In general, the process of spin squeezing is employed for atomic sensors that are essentially free from the effect of spontaneous emission. In the case of an atomic clock based on coherent population trapping, spontaneous emission plays a key role. Specifically, when the clock is realized in the Ramsey configuration employing a pair of pulses separated in time, it is the spontaneous emission process during the first pulse that creates the coherent population trapping, by optically pumping the atoms into the so-called dark state. We show in this talk that it is still possible to apply the process of spin squeezing to enhance the sensitivity of such a clock, by designing carefully the sequence of steps in the protocol. Specifically, we consider the approach of using the maximally entangled Schroedinger Cat states, produced via one axis twist squeezing, to achieve Heisenberg Limited sensitivity, representing an improvement in sensitivity by as much as four orders of magnitude.
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