Unveiling hidden wavepacket dynamics in time-resolved x-ray scattering data via singular spectrum analysis

Time-resolved x-ray liquidography (TRXL) is a powerful technique for directly tracking ultrafast structural dynamics in real space. However, resolving the motion of vibrational wavepackets generated by femtosecond laser pulses remains challenging due to the limited temporal resolution and signal-to-noise ratio (SNR) of experimental data. This study addresses these challenges by introducing singular spectrum analysis (SSA) as an efficient method for extracting oscillatory signals associated with vibrational wavepackets from TRXL data. To evaluate its performance, we conducted a comparative study using simulated TRXL data, demonstrating that SSA outperforms conventional analysis methods such as the Fourier transform of temporal profiles and singular value decomposition, particularly under low SNR conditions. We further applied SSA to experimental TRXL data on the photodissociation of triiodide ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>I</mml:mi></mml:mrow> <mml:mn>3</mml:mn> <mml:mo>-</mml:mo></mml:msubsup> </mml:mrow> </mml:mrow> </mml:math> ) in methanol, successfully isolating oscillatory signals arising from wavepacket dynamics in ground-state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>I</mml:mi></mml:mrow> <mml:mn>3</mml:mn> <mml:mo>-</mml:mo></mml:msubsup> </mml:mrow> </mml:mrow> </mml:math> and excited-state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>I</mml:mi></mml:mrow> <mml:mn>2</mml:mn> <mml:mo>-</mml:mo></mml:msubsup> </mml:mrow> </mml:mrow> </mml:math> , which had been challenging to resolve in previous TRXL studies. These results establish SSA as a highly effective tool for analyzing ultrafast structural dynamics in time-resolved experiments and open new opportunities for studying wavepacket dynamics in a wide range of photoinduced reactions.