Control of the blackbody radiation shift in hydrogen and hydrogen-like optical computable clocks using a magic temperature

The blackbody radiation (BBR) shift is a significant systematic shift for atomic clocks on the 10 −18 scale. We investigate the BBR shift of the hydrogen and hydrogen-like systems and present a method to reduce the uncertainty due to the BBR shift of the 1S–2S clock transition to the 10 −21 range. This feature is due to the single-electron system’s energy level structure and a close dipole-allowed resonance to the excited 2S state. We present detailed calculations and analyses of the magic temperature where the BBR shift mathematically cancels. We also present the operational magic temperature, a stationary point where the shift becomes insensitive to the temperature. This shift is precisely calculable, in contrast to all other optical clocks.