Non-Gaussian Photon Correlations in Weakly Coupled Atomic Ensembles

Abstract

We develop a scattering theory formalism and use it to predict that a resonantly driven atomic ensemble weakly coupled to an optical mode can generate light with non-Gaussian correlations. Our approach -- based on a perturbative diagrammatic expansion of multi-photon interactions -- shows that photon-photon interaction mediated by the emitters causes the transmitted light to have a non-vanishing connected third-order correlation function $g_c^{(3)}$. We explain the temporal pattern of $g_c^{(3)}$ using the interaction processes in our diagrammatic expansion. A quantitative comparison with cascaded master equation simulations for small ensembles with optical depth $\mathrm{OD}\leq 2$ confirms that the perturbative results remain accurate across experimentally relevant optical depths and for drive strengths large enough to make the predicted non-Gaussian signatures detectable. We anticipate that state-of-the-art nanofibre-coupled atomic ensembles can experimentally demonstrate our predictions.

Figures (3)

• Figure 1: An array of $M$ chirally coupled two-level atoms (depicted as blue balls) resonantly driven by an external coherent field $\ket{\alpha}$ producing a strongly correlated output photon state $|\text{out}\rangle$. Each atom couples to the waveguide with a decay rate $\beta\Gamma_{\text{tot}}$ and to external loss channel with a decay rate $(1-\beta)\Gamma_{\text{tot}}$.
• Figure 2: Diagrammatic representation of the terms in $T^{(1)}$, which is the major contribution to the non-Gaussianity of outgoing light. The diagram including one three-photon interaction is called 3-vertex diagram, and the diagram including two two-photon interactions is called 4-vertex diagram. The momentum of the photons after the interaction is labeled above the horizontal line. The line piece without momentum labels mean the photon is on resonance with the atom. The order estimates below each diagram show their respective scaling behavior in the large optical depth regime.
• Figure 3: Connected third-order correlation function with various OD $g_c^{(3)}(R,\eta,\zeta)$ in Jacobi coordinates, with center of mass $R=0$. The six-fold symmetry reflects three symmetry axes corresponding to two-photon coincidences. $g_c^{(3)}$ is computed at tree-level diagram for $\beta=1\%$ while the loop order correction is added for $\beta= 5\%$