## 1 Introduction
The time-energy bandwidth product results in broad energy distribution in the continuum in the case of a single-attosecond pulse (SAP, green) and two narrow lines in the case of an attosecond pulse train (APT, red). The continuum wave packet \(\Phi(z)\), i.e., a single electron wave packet (streaking) or an electron pulse train (RABBITT), travels toward the surface and is emitted into the vacuum (schematic wave packet and laser-pulse plots are not true to scale). As soon as the photoelectron leaves the surface, it starts interacting with the infrared (IR) pulse (violet). In the case of a single electron wave packet, the energy distribution accumulates a shift determined by IR vector potential. This results in a streaking spectrogram (upper-right panel). Here, the white solid line corresponds to the streaked momentum expectation value, while the white dashed line corresponds to the momentum expectation value without IR interaction. White vertical lines indicate the delay between streaking trace and zero IR-EUV pulse delay. If it is excited by an APT (RABBITT), at each half-cycle of the IR field, a photoelectron wave packet is emitted. Absorption and emission of IR photons leads to the formation of side bands in the RABBITT spectrum (lower-right panel). Intensity oscillation in the central side band (between white dashed lines) is shifted with respect to zero IR-EUV pulse delay (white vertical lines). In a streaking experiment, the photoelectron is excited at \(t=0\) inside the solid. At a certain point in time \(t_{\text{PE}}\), when the electron passes the surface, the electron starts interacting with the IR field in the vacuum that, in our model, is completely screened inside the material. This photoemission time \(t_{\text{PE}}\) corresponds to the time that the whole photoemission process takes from excitation until emission into the vacuum. In a classical picture, photoemission time \(t_{\text{PE}}\) is the transport time from the emitter atom to the surface. In vacuum, the electron is accelerated by the IR field in its polarization direction (Figure 1a):  
\[\dot{p}(t)=-e\ E_{\text{IR}}(t). \tag{1}\]  
After the IR pulse has interacted with the photoelectron (\(t\rightarrow\infty\)), the photoelectron has acquired the momentum  
\[ \begin{split} p(t=\infty)=p_{0}-e&\int_{t_{\text{PE }}}^{\infty}dt\ E_{\text{IR}}(t-\tau_{\text{IR-EUV}})=p_{0}-eA_{\text{IR}}(t_{ \text{PE}}-\tau_{\text{IR-EUV}})\\ &\simeq p_{0}-eA_{\text{IR}}\Big{(}\tau_{\text{streaking}}-\tau_ {\text{IR-EUV}}\Big{)}\.\end{split}  \tag{2}\]  
Hence, variation of IR-EUV time delay results in a replica of the vector potential \(A_{\text{IR}}\) of IR pulse shifted by a delay \(\tau_{\text{streaking}}\) with respect to zero delay between EUV and IR pulse (upper-right panel of Figure 1). Equation (2) is valid for vanishing IR fields inside the solid, and instantaneous EUV excitation [29]. Under these conditions, streaking delay \(\tau_{\text{streaking}}\) is equal to absolute photoemission time \(t_{\text{PE}}\)[22]. Note that this is a rather classical view on the streaking process, motivated here by the fact that the correspondence principle is applicable. The quantum wave packet for the streaking process converges toward classical behavior for large quantum numbers. In a RABBITT experiment, an attosecond pulse train is used to photoexcite the system. The excitation spectrum consists of a series of rather narrow lines located at the odd multiples of fundamental energy \(E_{\text{kin}}=N\hbar\omega_{\text{IR}}-\varepsilon_{0}\), where \(\varepsilon_{0}\) is the initial state energy of the core level under investigation (Figure 1b) [2]. The photoelectron wave packet is then composed of several subpulses. Interaction with the IR field leads to side bands in photoemission spectra located at the even multiples of fundamental IR energy \(N\hbar\omega_{\text{IR}}-\varepsilon_{0}\) by absorbing or emitting an additional IR photon. This is the well-known laser-assisted photoemission process at solid surfaces (LAPE) [30].