Multidimensional attosecond photoelectron spectroscopy with shaped pulses and quantum optical fields

Correlation function expressions for multidimensional photoelectron signals obtained for the response of electrons and nuclei in molecules to multiple ultrafast optical or x-ray pulses are derived using a superoperator formalism. For classical fields and quantum matter, these signals are recast as modulus squares of transition amplitudes which depend on the pulse bandshapes. A vibrational wave-packet representation which does not involve amplitudes is derived when the nuclear dynamics is calculated classically. In the case of a quantum radiation field, the signals depend on multipoint correlation functions of field operators. Photoelectron spectroscopy with entangled photons may be studied using this formalism.

Figure 1

Schematic depiction of a photoelectron signal, given by Eq. (12). The shaded area in the left (right) branch of the loop represents $T_{\mathit{fg}}$ ($T_{\mathit{gf}}^{†}$). The signal depends parametrically on the time delays between the various pulses.

Figure 2

The pump-probe pulse configuration. The system interacts with several well-separated pulses, centered at times ${\tau }_i$. The time delays between the pulses are $t_i={\tau }_{i+1}-{\tau }_i$.