In high-harmonic generation (HHG), ultraviolet and soft x-ray radiation is produced by the laser-driven recollision of an electron with its parent ion. The radiated field is well described by the quantum version of the three-step model [1], in which the quantum paths associated with classical electron trajectories are summed coherently [2]. Generally, several quantum paths contribute to the same harmonic frequency of the single-atom response, although the macroscopic conditions are often chosen such that certain paths dominate the observed field. If the conditions are such that multiple paths are observed, then at present it is not possible to discern the amplitudes and phases of the contributions; only their sum is experimentally available. However, the ability to “decompose” the observed field into individual quantum-path contributions would be useful: it could extend the time range of attosecond dynamics experiments [3] and enable observation of weaker contributions such as multiple return trajectories and recently suggested continuum-continuum interference [4]. Here, we propose a general technique towards this end: we perform quantum-path interferometry (QPI) by perturbing the phase of each quantum path using one or more control fields. Because each path responds differently to the control field, each can be distinguished. We shall develop the theory of QPI and provide numerical examples illustrating the retrieval the amplitude and relative phases of an arbitrary number of contributions, including those from long, short and multiple-return trajectories.
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