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We realize a mechanical analogue of the Dicke model, achieved by coupling thespin of individual neutral atoms to their quantized motion in an opticaltrapping potential. The atomic spin states play the role of the electronicstates of the atomic ensemble considered in the Dicke model, and the in-trapmotional states of the atoms correspond to the states of the electromagneticfield mode. The coupling between spin and motion is induced by an inherentpolarization gradient of the trapping light fields, which leads to a spatiallyvarying vector light shift. We experimentally show that our system reaches theultra-strong coupling regime, i.e., we obtain a coupling strength which is asignificant fraction of the trap frequency. Moreover, with the help of anadditional light field, we demonstrate the in-situ tuning of the couplingstrength. Beyond its fundamental interest, the demonstrated one-to-one mappingbetween the physics of optically trapped cold atoms and the Dicke model pavesthe way for implementing protocols and applications that exploit extremecoupling strengths.

Observation of ultra-strong spin-motion coupling for cold atoms in optical microtraps