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The coherent population trapping (CPT) effect is used for making compactatomic clocks. There are two types of CPT clocks: the one in which the Ramanbeams are applied continuously and the one in which two CPT pulses separated bya dark period are applied (Ramsey scheme). It is obvious that the technique ofspin squeezing can only be applied to the Ramsey CPT clock to enhance thesensitivity. However, it is not apparent how to adapt to the CPT clock theprotocols for the microwave clock using one-axis-twist squeezing (OATS), sincethe Ramsey CPT clock is not trivially equivalent to the Ramsey microwave clock.In this paper, we show explicitly how to adapt two protocols using OATS, namelythe Schr\"odinger cat state protocol (SCSP) and the generalization thereof, andthe echo squeezing protocol (ESP), to the CPT clock. The ESP magnifies thephase shift by a factor of the square-root of (N/e), while the SCSP magnifiesthe phase shift by a factor of N/2 , making it able to achieve a highersensitivity in the presence of excess noise.

Spin Squeezing Induced Enhancement of Sensitivity of an Atomic Clock using Coherent Population Trapping