Negative-travel-time quantum orbits in strong-field ionization by an elliptically polarized laser field

A long-standing problem in quantum-orbit theory has been exactly which solutions of the saddle-point equations to include in the decomposition of the ionization or harmonic-generation amplitude. Up to now, solutions corresponding to a negative travel time have always been discarded. For the case of an elliptically polarized driving laser field, we show that certain solutions with a negative travel time are relevant and have to be included, in addition to the customary orbits with positive travel times, in order to achieve good agreement with the result of a numerical evaluation. In fact, these solutions are responsible for a pronounced qualitative effect in the high-order above-threshold ionization amplitude: a feature with the shape of a coffee bean split along the direction of the major polarization axis, which dominates the velocity map especially for long wavelength. We also discuss the electron trajectories in complex space and time that correspond to these orbits.