Optical cooling of AlH$^+$ to the rotational ground state

We demonstrate cooling of the rotational degree of freedom of trapped diatomic molecular ions to the rotational ground state. The molecule of interested, AlH$^+$, is co-trapped and sympathetically cooled with Ba$^+$ to milliKelvin temperatures in its translational degree of freedom. The nearly diagonal Franck-Condon-Factors between the electronic X and A states of AlH$^+$ create semi-closed cycling transitions between the vibrational ground states of X and A states. A spectrally filtered femtosecond laser is used to optically pump the population to the two lowest rotational levels, with opposite parities, in as fast as 100 $\mu$s via driving the A-X transition. In addition, a cooling scheme relying on vibrational relaxation brings the population to the $N=0$ positive-parity level in as fast as 100 ms. The population distribution among the rotational levels is detected by resonance-enhanced multiphoton dissociation (REMPD) and time-of-flight mass-spectrometry (TOFMS). Although the current two-photon state readout scheme is destructive, a scheme of single-molecule fluorescence detection is also considered.