Robust offset locking of laser frequency with electronically tunable LC circuits for sub-millihertz uncertainty

Laser frequency stabilization is one of the essential technique in atomic, molecular, and optical physics, quantum optics, optical communications, and fundamental physics. Optical offset locking is the technique to stabilize optical frequency of a single-mode laser (slave laser) with respect to another well-stabilized laser (master laser). Optical phase lock loop (OPLL) [1] is one of the offset locking schemes, with which the slave laser frequency can be stabilized very precisely (less than the uncertainty of 10^-18). However, especially in noisy experimental circumstances, the OPLL does not work because its capture range is not so wide that the locking fails for large amount of frequency jitters. In order to keep the locked condition, another offset locking with wider capture range is sometimes required. Examples of such locking schemes are digital processing technique, optical frequency locking to resonance frequency of a high-finesse cavity [2], offset locking with an electrical delay line [3], and offset locking with electric LC resonant circuit [4]. The offset locking with the electric LC circuit (LC locking) has been introduced by W.-Y. Cheng et al, and with employing this scheme with the OPLL the beat-note frequency can be stabilized as precise as one millihertz.