2021, Habibović, Dino, Becker, Wilhelm, Milošević, Dejan B.

Using the strong-field approximation we systematically investigate the selection rules for high-order harmonic generation and the symmetry properties of the angle-resolved photoelectron spectra for various atomic and molecular targets exposed to one-component and two-component laser fields. These include bicircular fields and orthogonally polarized two-color fields. The selection rules are derived directly from the dynamical symmetries of the driving field. Alternatively, we demonstrate that they can be obtained using the conservation of the projection of the total angular momentum on the quantization axis. We discuss how the harmonic spectra of atomic targets depend on the type of the ground state or, for molecular targets, on the pertinent molecular orbital. In addition, we briefly discuss some properties of the high-order harmonic spectra generated by a few-cycle laser field. The symmetry properties of the angle-resolved photoelectron momentum distribution are also determined by the dynamical symmetry of the driving field. We consider the first two terms in a Born series expansion of the T matrix, which describe the direct and the rescattered electrons. Dynamical symmetries involving time translation generate rotational symmetries obeyed by both terms. However, those that involve time reversal generate reflection symmetries that are only observed by the direct electrons. Finally, we explain how the symmetry properties, imposed by the dynamical symmetry of the driving field, are altered for molecular targets.

2020, Esquembre Kučukalić, Ali, Becker, Wilhelm, Milošević, Dejan B.

We consider the problem of the choice of gauge in nonrelativistic strong-laser-field physics. For this purpose, we use the phase-space path-integral formalism to obtain the momentum-space matrix element of the exact time-evolution operator. With the assumption that the physical transition amplitude corresponds to transitions between eigenstates of the physical energy operator rather than the unperturbed Hamiltonian H0=(−i∂/∂r)2/2+V(r), we prove that the aforementioned momentum-space matrix elements obtained in velocity gauge and length gauge are equal. These results are applied to laser-assisted electron-ion radiative recombination (LAR). The transition amplitude comes out identical in length gauge and velocity gauge, and the expression agrees with the one conventionally obtained in length gauge. In addition to the strong-field approximation (SFA), which is the zeroth-order term of our expansion, we present explicit results for the first-order and the second-order terms, which correspond to LAR preceded by single and double scattering, respectively. Our general conclusion is that in applications to atomic processes in strong-field physics the length-gauge version of the SFA (and its higher-order corrections) should be used. Using the energy operator as the basis-defining Hamiltonian, we have shown that the resulting transition amplitude is gauge invariant and agrees with the form commonly derived in length gauge.