Simple vibration-insensitive cavity for laser stabilization at the 10 super(-16) level

We present the design and realization of two reference cavities for ultra-stable lasers addressing narrow transitions in mixed-species ( super(115)In super(+) / super(172)Yb super(+)) Coulomb crystals. With a simple set-up, we achieve a fractional frequency instability close to the thermal noise limit of a 12-cm-long cavity, reaching sigma sub(y ) = 4.7 10 super(-16) at 10 s with a linear drift of 53 mHz/s. We discuss the individual instability contributions and show that in a set-up with a lower thermal noise floor and vibration sensitivity, an instability of 1 10 super(-16) can be reached. To achieve this, we implement a vibration-insensitive design for a 30-cm-long cavity mounted horizontally and conduct first tests that show a sensitivity of 1.8 10 super(-11) ms super(-2) to vertical accelerations. This is about a factor of 20 less than the value observed for the short cavity. Mechanical tolerances and ways to further reduce the sensitivity are discussed.