Towards ultrafast dynamics with split-pulse X-ray photon correlation spectroscopy at free electron laser sources

One of the important challenges in condensed matter science is to understand ultrafast, atomic-scale fluctuations that dictate dynamic processes in equilibrium and non-equilibrium materials. Here, we report an important step towards reaching that goal by using a state-of-the-art perfect crystal based split-and-delay system, capable of splitting individual X-ray pulses and introducing femtosecond to nanosecond time delays. We show the results of an ultrafast hard X-ray photon correlation spectroscopy experiment at LCLS where split X-ray pulses were used to measure the dynamics of gold nanoparticles suspended in hexane. We show how reliable speckle contrast values can be extracted even from very low intensity free electron laser (FEL) speckle patterns by applying maximum likelihood fitting, thus demonstrating the potential of a split-and-delay approach for dynamics measurements at FEL sources. This will enable the characterization of equilibrium and, importantly also reversible non-equilibrium processes in atomically disordered materials.

X-ray photon correlation spectroscopy1 (XPCS) is a powerful tool to study slow dynamics in complex systems and is routinely used at storage ring sources on time scales of milliseconds to hours. Applied with ultrashort coherent X-ray pulses available at current free electron laser (FEL) sources2,3,4, it can potentially track atomic scale fluctuations5,6,7 in liquid metals8, multi-scale dynamics in water9, fluctuations in the undercooled state10,11,12, heterogeneous dynamics about the glass transition13,14,15, and atomic scale surface fluctuations16,17. In addition, time-domain XPCS18,19 at FEL sources is well suited for studying fluctuations in reversible non-equilibrium processes that go beyond time-averaged structural descriptions. Such pump (split-pulse) probe experiments are feasible for non-equilibrium processes that are reversible on the timescale defined by the repetition rate of the experiment. This will allow the elucidation of dynamics of ultrafast magnetization processes20,21,22 and can address open questions concerning photo-induced phonon dynamics23,24 and phase transitions25.

We have used split-pulse XPCS to enable sub-ns dynamics to be measured at hard X-ray FEL sources that operate mostly with pulse spacings in the 10 ms regime2,3. This approach relies on diffractive optics26,27,28,29 capable of splitting individual FEL pulses and introducing a tunable time delay Δ t between the two sub-pulses that both diffract from the sample into a detector and produce a single speckle pattern. Analyzing the contrast of such patterns can give access to the underlying sample dynamics since dynamic processes with time constants longer than Δ t will not influence the contrast, while processes faster than Δ t will lead to a decorrelation of the speckle pattern and thus decrease its contrast. Sample dynamics are then probed by measuring split-pulse speckle contrast β(q, Δ t ) as a function of scattering wave vector q30 and pulse separation. This approach can span timescales from tens of femtoseconds (the pulse width of the FEL) to several nanoseconds, well beyond the time resolution of any X-ray area detector.

Here, we addressed two key issues critical to this approach. First, reliable contrast values can be extracted from single split-pulse pattern only in very exceptional cases31,32. Since averaging of single split-pulse speckle patterns would eliminate the contrast information, we developed a method for reliably extracting contrast values individually from thousands of split-pulse patterns of low photon content from weakly scattering disordered systems. Second, we successfully accounted for the fact that the split-pulse contrast depends on the degree of decoherence (for example geometrical overlap) and splitting ratio between the two beams, both of which will change at today's FEL sources on a shot-to-shot basis.

In this work, we have demonstrated the feasibility of the split-pulse approach by measuring nanosecond dynamics of nanoparticles in suspension. This was accomplished by first calibrating the hard X-ray split-and-delay system at the XCS beamline at the Linac Coherent Light Source (LCLS)33 by determining split-pulse contrast from a static sample. The device was tuned to a pulse delay of 1.3 ns, and split-pulse speckle patterns were obtained from a suspension of 1-nm-radius gold nanoparticles over a range of scattering vectors q. This sample was chosen such that the correlation times τ c  = 1/(D0q2) describing the Brownian motion of the gold particles could be easily tuned to values below and above the selected instrumental delay time Δ t by changing the momentum transfer q. This allowed us to map out the contrast β(q, Δt ) as a function of q for a given Δ t and thus determine the diffusion coefficient. Our results confirm the expected dynamics of the system, and demonstrate the successful application of hard X-ray split-and-delay XPCS at free electron laser sources.

Static split-pulse speckle contrast

The split-pulse XPCS experiment was carried out using the setup shown in Fig. 1. A static film of 150-nm-radius silica particles was used to determine the baseline contrast in terms of the pulse intensity splitting ratio rsp and the degree of decoherence σd of the two pulses at the sample (see Supplementary Note 3). Split-pulse data were collected with a pnCCD area detector34. The average count rates in a single split-pulse frame were in the range of 0.002–0.004 photons/pixel/pulse. A strong split-pulse speckle pattern from the static sample (after processing with photon fitting (see Supplementary Note 1)) is shown in Fig. 2a. A region of interest from this pattern is shown in Fig. 2chighlighting the low probability that a given pixel will contain single, double or triple photon hits. Despite the low count rate of any single split-pulse speckle pattern, the sum and azimuthally averaged mean intensity profile of thousands of such scattering patterns (Fig. 2b, d) show the average scattering behavior expected from the spherical particles.