  The coherent population trapping (CPT) effect is used for making compact
atomic clocks. There are two types of CPT clocks: the one in which the Raman
beams are applied continuously and the one in which two CPT pulses separated by
a dark period are applied (Ramsey scheme). It is obvious that the technique of
spin squeezing can only be applied to the Ramsey CPT clock to enhance the
sensitivity. However, it is not apparent how to adapt to the CPT clock the
protocols for the microwave clock using one-axis-twist squeezing (OATS), since
the 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, namely
the Schr\"odinger cat state protocol (SCSP) and the generalization thereof, and
the echo squeezing protocol (ESP), to the CPT clock. The ESP magnifies the
phase shift by a factor of the square-root of (N/e), while the SCSP magnifies
the phase shift by a factor of N/2 , making it able to achieve a higher
sensitivity in the presence of excess noise.
