Abstract

We extend the covariance matrix description of atom–light quantum interfaces, originally developed for real and effective spin-1/2 atoms, to include ‘spin alignment’ degrees of freedom. This allows accurate modelling of optically probed spin-1 ensembles in arbitrary magnetic fields. We also include technical noise terms that are very common in experimental situations. These include magnetic field noise, variable atom number and the effect of magnetic field inhomogeneities. We demonstrate the validity of our extended model by comparing numerical simulations to a free–induction decay measurement of polarized 87Rb atoms in the f = 1 ground state. We qualitatively and quantitatively reproduce experimental results with no free parameters. The model can be easily extended to larger spin systems, and adapted to more complicated experimental situations.

Highlights

  • We have presented a method for describing the quantum dynamics of spin-1 atomic ensembles, extending the method introduced for quantum light interfaces [13, 15, 16], developed for spin-1/2 atomic ensembles by Madsen and Mølmer [14] and generalized by Koschorreck et al [17] and Toth et al [42]

  • For spin-1 our description is complete within the Gaussian approximation, while for larger spins it is still useful when octopole and higher spin moments can be neglected

  • We include the important technical noise associated with magnetic fields and noise due to uncertain atom number, as typically arises due to stochastic trap-loading processes

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Summary

Formalism

We work with collective operators describing macroscopic numbers of particles, for which a CV description is appropriate. Throughout, we use the covariance matrix techniques [14, 17], which are sufficient to describe the Gaussian states encountered in the great majority of CV experiments

Quantum polarization description
Description of spin-1 ensembles
Spin visualization
Commutation relationships
Collective spin operators
Covariance matrix
Dynamics
Light–atom interactions
Linearization
Optically induced decoherence
Atom–field interaction
Combined effects
Measurement
Initial state and technical noise contributions
An example: free-induction decay of collective atomic spin
Simulation of free-induction decay
Conclusions

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