The First Measurement of the $2^{3\!}S_1 - 2^{3\!}P / 3^{3\!}P$ Tune-Out Wavelength in He*

Abstract: The workhorse of atomic physics, quantum electrodynamics, is one of the best-tested theories in physics. However recent discrepancies have shed doubt on its accuracy for complex atomic systems. To facilitate the development of the theory further we aim to measure transition dipole matrix elements of metastable helium (He*) (the ideal 3 body test-bed) to the highest accuracy thus far. We have undertaken a measurement of the `tune-out wavelength' which occurs when the contributions to the dynamic polarizability from all atomic transitions sum to zero; thus illuminating an atom with this wavelength of light then produces no net energy shift. This provides a strict constraint on the transition dipole matrix elements without the complication and inaccuracy of other methods. Using a novel atom-laser based technique we have made the first measurement of the tune-out wavelength in metastable helium between the $3^{3}P_{1,2,3}$ and $2^{3}P_{1,2,3}$ states at 413.07(2) nm which compares well with the predicted value [PhysRevA.88.052515] of 413.02(9) nm. We have additionally developed many of the methods necessary to improve this measurement to the 100 fm level of accuracy where it will form the most accurate determination of transition rate information ever made in He* and provide a stringent test for atomic QED simulations. We believe this measurement to be one of the most sensitive ever made of an optical dipole potential, able to detect changes in potentials of $\sim$200 pK and is widely applicable to other species and areas of atom optics.