Three-dimensional theory for light-matter interaction

Abstract

We present a full quantum mechanical three dimensional theory describing an electromagnetic field interacting with an ensemble of identical atoms. The theory is constructed such that it describes recent experiments on light-matter quantum interfaces, where the quantum fluctuations of light are mapped onto the atoms and back onto light. We show that the interaction of the light with the atoms may be separated into a mean effect of the ensemble and a deviation from the mean. The mean effect of the interaction effectively give rise to an index of refraction of the gas. We formally change to a dressed state picture, where the light modes are solutions to the diffraction problem, and develop a perturbative expansion in the fluctuations. The fluctuations are due to quantum fluctuations as well as the random positions of the atoms. In this perturbative expansion we show how the quantum fluctuations are mapped between atoms and light while the random positioning of the atoms give rise to decay due to spontaneous emission. Furthermore we identify limits, where the full three dimensional theory reduce to the one dimensional theory typically used to describe the interaction.

Creating single collective atomic excitations via spontaneous Raman emission in inhomogeneously broadened systems: Beyond the adiabatic approximation

“…However, it may also be possible to extend the three-dimensional descriptions of Refs. [10,29] to the inhomogeneous case.…”

Three-dimensional light-matter interface for collective spin squeezing in atomic ensembles

“…The coupling of collective atomic observables to paraxial modes thus describes the coherent atom-photon light-shift interaction, mediated by the Hermitian part of the atomic polarizability operator. The diffuse modes, in contrast, couple to the density fluctuations in the ensemble due to the discrete atomic positions and thus act locally on each atom [20]. In the usual Born-Markov approximation, tracing over these modes leads to decoherence and is described by the antiHermitian part of the atomic polarizability [37].…”

“…The discrete random atomic positions are associated with the density fluctuations that give rise to diffuse scattering into 4π steradians [20]. We consider light far detuned from any atomic resonance in a highly transparent regime, and thus we can safely neglect the small attenuation of the laser probe associated with this absorption.…”

“…Thus, a great deal of qualitative and quantitative information can be obtained from classical radiation theory. In a rigorous field-theoretic analysis, Sørensen and Sørensen showed that the mean-field effect of the light interacting with an atomic ensemble gives rise to an index of refraction of the gas, while fluctuations are due to the random positions of the atoms and the vacuum noise of the light [20]. In particular, the index of refraction is due to the spatiallyaveraged local density of the atoms, while the diffuse scattering into 4π arises from the random positions of the point atomic scatterers and is equivalent to decoherence by local spontaneous emission.…”

“…A rigorous field-theoretic treatment separates the mean-field classical effects from the quantum fluctuations and noise, including the spatial inhomogeneities of atoms and light modes [20]. Models that include spatial modes have been developed in a variety of contexts [21][22][23][24].…”