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.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.

arXiv:quant-ph/0501033Physical Review AApr 24, 200698 citations

Polarizabilities of Sc and Ti atoms and dispersion coefficients for their interaction with helium atoms

Xi Chu, A. Dalgarno, Gerrit C. Groenenboom

The dynamic scalar and tensor polarizabilities of Sc and Ti are computed with time-dependent density functional theory. These polarizabilities are used to compute the isotropic and anisotropic dispersion interactions in ScHe and TiHe. We find ${C}_{6,0}(\mathrm{ScHe})=30.00$ , ${C}_{6,2}(\mathrm{ScHe})=\ensuremath{-}1.63$, ${C}_{6,0}(\mathrm{TiHe})=28.40$ , and ${C}_{6,2}(\mathrm{TiHe})=\ensuremath{-}0.90$ $({E}_{h}{a}_{0}^{6})$ . We show that an estimate of the dispersion anisotropy based on static polarizabilities results in an overestimation by a factor of 2.The dynamic scalar and tensor polarizabilities of Sc and Ti are computed with time-dependent density functional theory. These polarizabilities are used to compute the isotropic and anisotropic dispersion interactions in ScHe and TiHe. We find ${C}_{6,0}(\mathrm{ScHe})=30.00$, ${C}_{6,2}(\mathrm{ScHe})=\ensuremath{-}1.63$, ${C}_{6,0}(\mathrm{TiHe})=28.40$, and ${C}_{6,2}(\mathrm{TiHe})=\ensuremath{-}0.90$ $({E}_{h}{a}_{0}^{6})$. We show that an estimate of the dispersion anisotropy based on static polarizabilities results in an overestimation by a factor of 2.

Physical Review ASep 7, 200521 citations

Polarizability Measurements in a Multi-Species Atom Interferometer

Melissa Revelle

Bulletin of the American Physical SocietyMay 21, 20090 citations

Scalar, tensor, and vector polarizability of Tm atoms in a 532-nm dipole trap

V. V. Tsyganok, D. A. Pershin, E. T. Davletov +2 more

Dipolar atoms have unique properties, making them interesting for laser cooling and quantum simulations. But, due to relatively large orbital momentum in the ground state these atoms may have large dynamic tensor and vector polarizabilities in the ground state. This enables the formation of spin-dependent optical traps. In this paper the real part of tensor and vector dynamic polarizability was experimentally measured and compared to a theoretical simulation. For an optical dipole trap operating around 532.07 nm, tensor polarizability was found to be $\ensuremath{-}145\ifmmode\pm\else\textpm\fi{}53\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ and vector polarizability was $680\ifmmode\pm\else\textpm\fi{}240\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ The measurements were compared with simulations, which were done based on the known set of levels from a thulium atom. The simulations are in good agreement with experimental results. In addition, losses of atoms from the dipole trap were measured for different trap configurations and compared to the calculated imaginary part of vector and tensor polarizabilities.Dipolar atoms have unique properties, making them interesting for laser cooling and quantum simulations. But, due to relatively large orbital momentum in the ground state these atoms may have large dynamic tensor and vector polarizabilities in the ground state. This enables the formation of spin-dependent optical traps. In this paper the real part of tensor and vector dynamic polarizability was experimentally measured and compared to a theoretical simulation. For an optical dipole trap operating around 532.07 nm, tensor polarizability was found to be $\ensuremath{-}145\ifmmode\pm\else\textpm\fi{}53\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ and vector polarizability was $680\ifmmode\pm\else\textpm\fi{}240\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ The measurements were compared with simulations, which were done based on the known set of levels from a thulium atom. The simulations are in good agreement with experimental results. In addition, losses of atoms from the dipole trap were measured for different trap configurations and compared to the calculated imaginary part of vector and tensor polarizabilities.

arXiv:1905.03842Physical Review AOct 4, 201917 citations

Differential atom interferometry beyond the standard quantum limit (10 pages)

P. Hyllus, K. Eckert

Physical Review AJan 1, 20060 citations

{C}_{6,0}(\mathrm{ScHe})=30.00

, ${C}_{6,2}(\mathrm{ScHe})=\ensuremath{-}1.63$,

{C}_{6,0}(\mathrm{TiHe})=28.40

, and ${C}_{6,2}(\mathrm{TiHe})=\ensuremath{-}0.90$

({E}_{h}{a}_{0}^{6})

. We show that an estimate of the dispersion anisotropy based on static polarizabilities results in an overestimation by a factor of 2.