Controlling electron quantum paths for generation of circularly polarized high-order harmonics by H2+ 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 $\omega$ by using tailored bichromatic ($\omega$, $2\omega$) 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 ($\omega$, $2\omega$) 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.