Higher-order spatial photon interference versus dipole blockade effect

Abstract

The steady-state quantum dynamics of three dipole-dipole coupled two-level emitters, fixed at the vertices of an equilateral triangle, and interacting via the environmental thermostat is investigated. We have analytically obtained the populations of the involved three-atom cooperative states as well as of the second- and third-order spatial photon correlation functions of the light scattered by the few-qubit sample. As a consequence, we have demonstrated that this incoherently excited system spontaneously generates streams of single photons possessing sub-Poissonian photon statistics. In analogy to the dipole-dipole blockade, one may expect that at smaller inter particle distances, compared to the photon emission wavelength, the reported phenomenon has the same origin. However, we have shown that the quantum photon features are due to the interaction's nature of the few symmetrically arranged two-level emitters with the surrounding thermal reservoir. Respectively, at larger atomic intervals the effect occurs because of high-order spatial interference phenomena. Sub-wavelength interference fringes can be observed too, via measurements of spatial higher-order photon correlation functions.

Figures (3)

• Figure 1: Schematic picture of the considered system. Three atoms, $j \in \{1,2,3\}$, are arranged to form an equilateral triangle. Detectors $D_{k}$, placed at ${\bf R_{k}}$, $k \in \{1,2,3\}$, detect the spontaneously scattered photons by the atomic sample. Respectively, ${\bf r_{jl}}$ are the inter atomic distance vectors and one assumes that $|{\bf R_{k}}| \gg |{\bf r_{jl}}|$.
• Figure 2: The energy diagram of a spatially equidistant three-atom sample. The anti-symmetrical states $\{|6\rangle, |7\rangle \}$ and $\{|3\rangle, |4\rangle \}$ are shifted by the dipole-dipole coupling strength among the emitters, i.e. $+\delta$, whereas the symmetrical states $\{|5\rangle,|2\rangle\}$ are shifted by the doubled dipole-dipole coupling, $-2\delta$, respectively.
• Figure 3: The steady-state higher-order photon correlation functions $g^{(k)}(0)$ versus $x/\pi$, where $x=\sqrt{3}\omega_{0}r/(2c)$, based on Exp. (\ref{['g2kp']}) and Exp. (\ref{['g3kp']}), respectively. The solid line depicts the second-order photon correlation function, i.e. $k=2$, whereas the long-dashed curve stands for the third-order photon correlation function, where $k=3$.