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