Single photon zeptosecond interferometry

TL;DR

This work demonstrates zeptosecond-level interferometry in the XUV using a self-referencing, two-beam HHG-based interferometer that yields phase-locked attosecond pulse trains. By employing phase masks (including Gaussian and Bessel-Gauss beams) and careful photon-counting conditioning, the authors achieve a phase-resolved, high-stability XUV interferometry with sub-100 zs resolution and a minimum Allan deviation of about $3.5$ zs, enabling single-photon interferometry and potential quantum-optics–like attosecond experiments. The study shows that HHG photons carry the full harmonic spectrum independently of photon number, finds no strong spectral–spatial correlations between harmonics, and provides a rigorous two-beam interferometric theory that includes macroscopic propagation and diffraction phases. Numerical simulations and multi-electron dynamics (via TDCIS) corroborate the experimental phase retrieval and reveal a linear dependence of harmonic spectral phase on relative CEP, supporting the interpretation and suggesting future tests of temporal aspects of QED, time-dependent QED imaging, and non-local measurements in solids. Overall, the work opens the door to quantum-optics–style control and measurement at zeptosecond timescales in the XUV, with broad implications for interferometric transient absorption spectroscopy, nonlocal correlations, and molecular quantum tomography.

Abstract

We demonstrate the generation of a train of attosecond XUV pulses that are in a superposition of wavefront states. Such superposition yields a high precision, self-referencing, common path XUV interferometer setup to produce pairs of spatially separated and independently controllable XUV pulses that are locked in phase and time with a temporal jitter of 3.5 zs (zs = zeptoseconds = $10^{-21}$). In our approach, we can independently control the relative phase/delay of the two optical beams with a resolution of 52 zs. Since the jitter is on the order of the Compton time scale, we explore the level of correlation between the non-local photons by comparing different spatial mode superpositions. Further, thanks to the stability of the interferometer we can retrieve the interference pattern through photon counting. Through post-selection of different particle events we can analyze one, two or more photon events. We argue that this zeptosecond level of temporal precision will open the door for new dynamical QED tests at lower intensities while photon counting experiments can also have an impact on the emerging field of quantum light in strong fields. We also discuss the potential impact on other areas, such as time-dependent QED, imaging, measurements of non-locality, and molecular quantum tomography.

Figures (12)

• Figure 1: Sketch of the experimental setup. A spatial light modulator (SLM) is used to separate the incoming beam into multiple (here two) phase locked beams. They are used to generate spatially separated but phase locked harmonics which interfere in the far field and are detected with an XUV spectrometer. Note that each photon is in a superposition of two wavefronts after interacting with the SLM. $\chi^{(n)}$ represents an n-order nonlinearity.
• Figure 2: (a) The phase evolution of harmonics 15-21, generated in Ar, as a function of fundamental phase difference. These harmonics show resolutions of around 75zs. Inset, a finer scan of the phase evolution in time of the 7th harmonic (113 nm) showing a resolution of 52 zs (0.86 mrad). Here the resolution is close to the intended step size of the scan (84 zs) and is shown as the horizontal error bars. The vertical error bars show the precision achieved at each step. (b) The error when characterizing the phase of a single mask as a function of the measurement time. The error is measured via three quantities. First the standard errors $\sigma_s$ in red, which reaches a minimum value of 18 zs for the 9th harmonic. Then the differential errors $\sigma_D$ in blue, which reaches a minimum value of 9 zs after 26 hours. Finally, in yellow are the Allan deviations $\sigma_A$ for the two harmonics. The 9th reaches a minimum value of 3.5 zs after approximately 20 seconds.
• Figure 3: (a) Measured XUV spectra after conditioning for a certain number of photons in the data for 2 beam profiles: 2 Gaussian foci and 2 foci formed by the interference of beams with $l=\pm 1$ OAM. (b) Spectra formed from spectrally conditioning the same beam profiles. The gated harmonic is strongly amplified, yet the rest of the spectrum is identical.
• Figure 4: Accumulated image imposing two conditions on the detected photons: First, exactly two photons are detected within one image. Second, one photon is detected within a predefined gate. The gate for this image is depicted in blue. Right side shows the projection of the brightest harmonic onto the y-axis for two different gates and for the single-photon data. The gates used for these fringes are indicated in the image in red and blue.
• Figure 5: (a) Standard error in zs of two balanced Gaussian beams as a function of the number of shots. Data is shown for the 15th - 21st harmonic. (b) Unbalanced fringes for the 7th with the fundamental beam split 1-to-1 and 1-to-0.8