State-selective Pump-probe Studies on CO$_{\mathrm{2}}$ with Extreme Ultraviolet (XUV) and Near-infrared (NIR) Pulses*

State-selective excitation to a single (or a small subset of) excited neutral or ionic state(s), versus excitation to many possible states, with a broadband pulse is a powerful tool for the study and control of ultrafast molecular dynamics. We use a single-harmonic extreme ultraviolet (XUV) pulse, produced as the 11$^{\mathrm{th}}$ harmonic of an 800-nm near-infrared (NIR) laser, to ionize carbon dioxide (CO$_{\mathrm{2}})$ to the vibrationally excited ground (X $^{\mathrm{2}}\prod_{\mathrm{g}})$ state or to the first excited (A $^{\mathrm{2}}\prod_{\mathrm{u}})$ state of the mono-cation (CO$_{\mathrm{2}}^{\mathrm{+}})$. Using a delay-controlled NIR probe pulse, the mono-cation is fragmented via different pathways to yield CO$^{\mathrm{+}}$ or O$^{\mathrm{+}}$ fragments. By comparing the results to a second measurement performed with the 13$^{\mathrm{th}}$ harmonic and to a similar pump-probe experiment with a comb of harmonics, where the excited ionic state is determined by photoelectron and photo-ion coincidence, we can clearly separate the role played by each ionic state and confirm the role of molecular rotation in the time-dependent ion yields.