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We consider how to measure collective spin states of an atomic ensemble basedon the recent multi-pass approaches for quantum interface between light andatoms. We find that a scheme with two passages of a light pulse through theatomic ensemble is efficient to implement the homodyne tomography of the spinstate. Thereby, we propose to utilize optical pulses as a phase-shifter thatrotates the quadrature of the spins. This method substantially simplifies thegeometry of experimental schemes.

Measurement schemes for the spin quadratures on an ensemble of atoms