The dynamic dipole polarizabilities for the four lowest triplet states (
23S,33S,23P, and
33P) of helium are calculated using the
B-spline configuration interaction method. Present values of the static dipole polarizabilities in the length, velocity, and acceleration gauges are in good agreement with the best Hylleraas results. Also the tune-out wavelengths in the range 400 nm--4.2 $\ensuremath{\mu}\mathrm{m}$ for the four lowest triplet states are identified, and the magic wavelengths in the range 460 nm--3.5 $\ensuremath{\mu}\mathrm{m}$ for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}S, 2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{3}P$, and $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}P$ transitions are determined. We show that the tune-out wavelength of
23S state is
413.03828(3) nm, which corroborates the value of Mitroy and Tang [Phys. Rev. A 88, 052515 (2013)], and the magic wavelength around 1066 nm for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}3{\phantom{\rule{0.16em}{0ex}}}^{3}P$ transition can be expected for precision measurement to determine the ratio of transition matrix elements $(2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{3}P)/(3{\phantom{\rule{0.16em}{0ex}}}^{3}P\ensuremath{\rightarrow}6{\phantom{\rule{0.16em}{0ex}}}^{3}S)$.
The six longest tune-out wavelengths for the He(
1s2s3S1e) metastable state are determined by explicit calculation. The tune-out wavelength at 413.02 nm is expected to be sensitive to finite mass, relativistic, and quantum electrodynamic effects upon the transition matrix elements and its measurement would provide a nonenergy test of fundamental atomic structure theory.
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
33P1,2,3 and
23P1,2,3 states at 413.07(2) nm which compares well with the predicted value\cite{Mitroy2013} 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.