Magic Wavelength for Hydrogen 1S-2S Transition

TL;DR

This paper calculates the magic wavelength for hydrogen's 1S-2S transition to optimize optical trapping and minimize AC Stark shifts, aiding high-precision spectroscopy.

Contribution

It determines the specific magic wavelength at 513 nm for hydrogen, enabling better optical trapping conditions for precision measurements.

Findings

Magic wavelength at 513 nm for hydrogen 1S-2S transition.

AC Stark shift magnitude of -1.19 kHz/(10kW/cm^2).

Slope of shift at magic wavelength is -27.7 Hz/(GHz·10 kW/cm^2).

Abstract

The magic wavelength for an optical lattice for hydrogen atoms that cancels the lowest order AC Stark shift of the 1S-2S transition is calculated to be 513 nm. The magnitude of AC Stark shift $\Delta E=-1.19$ kHz/(10kW/cm$^2$) and the slope $d\Delta E/d\nu = -27.7$ Hz/(GHz $\cdot$ 10 kW/cm$^2$) at the magic wavelength suggests that a stable and narrow linewidth trapping laser is necessary to achieve a deep enough optical lattice to confine hydrogen atoms in a way that gives a small enough light shift for the precision spectroscopy of the 1S-2S transition.