Measurement and assignment of E-symmetry states in the 6010-6110 cm−1 and 8940-9150 cm−1 ranges of methane using optical frequency comb double-resonance spectroscopy

We use sub-Doppler optical-optical double-resonance (OODR) spectroscopy with a 3.3 $μ$m single-frequency pump and a cavity-enhanced 1.65 $μ$m comb probe to measure 33 ladder-type (3$ν$${_3}$ ${\leftarrow}$ $ν$${_3}$) and 8 V-type (2$ν$${_3}$) transitions in the 5880-6090 cm$^{-1}$ range of methane, reaching states with rotational E symmetry in the region of the P6 and P4 polyads, respectively. We assign the ladder-type transitions using new Hamiltonian predictions and the ExoMol line list, and the V-type transitions using the new Hamiltonian, ExoMol, HITRAN2020, and the WKLMC line lists. While 7 of the states in the 3$ν$${_3}$ range have been previously observed either in earlier OODR work (without cavity enhancement) with 1.5 MHz accuracy or in FTIR measurements of cold bands with 150 MHz resolution, the states reported here have uncertainties down to 150 kHz (5 $\times$ 10$^{-6}$ cm$^{-1}$). The E-symmetry states exhibit first-order Stark splitting, which will be reported in our future work.