We propose a compact atomic clock based on ultracold Rb atoms that aremagnetically trapped near the surface of an atom microchip. An interrogationscheme that combines electromagnetically-induced transparency (EIT) withRamsey's method of separated oscillatory fields can achieve atomic shot-noiselevel performance of 10^{-13}/sqrt(tau) for 10^6 atoms. The EIT signal can bedetected with a heterodyne technique that provides noiseless gain; with thistechnique the optical phase shift of a 100 pW probe beam can be detected at thephoton shot-noise level. Numerical calculations of the density matrix equationsare used to identify realistic operating parameters at which AC Stark shiftsare eliminated. By considering fluctuations in these parameters, we estimatethat AC Stark shifts can be canceled to a level better than 2*10^{-14}. Anoverview of the apparatus is presented with estimates of duty cycle and powerconsumption.
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