High-resolution Interferometric Diagnostics for Ultrashort Pulses

8. QUANTUM-PATH INTERFEROMETRY IN HIGH-HARMONIC GENERATIONAnother technique for distinguishing trajectories lies in the different intensity dependence oftheir phases [381, 423]. This can be seen as a special case of the method described in this chapter,obtained when the control field is set equal to the drive field. In simulations, this techniquehas played an important role in understanding HHG, but the difficulty of eliminating macroscopiceffects in experimental situations has made experimental observation challenging. Recently, experimentalconditions with reduced macroscopic effects has provided access to the single-atomresponse, leading to the observation of intensity-dependent interference [424, 425]. This providesestimates of the relative amplitude and phase of the quantum paths, and the proposed method ofthis chapter can be seen as a generalization offering greater precision and flexibility.The use of superposed drive and control fields of different wavelengths is essential to thepresent technique. Such two-color HHG experiments have an extensive history, with results includingsteering electronic motion [367, 426, 427] and temporal gating for isolated attosecondpulse generation [428–430]. For many-cycle drive fields, one ubiquitous effect of adding a controlfield is the appearance of even harmonics due to the broken symmetry between the positiveand negative harmonics. This effect has been used to diagnose the emission times of the quantumpaths [431]. Another concept related to the work of this chapter is heterodyne mixing, in which theeffect of the weak control field is multiplied by the strong drive field. This has been demonstratedthrough a shift in the classical cutoff [432] due to a control field.8.3 Action-shift induced by a weak control-fieldThis section commences the theoretical analysis of control-field mediated quantum-path analysis.The aim of this section is to derive, within in the framework of the SFA, the change in the actionintegral, and hence the change in phase, of a quantum path in response to a weak control field.8.3.1 Single orbit analysisOne writes the electric field as the sum of a strong drive field D (t ) and a weak control field θ C (t ),where θ parameterizes the strength of the control field: (t )= D (t )+θ C (t ). (8.1)188