Emission photon statistics in collectively interacting dipole atom arrays in the low-intensity limit

Abstract

We investigate the photon statistics of light emitted from a system of collectively interacting dipoles in the low-intensity regime, incorporating double-excitation states to capture beyond-single-excitation effects. By analyzing the eigenstates of the double-excitation manifold, we establish their connection to the accessible single-excitation eigenmodes and investigate the role of decay rates in shaping the zero-time-delay photon correlation function $g^{(2)}(τ= 0)$ under different detection schemes. The photon emission statistics can be arbitrarily controlled by interfering two beams of light that selectively address orthogonal eigenmodes. This can act as a tunable nonlinearity that enables both enhancement or suppression of two-photon emission.

Figures (5)

• Figure 1: An example schematic of the atomic energy levels for $N = 4$ atoms. 0 and 1 represent the atoms being in the ground and excited state, respectively. $|g\rangle$ represents the collective ground state. $|e_j\rangle$ represents the single-excitation states and $|ee_{\mu}\rangle$ represents the double-excitation states.
• Figure 2: The decay rate of the second photon ($\zeta_\beta$) versus the decay rate of the first photon ($\gamma_{\beta}^{(2)}$) from a double-excitation eigenmode $\beta$. The separation has been varied from 0.3 to 1.0 $\lambda$. The color shows the separation $d$ of the atoms in the array. The dashed line corresponds to $\zeta_\beta = \gamma_{\beta}^{(2)}/2$.
• Figure 3: The overlap between single and double-excitation eigenmodes. (a) The $\vert X_{\alpha\beta}\vert$ of the single-excitation eigenmode $\alpha$ and double-excitation eigenmode $\beta$ versus the difference in decay rate $(\gamma_{\beta}^{(2)} - 2 \gamma_\alpha)/\Gamma_0$. (b) The $\vert L_{\alpha_1 \alpha_2 \beta}\vert$ of the single-excitation eigenmodes $\alpha_1$, $\alpha_2$ and the double-excitation eigenmode $\beta$ versus the difference in decay rate $(\gamma_{\beta}^{(2)} - \gamma_{\alpha_1} - \gamma_{\alpha_2})/\Gamma_0$, where $\alpha_1 \neq \alpha_2$. The data is shown for inter-atom separation of $d = 0.4 \lambda$. The contour depicts the density of points. The data is calculated for a square array of 25 atoms.
• Figure 4: The $g^{(2)}(0)$ when excited using a single eigenmode $\alpha$ for an ensemble of 25 atoms arranged in a square array, versus the decay rate of the eigenmode ($\gamma_\alpha$). (a) depicts the situation when the detection is also in mode $\alpha$, where subradiant states exhibit anti-bunching despite the presence of double-excitation states. (b) corresponds to detection over all of free space, in which subradiant states instead display bunched emission. The separation has been varied from 0.3 to 1.0 $\lambda$. The color shows the separation $d$ of the atoms in the array. The dotted line shows the independent-emitter incoherent emission $g^{(2)}(0)$ for $25$ atoms.
• Figure 5: The $g^{(2)}(0)$ when two eigenmodes are incident and the light emitted into one mode is detected. (a) depicts the dependence on the relative phase $\phi$ at relative amplitude $A = 2.8$ and (b) depicts the maximum and minimum range of $g^{(2)}(0)$ possible when the relative amplitude $A$ is varied. The black dotted line is a reference for $g^{(2)}(0) = 1$.