Fig. 1. Experimental scheme. (a) Schematic illustration of the experimental setup to study the RSE of the ${\mathrm{H}}_2$ molecules with BCTC laser fields. (b), (c) Measured (b) PEPICO and (c) PIPICO spectrum of the ${\mathrm{H}}_2$ molecule. The ${\mathrm{H}}_2^{+}$ signals created from the postpulse ionization of ${{\mathrm{H}}_2}^{*}$ and from the strong-field ionization ${\mathrm{H}}_2$ can be distinguished in the PEPICO spectrum, while the $({\mathrm{H}}^{+},{\mathrm{H}}^{*})$ and $({\mathrm{H}}^{+},{\mathrm{H}}^{+})$ channels can be unambiguously identified in the PIPICO spectrum. (d), (e) Combined electric fields $E_y$ versus $E_z$ as well as the corresponding vector potential $A_y$ versus $A_z$ for the (d) counterrotating and (e) co-rotating circularly polarized two-color laser fields with a field ratio of $E_{\mathrm{SH}}/E_{\mathrm{FW}}=1.5$.

Fig. 2. Manipulation of RSE yield by BCTC laser pulses. (a) Experimentally measured yields of the Rydberg fragments of ${{\mathrm{H}}_2}^{*}$ and $({\mathrm{H}}^{+},{\mathrm{H}}^{*})$ channels created in the interaction of the ${\mathrm{H}}_2$ molecules with BCTC laser fields. Solid and open symbols represent the counterrotating and co-rotating cases, respectively. The thick arrows near the right ordinate indicate the measured yield of the ${{\mathrm{H}}_2}^{*}$ and $({\mathrm{H}}^{+},{\mathrm{H}}^{*})$ channels employing a single-color SH circularly polarized laser pulse. The yield of each data point is normalized to a single laser shot. (b) The corresponding yield ratios between the counterrotating and co-rotating cases of the RSE channels displayed in panel (a). The shapes of combined electric fields of the BCTC fields for different field ratios and polarization helicities are illustrated in the inset of panel (b). (c) Numerically simulated Rydberg yields of ${\mathrm{H}}^{*}$ for the counterrotating and co-rotating cases of the BCTC laser pulse. The yield of each data point is normalized to the simulated total number of released electrons. The right ordinate shows the inverse of the magnitude of the vector potential $[-A(t)]$ of the counterrotating and co-rotating fields where the field amplitude maximizes. The case without the photon effect is shown in blue, and the other case with the photon effect included is shown in orange. (d) The corresponding yield ratios between the counterrotating and co-rotating cases of the simulated Rydberg yield of ${\mathrm{H}}^{*}$ for the two cases in panel (c).

Fig. 3. Field-ratio-resolved KER spectra of the fragmentation channels in the co-rotating case. (a), (b) Measured KER distributions of the nuclear fragments of (a) the $({\mathrm{H}}^{+},\mathrm{H})$ channel and (b) the $({\mathrm{H}}^{+},{\mathrm{H}}^{*})$ channel using co-rotating BCTC laser fields at various $E_{\mathrm{SH}}/E_{\mathrm{FW}}$ (colored solid curves) as well as applying single SH pulses (black dashed curves) with an intensity of $\sim 6.0\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.