Floquet wavepacket

Second, the properties of Floquet eigenstates are such as to produce a very simple stroboscopic way of following the motion of a general wavepacket of the time-dependent laser-driven system Consider the evolution operator W(f -I- T,t) between times f and t + T. Starting at time t from a Floquet state... 

This shows that the time evolution is exactly like that of a stationary state of a fime-independenf Hamiltonian, provided the probing is limited to T, or any multiple of T. Since, (0)) is equal fo 4> (0)), Eq. (27) also shows fhaf exp ( - iEiT/h) is an eigenvalue of fhe evolution operator over one period of the field. Suppose now thaf we wish to follow fhe developmenf in fime of an arbitrary initial wavepacket rj 0). We can expand it over the complete set of Floquet eigenfunctions of a given Brillouin zone af fime f = 0 ... 

This dependence of the H+ KE on the XUV-IR delay in this case of the longer, 35 fs FWHM, IR pulse can be understood in terms of the adiabatic-ity of the Floquet dynamics underlying the dissociation processes, and the way that the IR intensity affects both the preparation and the propagation of the Floquet components of the wavepackets. More precisely, the IR probe pulse projects the various vibrational components of the wavepacket onto Floquet resonances, whose widths vary with the intensity of the IR pulse. We recall that these resonances are of two types Shape resonances supported by the lower adiabatic potential defined at the one-photon crossing between the dressed (g, n), (u, n ) channels and leading to efficient dissociation through the BS mechanism, or Feshbach resonances, vibrationally trapped in the upper adiabatic potential well. 

The sum is taken over all the discrete vibrational levels if of state g>. Vr (f) is the component of the wavepacket on the g channel evolved up to time t from the field-free vibrational state v > prepared at time f = 0. Note that Pbound(y if) actually represents the total bound state population at any time after tj, since no further decay is then possible, the laser being turned off at such a time. It is clear that Eq. (71) gives a useful approximation for the result of a full time-dependent wavepacket evolution, [Eq. (73)], only if the assumption of an adiabatic transport of Floquet states is valid. 

In order to analyze the dynamics behind each pattern, we show in Fig. 8.2 selected snapshots of wavepackets represented by the squared amplitude of the dominant Floquet state. The time-dependent behavior of the related QESs are also superimposed in the figure. One can observe that the... 

Fig. 8.2 Snapshots of the squared wavepacket amplitude and Floquet quasienergy surface. Each panel shows the snapshot at the time point which is indicated at the right top. For each panel, the black solid line represent the squared amplitude of the dominant Floquet state, and the gray dashed curve does the corresponding quasienergy surface. Another closely related QES is also plotted with black dotted line for reference. Three panels in each vertical row show snapshots of the dynamics starting from the initial vibrational state and the peak field intensity indicated at the top. We also plotted approximate position of resonant points by gray arrow. The arrow in panel (a-1) shows the 3lo resonance point while that in panel (d-3) shows Itv resonance point. (Reprinted with permission from K. Hanasaki et al., Phys. Rev. A 88, 053426 (2013)).

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