High-resolution Interferometric Diagnostics for Ultrashort Pulses

8.2 Related workgeneral technique for recovering classical mechanics, or semi-classical interpretations, from thepath-integral formulation of quantum mechanics. Mathematically, it is an asymptotic approximationto the path integral which becomes exact in the limit ħh → 0. Whether or not the underlyingquantum mechanics is exact or an approximation is in principle immaterial for its application.The implications of this for HHG and other strong-field processes is that going beyond theSFA does not necessarily mean losing the quantum orbits picture. It simply means that the natureof the quantum orbits will change. For example, including the effect of the core potential on theorbits may change their birth and return times, and will require corrections to the action integral.More drastic corrections in some hypothetical theory may change the parameterization (currentlybirth time, return time, and canonical momentum) itself. Regardless of the details, provided thati) the result is expressed as an integral over paths and ii) some of the important processes areamenable to classical interpretation, the SPA will be applicable and accurate, yielding both usefulphysical insight and computational efficiency by reducing the integral to a sum. This leads to thesecond motivation for experimental quantum path analysis: the ability to simultaneously observethese stationary paths at once independently and as a whole.8.2 Related workQuantum path analysis has been a key plank in the theory of HHG since the development of theLewenstein model [368]. Almost all numerical models which do not involve direct solution of theTDSE involve some form of quantum path analysis, whilst experimental methods exist to restrictefficient harmonic production to only a single quantum path. However, the technique describedin this chapter distinguishes the contributions of quantum paths in the single-atom response itself(as opposed to theoretical analyses starting from the laser field). One technique, similar inintent, is spectrography, which separates quantum paths based on their different emission timesand frequencies. The limitation of spectrography is that it requires full amplitude and phase characterizationof the harmonics which is generally not achieveable for experimental data. Spectrographyis therefore primarily used in interpreting the results of simulations. Furthermore it cannotdistinguish between trajectories with similar return times and emission frequencies.187