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arXiv:1305.0444 · New Journal of Physics

Quantum atom–light interfaces in the Gaussian description for spin-1 systems

Giorgio Colangelo, R. J. Sewell, N. Behbood, Ferran Martin Ciurana, Gil Triginer, Morgan W. Mitchell

Published Oct 7, 2013• 42 citations
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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 87 Rb 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.

DOI
10.1088/1367-2630/15/10/103007

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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 87 Rb 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.
We show how a variety of real-world effects can be incorporated into continuous-variable models of atom-light interfaces within a single, consistent framework.The approach is similar to that of Madsen and Mølmer (2004 Phys.Rev. A 70 052324), but uses physical, not canonical, variables.We show how to include spatial and temporal inhomogeneities, external fields, coherent atom-light interactions, loss, decoherence, atomic transport and projective measurements within a covariance-matrix description.The model can be applied to many experimental situations ranging from room temperature vapour cells to sub-mK atomic clouds.As first applications, we calculate the effect of detector time resolution, spatial inhomogeneities and atomic motion on the spin squeezing dynamics of rubidium 87 on the D 2 transition.
We present a model which describes coherent and incoherent processes in continuous-variable atom-light interfaces. We assume Gaussian states for light and atoms and formulate the system dynamics in terms of first and second moments of the angular momentum operators. Spatial and temporal inhomogeneities in light and atom variables are incorporated by partitioning the system into small homogeneous segments. Furthermore, other experimental imperfections as for instance limited detector time-resolution and atomic motion are simulated. The model is capable of describing many experimental situations ranging from room temperature vapor cells to sub-mK atomic clouds. To illustrate the method, we calculate the effect of detector time-resolution, spatial inhomogeneities and atomic motion on the spin squeezing dynamics of rubidium 87 on the D2 transition.
Quantum interfaces between polarized atomic ensembles and coherent states of light, applied recently to manipulate bipartite and multipartite entanglement, are revisited by means of a continuous-variable formalism. The explicit use of the continuous-variable formalism facilitates significantly the analysis of entanglement between different modes, reducing it to the study of the properties of a final covariance matrix which can be found analytically. Furthermore, it allows to study matter-light interfaces for mixed states, adapting the formalism to the experimental situations in which the initial prepared Gaussian states are, unavoidably, affected by a certain amount of noise. A multipartite scenario, leading to the generation of macroscopic cluster states is presented and analyzed in detail within this formalism.
We describe nonlinear quantum atom–light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in 87 Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the 'Heisenberg limit' ∝1/ N , where N is the number of photons. In contrast to other proposed nonlinear metrology systems, the atom–light interface allows both linear and nonlinear estimation of the same atomic quantities.
We consider an ensemble of trapped atoms interacting with a continuous-wave laser field. For sufficiently polarized atoms and for a polarized light field, we may approximate the nonclassical components of the collective spin angular momentum operator for the atoms and the Stokes vectors of the field by effective position and momentum variables for which we assume a Gaussian state. Within this approximation, we present a theory for the squeezing of the atomic spin by polarization rotation measurements on the probe light. We derive analytical expressions for the squeezing with and without inclusion of the noise effects introduced by atomic decay and by photon absorption. The theory is readily adapted to the case of inhomogeneous light-atom coupling [A. Kuzmich and T.A.B. Kennedy, Phys. Rev. Lett. 92, 030407 (2004)]. As a special case, we show how to formulate the theory for an optically thick sample by slicing the gas into pieces, each having only small photon absorption probability. Our analysis of a realistic probing and measurement scheme shows that it is the maximally squeezed component of the atomic gas that determines the accuracy of the measurement.