Fig. 2: Spectroscopic nature of Keldysh Green’s function G<.
From: Sub-cycle multidimensional spectroscopy of strongly correlated materials
a, Cartoon view of the key many-body states corresponding to the spectroscopic signal at energies of the LHB, QP and UHB. The orange circles stand for lattice sites; green circle, an electron localized on a lattice site; white arrows, orientation of electron spin; grey circle and grey cloud, a delocalized electron; and two oppositely oriented white arrows, a doubly occupied site. The double-headed arrows indicate the possible sub-cycle transitions driven by the field in the phase-locking regime (Fig. 1f). b, Scanning delay τ between the pump and probe pulses (violet) and delay t between the pump–probe pair and the control pulse (red) form a two-dimensional dataset for Green’s function G<(t, t − τ), emulating the photoionization signal. Scanning the CEP (ϕCEP) of the control pulse yields the third dimension of the spectroscopic signal G<(t, t − τ, tCEP). c, Fourier transform of G<(t, t − τ, tCEP) with respect to all the arguments yields G<(Ωτ, Ωt, ΩCEP). A cartoon view of ∣G<(Ωτ, Ωt, ΩCEP)∣ for Ωτ fixed at the energy corresponding to the LHB. The red–brown peaks illustrate the associated Floquet ladder representing the laser-dressed LHB state. The appearance of green peaks at QP ± nω and UHB is due to non-adiabatic transitions between the laser-dressed states, namely, LHB ↔ QP and UHB ↔ QP. The extension of green peaks in the ΩCEP dimension quantifies the sub-cycle response time.
