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Published April 1, 2006 | public
Journal Article Open

Tensor polarizability and dispersive quantum measurement of multilevel atoms


Optimally extracting information from measurements performed on a physical system requires an accurate model of the measurement interaction. Continuously probing the collective spin of an alkali-metal atom cloud via its interaction with an off-resonant optical probe is an important example of such a measurement where realistic modeling at the quantum level is possible using standard techniques from atomic physics. Typically, however, tutorial descriptions of this technique have neglected the multilevel structure of realistic atoms for the sake of simplification. We account for the full multilevel structure of alkali-metal atoms and derive the irreducible form of the polarizability Hamiltonian describing a typical dispersive quantum measurement. For a specific set of parameters, we then show that semiclassical predictions of the theory are consistent with our experimental observations of polarization scattering by a polarized cloud of laser-cooled cesium atoms. We also derive the signal-to-noise ratio under a single-measurement trial and use this to predict the rate of spin squeezing with multilevel alkali-metal atoms for arbitrary detuning of the probe beam.

Additional Information

©2006 The American Physical Society (Received 6 January 2005; revised 7 April 2005; published 24 April 2006) The authors would like to thank Poul Jessen, Ivan Deutsch, Andrew Silberfarb, Dima Budker, and especially Ramon van Handel and Andrew Doherty for numerous insightful discussions. We would also like to thank Sebastian de Echaniz, Jacob Sherson, and Eugene Polzik for pointing out important corrections. This work was supported by the Caltech MURI Center for Quantum Networks (Grant No. DAAD19-00-1-0374). J.M.G. acknowledges support from the Caltech Center for Physics of Information, and J.K.S. acknowledges support from Hertz Foundation.


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