Tune-out Wavelength of $\mathbf{^{4}}$He for the $\mathbf{1s2s}$ $\mathbf{^{3}}$S - $\mathbf{1s3p}$ $\mathbf{^{3}}$P Transition

Tune-out wavelengths are those where the dynamic polarizability of an atom is zero. Several applications include laser cooling, atomic clocks and quantum information, all for the Group II atoms [1]. Of the Group II's, helium is a useful subject as it is the simplest atom of two electrons. According to Mitroy and Tang, the tune-out wavelength closest to the $1s2s$ $^{3}S$ - $1s3p$ $^{3}P$ transition for metastable helium can serve as a useful low energy probe of atomic structure [2]. Our calculation of this wavelength, employing a full Hylleraas basis set as well as mass polarization for $^4$He, is 0.11030082982551(1) in reduced mass atomic units. In order to measure this tune-out wavelength, an interferometer is needed [2]. Methods of using laser beams as waveguides for matter waves have been explored, and such techniques can be applied to interferometry as stated by Baldwin et al. [3]. Our future calculations will include relativistic and QED corrections.\\[4pt] [1] B. Arora, M. S. Safronova, and C.W. Clark, Phys. Rev. A \textbf{84}, 043401 (2011).\newline [2] J. Mitroy and L.-Y. Tang, Phys. Rev. A \textbf{88}, 052515, (2013).\newline [3] R. G. Dall, S. S. Hodgman, M. T. Johnsson, K. G. H. Baldwin, and A. G. Truscott, Phys. Rev. A \textbf{81}, 011602(R) (2010).