A clock with 810^-19 systematic uncertainty

We report an optical lattice clock with a total systematic uncertainty of 8. 1 10^-19 in fractional frequency units, representing the lowest uncertainty of any clock to date. The clock relies on interrogating the ultra-narrow ¹S₀ ³P₀ transition in a dilute ensemble of fermionic strontium atoms trapped in a vertically-oriented, shallow, one-dimensional optical lattice. Using imaging spectroscopy, we previously demonstrated record high atomic coherence time and measurement precision enabled by precise control of collisional shifts and the lattice light shift. In this work, we revise the black body radiation shift correction by evaluating the 5s4d ³D₁ lifetime, necessitating precise characterization and control of many body effects in the 5s4d ³D₁ decay. Lastly, we measure the second order Zeeman coefficient on the least magnetically sensitive clock transition. All other systematic effects have uncertainties below 1 10^-19.