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arXiv:0802.0365

Non-ideal atom-light interfaces: modeling real-world effects

Marco Koschorreck, Morgan W. Mitchell

Published Feb 4, 2008• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.0802.0365

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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.
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 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.
In this dissertation, I explore interactions between matter and propagating light. The electromagnetic field is modeled as a reservoir of quantum harmonic oscillators successively streaming past a quantum system. Each weak and fleeting interaction entangles the light and the system, and the light continues its course. Within the framework of open quantum systems, the light is eventually traced out, leaving the reduced quantum state of the system as the primary mathematical subject. Two major results are presented. The first is a master equation approach for a quantum system interacting with a traveling wave packet prepared with a definite number of photons. In contrast to quasi-classical states, such as coherent or thermal fields, these N-photon states possess temporal mode entanglement, and local interactions in time have nonlocal consequences. The second is a model for a three-dimensional light-matter interface for an atomic ensemble interacting with a paraxial laser beam and its application to the generation of QND spin squeezing. Both coherent and incoherent dynamics due to spatially inhomogeneous atom-light coupling across the ensemble are accounted for. Measurement of paraxially scattered light can generate squeezing of an atomic spin wave, while diffusely scattered photons lead to spatially local decoherence.
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.
We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition (QND) measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.