Institute of Science and the Technion in Israel has now taken a major step toward solving this puzzle. They successfully generated and measured quantum correlations in extreme ultraviolet light pulses that last only a few hundred attoseconds. To do this, they used a clever trick involving a process called high-harmonic generation, where a powerful laser beam is fired into a gas, causing the atoms to release bursts of high-energy light. In this experiment, the researchers did not just use a standard laser beam; they added a second, weaker field of light that contained pairs of linked photons. This special light field, known as a two-mode bright squeezed vacuum, acted as a subtle nudge to the atoms in the gas. As the atoms responded to this nudge, they emitted bursts of extreme ultraviolet light that carried the same secret connections as the original infrared light, effectively translating the quantum link from a slow, familiar speed to the blistering pace of electron motion.

The researchers faced a significant hurdle: the light pulses they created were chaotic, with their brightness and timing fluctuating wildly from one burst to the next. If they had looked at the light from just one of the linked channels, the signal would have appeared as random noise, hiding any underlying pattern. However, by measuring the light from both channels simultaneously, they could see the hidden order. They discovered that while the individual pulses were noisy, the fluctuations in one channel were perfectly matched to the fluctuations in the other. It was as if two people were shouting random words, but if you listened to them together, their voices canceled out the noise, revealing a clear, synchronized rhythm. This allowed the team to prove that the quantum correlations survived the journey from the infrared spectrum, where they were created, all the way into the extreme ultraviolet spectrum, where the light pulses are short enough to track electron movement.

To confirm that these connections were not just about brightness but also about the precise timing of the light waves, the team used a unique property of the light they generated. The interaction between the laser and the gas produced a specific type of light pulse that only appeared when the two linked channels worked together in a precise way. By carefully adjusting the timing between the main laser and the linked light, they observed the intensity of these special pulses rise and fall in a rhythmic pattern. This oscillation proved that the two channels were not just linked in strength but were also locked in phase, meaning their wave peaks and troughs were synchronized with attosecond precision. This observation served as a direct measurement of the quantum connection, confirming that the researchers had successfully transferred the delicate quantum relationship into a new, ultrafast regime.

The most striking result came when the team reconstructed the actual shape of the light pulses in time. They found that while the individual pulses were a mess of random fluctuations, the combined signal revealed a structure that was almost silent for brief moments, followed by sudden bursts of intense noise. This transition from chaos to silence happened in just 30 attoseconds. This finding demonstrates that the quantum correlations are not just a statistical curiosity but a real, physical structure that can be manipulated and observed. The ability to generate and measure these correlations on the natural timescale of electrons opens a new door for science. It suggests that in the future, researchers could use these tools to watch how electrons interact with each other inside molecules and materials, potentially revealing new ways to control chemical reactions or understand the fundamental behavior of matter at its most basic level.

Technical Summary: Attosecond Correlation Interferometry

Problem Statement
Correlations between optical modes, ranging from classical fluctuations to quantum entanglement, are fundamental to modern optics and quantum technologies. While correlation measurements have been extended to the X-ray regime and optical correlations have been resolved on femtosecond timescales, probing these correlations on the natural timescale of electronic motion—the attosecond regime—remains a major challenge. Specifically, generating correlated photons within attosecond bursts and detecting their correlations with sub-cycle temporal resolution has been elusive. The authors aim to bridge this gap by transferring quantum-origin correlations from the infrared (IR) to the extreme ultraviolet (XUV) and resolving them with attosecond precision.

Methodology
The study employs a three-field configuration combining high-harmonic generation (HHG) with a non-degenerate two-mode bright squeezed vacuum (TMBSV).

Source Generation: An 800 nm IR pump laser is split. A strong coherent component drives HHG in a krypton gas jet. A weaker component pumps a non-degenerate spontaneous parametric down-conversion (SPDC) process in $\chi^{(2)}$ crystals to generate TMBSV. This creates spectrally separated "signal" ( $\omega_s \approx 0.9$ eV) and "idler" ( $\omega_i \approx 0.62$ eV) modes with complex thermal fluctuations and strong amplitude/phase correlations ( $n_s = n_i$ and $\phi_s + \phi_i \approx \text{const}$ ).
Perturbation: The TMBSV fields co-linearly perturb the strong-field-driven HHG process. This perturbation modifies the tunneling step and electron trajectories, imprinting the IR field's stochastic amplitude and phase fluctuations onto the emitted XUV spectrum.
Spectral Mapping: The interaction generates "fractional harmonics" (sidebands at $2N \pm \delta_{s,i}$ ) that inherit the IR correlations. Crucially, higher-order perturbative processes generate even harmonics ( $2N$ ), which arise from the joint contribution of both signal and idler fields within the same half-cycle.
Interferometric Detection: The even harmonics serve as an intrinsic attosecond coincidence interferometer. Because their generation involves two indistinguishable quantum pathways (e.g., absorption from one odd harmonic vs. emission from another), their intensity oscillates as a function of the delay between the pump and the TMBSV fields. This oscillation is sensitive to the phase sum of the fractional harmonics.
Reconstruction: By performing single-shot measurements of the XUV spectrum across varying delays, the authors reconstruct the temporal emission. They utilize the measured amplitude covariance and the phase information derived from the even-harmonic oscillations to perform a Fourier reconstruction of the attosecond pulse trains.

Key Contributions and Results

Transfer of Correlations: The experiment demonstrates the successful transfer of amplitude and phase correlations from femtosecond IR modes to broadband XUV modes. The spectral amplitude covariance matrix of the XUV reveals a four-lobed structure linking signal and idler-driven fractional harmonics, mirroring the IR TMBSV correlations across a $\sim$ 20 eV bandwidth.
Sub-Cycle Phase Resolution: The generation of even harmonics acts as a sub-cycle coincidence detector. While fractional harmonics individually exhibit random shot-to-shot phases, the even harmonics display pronounced oscillations at frequency $2\omega_p$ when scanning the delay. This confirms that the phase sum of the signal and idler driven fractional harmonics ( $\phi_{2N\pm\delta_s} + \phi_{2N\pm\delta_i}$ ) remains locked to the pump phase, effectively resolving phase correlations with attosecond precision.
Time-Domain Reconstruction: The joint temporal reconstruction of the two fractional-harmonic families reveals a distinct attosecond-scale noise pattern. While individual reconstructions show blurred sub-cycle structures due to thermal phase fluctuations, the joint field exhibits a clear transition from maximal fluctuations to near-silence within approximately 30 attoseconds. This demonstrates that the joint reconstruction suppresses fluctuations, revealing the underlying correlated dynamics.
Statistical Characterization: The study characterizes the statistics of the generated light. Fractional harmonics exhibit thermal statistics ( $g^{(2)}(0) \approx 1.4$ ), while even harmonics show enhanced fluctuations ( $g^{(2)}(0) \approx 3.2$ ) due to the multiplicative nature of the two-mode interaction.

Significance and Claims
The authors claim that this work establishes a framework for generating and probing quantum correlations on attosecond timescales. By utilizing HHG as a nonlinear frequency converter that preserves inter-mode correlation structures, the study opens the door to "quantum attosecond science." The ability to resolve both amplitude and phase correlations with sub-cycle precision allows for the observation of correlated electron dynamics on their natural timescale. The authors suggest this approach could enable new contrast mechanisms for ultrafast spectroscopy and microscopy, as well as the direct observation and control of many-body interactions and electronic correlations in matter, extending the concepts of non-classical light into the attosecond domain.

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