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We demonstrate Ramsey-Bord\'e (RB) atom interferometry for high performancelaser stabilization with fractional frequency instability $<2 \times 10^{-16}$for timescales between 10 and 1000s. The RB spectroscopy laser interrogates twocounterpropagating $^{40}$Ca beams on the $^1$S$_0$ -- $^3$P$_1$ transition at657 nm, yielding 1.6 kHz linewidth interference fringes. Fluorescence detectionof the excited state population is performed on the (4s4p) $^3$P$_1$ --(4p$^2$) $^3$P$_0$ transition at 431 nm. Minimal thermal shielding and novibration isolation are used. These stability results surpass performance fromother thermal atomic or molecular systems by one to two orders of magnitude,and further improvements look feasible.

Ramsey-Bord\'e matter-wave interferometry for laser frequency stabilization at $10^{-16}$ frequency instability and below