Controlling electron quantum paths for generation of circularly polarized high-order harmonics by H 2 + subject to tailored (ω, 2ω) counter-rotating laser fields

Recently, studies of high-order harmonics (HHG) from atoms driven by bichromatic counter-rotating circularly polarized laser fields as a source of coherent circularly polarized extreme ultraviolet (XUV) and soft-x-ray beams in a tabletop-scale setup have received considerable attention. Here, we demonstrate the ability to control the electron recollisions giving three returns per one cycle of the fundamental frequency $\ensuremath{\omega}$ by using tailored bichromatic ($\ensuremath{\omega}$, $2\ensuremath{\omega}$) counter-rotating circularly polarized laser fields with a molecular target. The full control of the electronic pathway is first analyzed by a classical trajectory analysis and then extended to a detailed quantum study of ${\mathrm{H}}_{2}{}^{+}$ molecules in bichromatic ($\ensuremath{\omega}$, $2\ensuremath{\omega}$) counter-rotating circularly polarized laser fields. The radiation spectrum contains doublets of left- and right-circularly polarized harmonics in the XUV ranges. We study in detail the below-, near-, and above-threshold harmonic regions and describe how excited-state resonances alter the ellipticity and phase of the generated harmonic peaks.