## 3 Actively Phase-Stabilized Continuous Optical Delay Scan with Attosecond Timing Accuracy
(**a**) Power spectral density for the upper layer (IL) (red), lower layer (OOL) with PID control (blue), and lower layer (OOL) without PID control (green) measurements. The instrument noise floor for the respective interferometers is shown in lighter colors. (**b**) Integrated timing jitter calculated from the PSD shown in (**a**). Temperature-related long-term drift is notable below ~0.4 mHz. The inset shows the time-domain measurement of the drift, which is significantly reduced by the active stabilization on longer time scales. of optical power on the respective photodiodes, effecting a higher noise floor and thus a higher apparent timing jitter in the upper layer measurement due to electronic noise. However, only the lower layer measurement provides the relevant stability assessment and upper limit for timing drift in pump-probe experiments, since it uses the DUV/XUV beam path. It is also worth emphasizing that the free-running measurement (PID control disabled) exhibits excellent passive stability across the entire frequency range due to careful vibrational decoupling of the delay chamber from the environment, maintaining a sub-20 as RMS timing jitter down to \(\sim\)0.4 mHz (\(\sim\)40 min). This is why active PID control only slightly improves the drift and jitter within this frequency range. The PID controller feedback loop operates close to its sensitivity limit as evidenced by its low-frequency behavior (\(<\)1 Hz), where the residual in-loop timing error exhibits a similar behavior as the natural (free-running) drift PSD (though it has only a negligible contribution to the integrated jitter). Temperature fluctuations in the laboratory on longer time scales lead to a total peak-to-peak timing drift of about 310 as over the 2 h measurement time without active PID control (see inset in Figure 3b). In contrast, the active stabilization reduces this long-term drift significantly to \(\sim\)80 as peak-to-peak. This residual lower-layer (OOL) drift, despite of active PID control, is due to differential mechanical drift of the two interferometer layers with temperature. A more rigid mount construction, e.g., a twin mirror mount from a single piece of metal, as well as better temperature control in the laboratory and in particular within the delay chamber could readily improve this temperature-related drift. In addition, an electronic low-pass filter at the output of the PID controller can be used to ensure the excellent passive performance above \(\sim\)15 Hz while reducing the timing drift at lower frequencies. This measurement demonstrates that the passive stability of our DLI is already sufficient to perform short-time (less than 40 min) measurements with sub-20 as RMS accuracy without using the PID controller. Active stabilization enables longer measurements over hours and potentially improves short-term stability if electronic high-frequency noise from the PID controller system is filtered out. The main purpose of the DLI is to provide a phase-locked continuous delay scan while maintaining attosecond timing precision. Figure 4 demonstrates a phase-locked continuous scan over the full optical delay range of 200 fs. The optical delay was scanned in \(\sim\)80 as steps by rotating the polarizer while maintaining active stabilization. At each delay position, the lower-layer (OOL) interference signal was sampled at a \(\sim\)83 kHz rate for 2 s. The averaged lower-layer signal is shown in Figure 4a with the interference fringes normalized to the \([-1,\,1]\) interval after fitting a sine function to the data. The fit yields a wavelength of 634.8 nm, which is within 0.3% of the actual 632.8 nm HeNe wavelength. After normalizing the sampled lower-layer signal, the signal spread at each delay step can be easily converted into optical delay jitter by applying the inverse sine function and calculating the standard deviation, which is depicted in Figure 4b.