High-Resolution “Magic”-Field Spectroscopy on Trapped Polyatomic Molecules

Rapid progress in cooling and trapping of molecules has enabled first experiments on high-resolution spectroscopy of trapped diatomic molecules, promising unprecedented precision. Extending this work to polyatomic molecules provides unique opportunities due to more complex geometries and additional internal degrees of freedom. Here, this is achieved by combining a homogeneous-field microstructured electric trap, rotational transitions with minimal Stark broadening at a“magic” offset electric field, and optoelectrical Sisyphus cooling of molecules to the low millikelvin temperature regime. We thereby reduce Stark broadening on the $J=5\leftarrow 4$ ($K=3$) transition of formaldehyde at 364 GHz to well below 1 kHz, observe Doppler-limited linewidths down to 3.8 kHz, and determine the magic-field line position with an uncertainty below 100 Hz. Our approach opens a multitude of possibilities for investigating diverse polyatomic molecule species.

Figure 1

(a) Illustration of the microstructured electric trap (not to scale). (b) Electric field distribution in the trap, based on a 3D electrostatic field simulation. The vertical lines mark the electric field range of the inset in Fig. 2. (c) Simplified sketch of the position-dependent electric fields.

Figure 2

Illustration of concepts used for magic-field spectroscopy. (a) A very flat extremum in the differential Stark shift between a pair of states with the same first-order Stark shift is achieved due to the competition of splittings at very low electric field and higher order Stark shifts at very high electric fields. (b) Differential Stark shift of the transition $|4,3,2⟩\leftrightarrow |5,3,3⟩$ of formaldehyde vs electric field. The minimum is marked with a dashed line in the inset.

Figure 3

Level scheme for spectroscopy on the $|4,3,2⟩\leftrightarrow |5,3,3⟩$ transition. Microwave (MW) transitions are driven between molecular states as shown.

Figure 4

Measured and simulated spectra for various molecule kinetic energy. Two measurements are performed at a higher and lower electric offset field as indicated (center panel), all other measurements are performed at the magic offset field in the trap. The FWHM and fitted magic-field frequency for the magic-field measurements are indicated. The horizontal lines mark the signals measured with the microwave (MW) left off and determine the base lines of the modeled spectra. Error bars and shaded regions specify the $1\sigma$ statistical error.