Experimental advances in the production of cold molecules in the last years have triggered a flurry of theoretical work in fields as diverse as precision spectroscopy, controlled chemistry, fundamental physics, or quantum computation and simulation [1,2]. Progress on these lines naturally demands an increasing level of precision in the measurement and control of molecular states and properties. In this talk, I will present two of our recent contributions to this end. First, I will review some ideas and tools of cold atomic physics and quantum information that underlie our work. Then, I will introduce a quantum spectroscopy protocol for molecular ions based on their interaction with trapped atomic ions and phase gates [3]. After this, I will show how these ideas can be generalized to enable the measurement of a polar molecule's electric dipole moment [4]. Finally, I will discuss some of our ongoing work to use cold polar molecules for quantum simulation and quantum metrology.
We have developed a combined Stark-velocity-filter--ion-trap apparatus for the purpose of reaction-rate measurements between cold trapped ions and slow polar molecules under ultrahigh vacuum conditions. The prerequisite steps such as the characterization of velocity-selected polar molecules (PM), namely ND
3, H
2CO, and CH
3CN, were performed using time-of-flight (TOF) measurements. We confirmed the generation of slow ND
3, H
2CO, and CH
3CN molecules having thermal energies of a few Kelvin. Additionally, the number densities of the slow velocity-filtered polar molecules were determined to be in the range of
n=104 to 10
6 cm${}^{\ensuremath{-}3}$ by calibrating the TOF signals. In a first experiment, the Stark velocity filter was connected to a cryogenic linear Paul trap and reaction-rate measurements between laser-cooled Ca
+ Coulomb crystals and velocity-selected polar molecules were carried out. The observed reaction rates are of the order of 10${}^{\ensuremath{-}5}$ s${}^{\ensuremath{-}1}$, which are much slower than typical reaction rates of molecular ion--polar-molecule reactions at low temperatures. The present results confirm that reaction-rate measurements between velocity-selected polar molecules and sympathetically cooled molecular ions cooled by a laser-cooled Ca
+ Coulomb crystal can be performed. Next we measured the reaction rates between sympathetically cooled nonfluorescent stored ion molecules namely N
2H
+ ions and velocity-selected CH
3CN molecules at the average reaction energy of about 3 K. The measured reaction rate of 2.0(2)$\ifmmode\times\else\texttimes\fi{}
10{}^{\ensuremath{-}3}$ s${}^{\ensuremath{-}1}$ is much faster than those of the Ca
++PM reactions. This is strong evidence that the velocity-selected polar molecules undergo reactive collisions. We also confirmed that the present reaction-rate constant of CH
3CN+N
2H
+ $\ensuremath{\rightarrow}$ CH
3CNH
++N
2 is consistent with the estimated values from the room temperature results and the trajectory-scaling formula of Su et al. In the future, the present velocity-filter combined cryogenic trap apparatus will enable us to perform systematic measurements of cold ion--polar-molecule reactions, which are important problems from a fundamental viewpoint and also contribute to astrochemistry.