  We present the experimental demonstration of non-destructive probing of the
1S0-3P0 clock transition probability in an optical lattice clock with 87Sr
atoms. It is based on the phase shift induced by the atoms on a weak
off-resonant laser beam. The method we propose is a differential measurement of
this phase shift on two modulation sidebands with opposite detuning with
respect to the 1S0-1P1 transition, allowing a detection limited by the photon
shot noise. We have measured an atomic population of 10^4 atoms with a signal
to noise ratio of 100 per cycle, while keeping more than 95% of the atoms in
the optical lattice with a depth of 0.1 mK. The method proves simple and robust
enough to be operated as part of the whole clock setup. This detection scheme
enables us to reuse atoms for subsequent clock state interrogations,
dramatically reducing the loading time and thereby improving the clock
frequency stability.
