Combined atomic clock with blackbody-radiation-shift-induced instability below 10−19 under natural environment conditions

We develop a method of synthetic frequency generation to construct an atomic clock with blackbody radiation (BBR) shift uncertainties below 10 ^−19 at environmental conditions with a very low level of temperature control. The proposed method can be implemented for atoms and ions, which have two different clock transitions with frequencies ν _1 and ν _2 allowing to form a synthetic reference frequency ν _syn = ( ν _1 − ɛν _2 )/(1 − ɛ ), which is absent in the spectrum of the involved atoms or ions. Calibration coefficient ɛ can be chosen such that the temperature dependence of the BBR shift for the synthetic frequency ν _syn has a local extremum at an arbitrary operating temperature T _0 . This leads to a weak sensitivity of BBR shift with respect to the temperature variations near operating temperature T _0 . As a specific example, the Yb ^+ ion is studied in detail, where the utilized optical clock transitions are of electric quadrupole ( S → D ) and octupole ( S → F ) type. In this case, temperature variations of ±7 K lead to BBR shift uncertainties of less than 10 ^−19 , showing the possibility to construct ultra-precise combined atomic clocks (including portable ones) without the use of cryogenic techniques.