High-resolution Interferometric Diagnostics for Ultrashort Pulses

8. QUANTUM-PATH INTERFEROMETRY IN HIGH-HARMONIC GENERATIONradiation. However, the probability amplitudes for the birth and recombination are not describedby the SFA. Instead, they are given by the atomic and/or molecular structure of the target species,which may potentially be in a highly perturbed and dynamic state. When HHG is viewed as aprobe of atomic and/or molecular structure and dynamics (as opposed to as a source of radiationfor other purposes), these amplitudes are the very information that one is seeking. In this context,the quantum orbits model is a means of connecting the (potentially rather complex) features ofthe emitted radiation to the atomic/molecular physics of the target species. However, when multiplequantum orbits are present, their contributions must be disentangled. Furthermore, it maybe useful to acquire amplitudes from multiple quantum orbits simultaneously.A specific example is the ultrafast dissociation of hydrogen discussed in section 6.1.2. Here,macroscopic phase matching was used to isolate the short trajectory, whilst a repetition of themeasurement with deuterium provided a calibration of the returning electron wavepacket. If onecould detect the short and long trajectories simultaneously, and possibly even higher-order trajectories,it would extend the time range of the experiment and possibly offer a self-referenced meansof characterizing the returning electron wavepacket without using a deuterated substitute. This isthe first motivation for experimental quantum path analysis.Despite its power, in many ways the SFA, upon which the standard quantum orbits model isbased, is a gross approximation. It ignores the effect of the laser on the ground state and the effectof the atomic/molecular potential on the continuum states, even during recombination whenthe electron overlaps with the core. Whilst good quantitative agreement with the TDSE has beenachieved for very high photon energies (compared to the ionization potential) and simple systems,the concordance breaks down at photon energies approaching the ionization potential, andis also expected to become inaccurate as the molecular size increases. However, the breakdownof the SFA does not necessarily prevent the use of the SPA and hence a quantum orbits approach,because the two sets of approximations are distinct and in many ways independent. The SFA isan approximation to the quantum mechanics: its essence is the partitioning of the wavefunctioninto core and continuum components, and the application of approximate, easily solvable Hamiltoniansto each component. By contrast, the SPA, which leads to the quantum-orbits model, is a186