Mutually phase-stable tunable attosecond soft X-ray attosecond pulses from a free-electron laser

We demonstrate the production of mutually phase-stable attosecond X-ray pulse pairs with tunable relative time delays and phases in a cascaded X-ray free-electron laser. We showcase the method in an experiment at the LCLS-II, in which a shaped electron beam is used in a split undulator configuration to generate the two attosecond pulses. We achieve mutual phase stability by reusing microbunching generated in the first undulator in order to seed the FEL process in the second at a detuned frequency. We measure controllable temporal delays between the two pulses directly in the time domain using angular streaking of photoelectrons, with a step size of 250 attoseconds. We then show that the behavior of the X-ray spectrum is consistent with phase stability between the two pulses, with a relative phase that can be easily tuned using inter-undulator phase shifters. This method is particularly well-suited to few to ten eV energy separations and sub to few femtosecond time delays, which are ideal for experiments in the soft X-ray regime for pushing the limits of our models for molecular dynamics and exerting direct coherent control over quantum systems.