Isotropic gases irradiated by long pulses of intense IR light can generatevery high harmonics of the incident field. It is generally accepted that, dueto the symmetry of the generating medium, be it an atomic or an isotropicmolecular gas, only odd harmonics of the driving field can be produced. Here weshow how the interplay of electronic and nuclear dynamics can lead to a markedbreakdown of this standard picture: a substantial part of the harmonic spectrumcan consist of even rather than odd harmonics. We demonstrate the effect usingab-initio solutions of the time-dependent Schr\"odinger equation for$H$$_2$$^+$ and its isotopes in full dimensionality. By means of a simpleanalytical model, we identify its physical origin, which is the appearance of apermanent dipole moment in dissociating homonuclear molecules, caused bylight-induced localization of the electric charge during dissociation. Theeffect arises for sufficiently long laser pulses and the region of the spectrumwhere even harmonics are produced is controlled by pulse duration. Our results(i) show how the interplay of femtosecond nuclear and attosecond electronicdynamics, which affects the charge flow inside the dissociating molecule, isreflected in the nonlinear response, and (ii) force one to augment standardselection rules found in nonlinear optics textbooks by consideringlight-induced modifications of the medium during the generation process.
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