Generalized velocity-gauge form of the light-matter interaction Hamiltonian beyond the dipole approximation

Abstract

The exact velocity-gauge minimal-coupling Hamiltonian describing the laser-matter interaction is transformed into another form by means of a series of gauge transformations. The Hamiltonian corresponding to this point of view is valid for an arbitrary time- and space-dependent laser field, also known as a nondipole field. In effect, the Hamiltonian represents a generalization of the original velocity-gauge minimal-coupling Hamiltonian in the sense that the particle's (classical) velocity in the laser propagation direction is also explicitly accounted for by a new operator term. Imposing the so-called long-wavelength approximation (LWA) on the field, i.e., assuming the laser wavelength being much larger than the extent of the atomic system, the spatial dependence of the field can be neglected and the interaction Hamiltonian reduces to a simpler form. Nevertheless, the resulting LWA Hamiltonian includes the effect of the magnetic-field component of the laser, which is in clear contrast with the usual dipole approximation Hamiltonian derived by imposing the LWA directly on the initial velocity-gauge minimal-coupling Hamiltonian. As such, the weak-field condition necessary to justify neglecting the magnetic field, and the LWA condition, can be considered independently in this formalism, making it an attractive alternative for a broad range of applications in strong-field physics. We demonstrate that, from a numerical perspective, this form of the light-matter interaction is advantageous compared to its standard velocity-gauge counterpart as it gives rise to faster convergence properties when describing ionization dynamics in superintense fields beyond the dipole approximation.