Treating branch cuts in quantum trajectory models for photoelectron holography

Most implementations of Coulomb-distorted strong-field approaches that contain features such as tunneling and quantum interference use real trajectories in continuum propagation, while a fully consistent approach must use complex trajectories throughout. A key difficulty in the latter case are singularities of the Coulomb potential in the complex time plane. These singularities have the form of branch points which generate corresponding branch cuts. We present a method for treating branch cuts in quantum-trajectory models, which is subsequently applied to photoelectron holography. Our method is not numerically intensive and is applicable to Coulomb-free and Coulomb-distorted trajectories. We show that the presence of branch cuts leads to discontinuities and caustics in the holographic fringes in above-threshold ionization (ATI) photoelectron momentum distributions. These artifacts are removed with our method, provided no hard recollision takes place during the interaction. A comparison with the full solution of the time-dependent Schrödinger equation is also performed, and a discussion of the applicability range of the present approach is provided