Attosecond Spectroscopy Resolves Quantum Fluctuations of Light and Matter with Attosecond Precision

The fundamental nature of light and its interaction with matter operates on timescales so rapid they were previously beyond direct observation, but a new study led by Matan Even Tzur, Chen Mor, and Noa Yaffe, with contributions from Michael Birk, Andrei Rasputnyi, and Omer Kneller, achieves a breakthrough in understanding these fleeting interactions. Researchers now directly observe and control quantum fluctuations in both light and matter using attosecond spectroscopy, a technique that captures events in mere fractions of a second. This work merges concepts from quantum optics with attosecond physics, allowing scientists to imprint the unique properties of squeezed vacuum, a special state of light with reduced quantum noise, onto attosecond pulses used to probe electron behaviour. By reconstructing the state of these pulses with unprecedented precision, the team resolves the squeezing of electron wavepackets during field-induced tunneling, establishing a foundation for attosecond electrodynamics and opening possibilities for manipulating electrons and photons with sub-cycle accuracy.

Quantum Perturbation of High Harmonic Generation

This research demonstrates how quantum fluctuations can influence high harmonic generation, a technique used to create extremely short bursts of light known as attosecond pulses. Scientists have shown that introducing quantum properties, specifically through the use of squeezed vacuum light, leads to observable deviations from classical predictions, pushing the boundaries of attosecond science and offering potential for new control over these incredibly fast pulses. The experimental setup combines a strong infrared laser, focused into a gas, to generate high harmonics with a specially prepared quantum state of light called a squeezed vacuum. This squeezed vacuum is created using a separate laser beam and a crystal, enhancing its quantum properties, and combined with the infrared laser using a sophisticated interferometer, allowing precise control over their interaction.

Crucially, the team can adjust the relative delay between the beams, enabling them to modulate the quantum influence on the harmonic generation process. The resulting extreme ultraviolet light is then detected using a sensitive detector. Researchers meticulously characterized the squeezed vacuum state, confirming its quantum nature through measurements of its spectral and spatial properties, and by analyzing its photon correlations. They also carefully calibrated the detection system to ensure accurate measurement of the harmonic intensities. A key finding was the observation of oscillations in the statistics of the generated harmonics as the delay between the beams was changed, directly demonstrating that the quantum fluctuations are modulating the harmonic emission.

Further analysis involved reconstructing the quantum state of a half-integer harmonic, revealing that it exhibits squeezing, a non-classical property. This reconstruction was achieved through precise measurements of the harmonic’s quadrature amplitude and subsequent data analysis. Scientists engineered a system combining bright squeezed vacuum with a strong laser field to drive high-harmonic generation, effectively imprinting the properties of the squeezed vacuum onto resulting extreme ultraviolet attosecond pulses, allowing for control of both the XUV pulse characteristics and fluctuations of matter on attosecond timescales. The team developed advanced attosecond interferometry to reconstruct the state of the XUV high harmonics and their associated attosecond pulses with attosecond precision. Researchers characterized the light by analyzing its photon number distribution and correlations, identifying the non-classical fingerprint of the XUV radiation.

Single-shot measurements of the XUV spectrum were conducted to obtain complete photon statistics at fixed two-color delays, revealing four distinct harmonic families, each exhibiting unique statistical properties. Scientists observed that the squeezed vacuum source is characterized by super-Poissonian photon statistics, displaying a long tail extending towards high photon numbers. Introducing the squeezed vacuum modified the harmonic distributions, reducing mean intensity and producing broader, asymmetric profiles, particularly in odd harmonics, reflecting anti-correlation between intensities and perturbation amplitude. Half-integer and even harmonics exhibited photon statistics similar to the input squeezed vacuum, with tails extending towards higher photon numbers.

To quantify XUV intensity fluctuations, the team calculated the second-order coherence, revealing super-bunching in both half-integer and even harmonics, matching the input squeezed vacuum value for half-integer harmonics and consistent with a two-squeezed vacuum-photon process for even harmonics. By tracking sub-cycle dynamics, researchers observed periodic modulations of mean intensity, corresponding to half the fundamental optical cycle. Statistical analysis demonstrated that the second-order coherence is modulated in phase with these mean intensity changes, originating from phase-locked amplitude fluctuations in the interferometer.

Quantum Control of Attosecond XUV Pulses

Scientists have achieved a breakthrough in attosecond physics by successfully transferring concepts from quantum optics into the realm of XUV light, enabling unprecedented control over both the properties of attosecond pulses and the fluctuations of matter at attosecond timescales. By combining bright squeezed vacuum with a strong laser field to drive high-harmonic generation, researchers imprinted the quantum properties of the squeezed vacuum onto the resulting XUV attosecond pulses. Experiments revealed detailed information about the quantum states of the generated harmonics using advanced attosecond interferometry. The team reconstructed the Husimi distribution, a key measure of quantum state, for harmonic orders 12, 12.

5, and 13. Notably, the half-integer harmonic exhibited a non-Gaussian distribution, displaying an elliptical envelope with two lobes and a central hole, a hallmark of squeezed vacuum. This observation signifies a departure from classical behavior, resembling a “cat-like” superposition state. In contrast, the even harmonic mirrored the input squeezed vacuum, while the odd harmonic showed a reduction in coherent-state emission as energy transferred into the harmonics. These observations represent the first experimental demonstration of quantum-state tomography in the XUV range.

Further analysis involved reconstructing the attosecond pulse train on a shot-by-shot basis, revealing the temporal evolution of quantum noise. The team quantified fluctuations using the time-dependent variance, which exhibited rapid sub-cycle fluctuations, directly manifesting the upconversion of quantum noise from the driving squeezed light into the XUV regime. The quadrature asymmetry observed in the spectral measurements was reflected as oscillations in the variance at twice the frequency of the mean value oscillations.

Squeezed Light Controls Attosecond Quantum Dynamics

This research successfully integrates concepts from quantum optics into the realm of attosecond physics, achieving unprecedented control over both the properties of XUV attosecond pulses and the fluctuations of matter on attosecond timescales. Scientists demonstrated the ability to imprint the quantum fluctuations of a bright squeezed vacuum onto sub-cycle ionization dynamics and the resulting high harmonics, effectively transferring quantum control from the optical to the XUV regime. Through advanced attosecond interferometry, they reconstructed the state of XUV high harmonics with attosecond precision, realizing optical tomography of quantum light in the XUV spectrum for the first time. A key achievement lies in the first observation of optical tunneling driven by squeezed light, revealing that sub-cycle ionization fluctuations directly reflect the quantum correlations of the driving field. The team established a direct link between quantum optical noise and the tunneling mechanism, demonstrating that the tunneling statistics themselves acquire a squeezed character.