Realizing split-pulse x-ray photon correlation spectroscopy to measure ultrafast dynamics in complex matter

Abstract

Split-pulse x-ray photon correlation spectroscopy has been proposed as one of the unique capabilities made possible with the x-ray free electron lasers. It enables characterization of atomic scale structural dynamics that dictates the macroscopic properties of various disordered material systems. Central to the experimental concept are x-ray optics that are capable of splitting individual coherent femtosecond x-ray pulse into two distinct pulses, introduce an adjustable time delay between them, and then recombine the two pulses at the sample position such that they generate two coherent scattering patterns in rapid succession. Recent developments in such optics showed that, while true 'amplitude splitting' optics at hard x-ray wavelengths remains a technical challenge, wavefront and wavelength splitting are both feasible, able to deliver two micron sized focused beams to the sample with sufficient relative stability. Here, we however show that the conventional approach to speckle visibility spectroscopy using these beam splitting techniques can be problematic, even leading to a decoupling of speckle visibility and material dynamics. In response, we discuss the details of the experimental approaches and data analysis protocols for addressing issues caused by subtle beam dissimilarities for both wavefront and wavelength splitting setups. We also show that in some scattering geometries, the Q-space mismatch can be resolved by using two beams of slightly different incidence angle and slightly different wavelengths at the same time. Instead of measuring the visibility of weak speckle patterns, the time correlation in sample structure is encoded in the 'side band' of the spatial autocorrelation of the summed speckle patterns, and can be retrieved straightforwardly from the experimental data. We demonstrate this with a numerical simulation.

Extracting contrast in an X-ray speckle visibility spectroscopy experiment under imperfect conditions

“…Depending on the magnitude of the overlap and angular misalignment, a proper binning of the detector along the direction of angular misalignment can partially recover the contrast. Recently, Sun et al (2020) proposed another approach to compensate for the shift of the speckle pattern by evaluating the autocorrelation function. In principle, both techniques yield similar results in partially recovering the original contrast, and should act as complementary tools to verify the results in a double-probe XSVS experiment.…”

“…The experimental setup in this case uses optics in a split-and-delay line to separate a coherent pulse into two identical probes, delaying one of the probes in time, and recombining them into two collinear signals (Yabashi et al, 2017). In practice, this is extremely difficult to achieve consistently (Sun et al, 2020), and there will often be an angular misalignment between the two pulses and a nonperfect overlap on the sample as illustrated in Fig. 1(b).…”

“…1(d) and 1(e) where the decay of contrast using the variance is evident in the system where k = 6 photons per pixel but fails for the case of k = 0.015 photons per pixel. This becomes problematic for a XSVS experiment since the typical signal produced from the interaction of a single or double pulse with a system, especially at large q values, is quite low (Sun et al, 2020). To overcome this impediment, we have to resort to photon counting statistics and measure the contrast in terms of coherent modes, M, where = 1/M.…”

Split-pulse X-ray photon correlation spectroscopy with seeded X-rays from X-ray laser to study atomic-level dynamics

“…This contrast reduction can be reasonably explained by the degree of decoherence between the sub-pulses. The angular mismatch parallel to the detector plane between the sub-pulses 50 , 0.15 mrad, creates the positional difference between two speckles ~ 0.15 mm on the detector plane, thereby reducing the contrast from 0.23 to ~0.15 ~ β ( Q , Δ t = 0). Note that the angular mismatch perpendicular to the detector plane can be ignored.…”

The Effect of Intensity Fluctuations on Sequential X-ray Photon Correlation Spectroscopy at the X-ray Free Electron Laser Facilities

“…At present, two modes of XPCS studies have been discussed and demonstrated at XFELs: (1) the sequential mode, where one XPCS speckle pattern is collected per X-ray pulse [19,20], similar to synchrotron-based XPCS experiments; (2) the split-pulse mode [16,[21][22][23][24][25], where one ultrafast X-ray pulse is split into two, and subsequently recombined with a relative delay from a few picoseconds up to nanoseconds. In the latter mode, each image collected from the X-ray detector is the sum of speckle intensities from two pulses.…”