Helium tune-out wavelength: Gauge invariance and retardation corrections

Abstract

The problem of calculating the tune-out wavelength for an atom interacting with a plane electromagnetic wave is formulated as a zero in the Rayleigh scattering cross section, rather than a zero in the dynamic polarizability. Retardation (finite wavelength) corrections are discussed in the velocity gauge, and possible gauge transformations to a length form are investigated. For the special case of S-states, it is shown that a pure length form exists for the leading pxz retardation correction, even though one does not exist in general. The results of high-precision calculations in Hylleraas coordinates are presented for the tune-out wavelength of helium near the 2 3 S − 3 3 P transition at 413 nm.

Measurement of a helium tune-out frequency: an independent test of quantum electrodynamics

“…Separately, we improved on the state-of-the-art calculation ( 28 ) of the tune-out frequency by accounting for finite nuclear mass, relativistic, QED, finite nuclear size, and finite wavelength retardation effects ( 27 , 29 ). We achieved a 10-fold improvement in precision and found a theoretical value of 725,736,252(9) MHz for f TO (−1,0).…”

“…Our measurement was sensitive to the retardation corrections not normally included in the theory of the frequency-dependent polarizability ( 27 , 29 ). The result was an ∼1.7σ difference between experiment and theory, which took into account the estimated uncertainty from terms not currently included in the theoretical calculation.…”

Testing QED by measuring a He* tune-out wavelength

“…Comparison between the first theoretical estimate [1] and our first experimental measurement [2] was limited due to theoretical uncertainty. Recent calculations formulate the tune-out as a zero in the Rayleigh scattering cross-section for an atom interacting with an electromagnetic plane wave [3]. Accounting for perturbative QED corrections, the effect of finite nuclear size, and finite wavelength retardation corrections yields a predicted value of 725.744841(7) THz [4], compared to our first experimental value of 725.7393(16stat)(35syst) THz [2].…”

Measurement of the 671-nm tune-out wavelength of Li7 by atom interferometry

“…There are also many calculations of tune-out wavelengths and, frequently, several tune-out wavelengths are calculated in the same paper. The calculation of the 413nm tune-out wavelength for He * has been made by several research groups [31,32] and in some works with very sophisticated methods [33][34][35]. Many works have been devoted to the alkali atoms: lithium [17,36], including a calculation with Hylleraas wave functions [37], sodium [17], potassium [17,38], rubidium [17,26,27,29], cesium [17], and francium [39,40].…”