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We consider the optical generation and verification of entanglement in atomicensembles under non-uniform interaction between the ensemble and an opticalmode. We show that for a wide range of parameters a system of non-uniformlycoupled atomic spins can be described as an ensemble of uniformly coupled spinswith a reduced effective atom-light coupling and a reduced effective atomnumber, with a reduction factor of order unity given by the ensemble-modegeometry. This description is valid even for complex entangled states witharbitrary phase-space distribution functions as long as the detection does notresolve single spins. Furthermore, we derive an analytic formula for theobservable entanglement in the case, of relevance in practice, where theensemble-mode coupling differs between state generation and measurement.

Entangled collective-spin states of atomic ensembles under non-uniform atom-light interaction