## 1 Introduction  
The control of material processes at the level of electron motion in real time has become one of the significant issues in fundamental science [1, 2, 3]. The triggering and complete measurement of valence orbitals of neutral electronic systems, which are the most relevant for chemical functions, has hitherto remained inaccessible. For the control of chemical dynamics in a new paradigm, therefore, we need to understand the dynamics beyond the Born Oppenheimer approximation where the electronic states are not stationary and influential. We need to explore how nonstationary electronic states are coupled to nuclear motion and subsequently understand how the manipulation of the electronic motion can be used to trigger a selective motion of the nuclei, thereby implementing a chemical reaction pathway [4, 5, 6, 7, 8, 9, 10]. Ultrafast charge migration and conical intersection dynamics are a few examples among many chemical dynamics [11, 12]. Ultrafast migration of a charge driven by electron correlation is manifested when ultrashort ultraviolet (UV) laser pulses create electronic wave packets, triggering pure electron dynamics in an ionized system [13].  
To facilitate our understanding and control of chemical dynamics in a new paradigm, an intense few-cycle deep-UV (DUV) beamline combined with ultrashort near-infrared(NIR) pulses and extreme ultraviolet (XUV) pulses for time-resolved experiments has been developed. Numerous studies have been conducted using the frequency upconversion method in noble gases to generate few-cycle DUV pulses [14; 15; 16] and XUV pulses [17; 18; 19].  
For investigations of few-cycle dynamics with high time resolution, the timing jitter between the pump and probe pulses should be controlled on the attosecond time scale. Several active stabilization methods have been established and are being used in the case of XUV pulses combined with a NIR beam [20; 21; 22]. The majority of them use a collinear scheme in which a continuous wave (CW) laser co-propagates as a reference together with the XUV and/or NIR beams in an interferometry setup. However, when few-cycle DUV pulses are combined with XUV pulses in the beamline, such a collinear scheme with a CW laser is not feasible due to spectrally incompatible dielectric and dichroic optics along the beam paths. To overcome these difficulties, a double-layer interferometry (DLI) system was implemented, providing an upper-layer beam path for the reference CW laser and a lower-layer path for the DUV and XUV beams with their respective specialized optics, while maintaining strong mechanical coupling via custom made Al double-mirror mounts and sharing the same mechanical delay stage. Thus, stabilizing and scanning the optical phase in the reference upper-layer interferometer ensures the same behavior of the lower-layer interferometer's beam path, since both layers are mechanically locked. Additionally, in conventional setups, the relative phase between the two arms of the interferometer must be relocked at each delay step because the intentional delay change breaks the relative phase relationship between the two arms. This becomes an issue when the data acquisition takes a long time and requires automation.  
In our DUV/XUV beamline, the DLI system is capable of continuous delay change while maintaining the relative phase between the two interferometer arms. We demonstrate that the relative phase between the few-cycle DUV and XUV arms can be maintained down to a precision of \(\sim\)13 as root-mean-square (RMS) on a few-second time scale with a maximum peak-to-peak phase drift of \(\sim\)80 as over 2 h while continuously scanning the delay for the pump-probe experiment.