Dipolar Dephasing of Rydberg $D$-State Polaritons

We experimentally study the effects of the anisotropic Rydberg interaction on $D$-state Rydberg polaritons slowly propagating through a cold atomic sample. We observe the interaction-induced dephasing of Rydberg polaritons at very low photon input rates into the medium. We develop a model combining the propagation of the two-photon wave function through our system with nonperturbative calculations of the anisotropic Rydberg interaction to show that the observed effect can be attributed to pairwise interaction of individual Rydberg polaritons at distances larger than the Rydberg blockade.

Figure 1

(a) EIT level scheme with weak probe field ${\mathcal{E}}_p$ and strong control field $\mathrm{\Omega }$. (b) Frequency scan of the weak probe field ${\mathcal{E}}_p$ showing the EIT transmission window averaged over the full pulse time. The transmission shows a strong nonlinearity with incident photon rate. (c) Geometric scheme of our setup consisting of EIT lasers at 780 nm ($w_0\approx 6\mu \mathrm{m}$) and 480 nm ($w_0\approx 12\mu \mathrm{m}$) focused onto a thermal cloud ($30\mu \mathrm{K}$) of ${}^{87}\mathrm{Rb}$ atoms with extensions of ${\sigma }_z=80\mu \mathrm{m}$ and ${\sigma }_r=25\mu \mathrm{m}$. The gray shadow shows the anisotropic blockade region caused by a $|100D_{5/2}⟩$ Rydberg excitation. (d) Time dependent transmission on two-photon resonance for different probe photon input rates.

Figure 2

(a) Effective optical density of the $|88D_{5/2}⟩$ EIT feature for different photon rates at fixed $\mathrm{\Omega }/2\pi =8.3\mathrm{MHz}$. The solid lines are linear fits to the data to extract the rates $R_{\mathrm{OD}}$ of additional ${\mathrm{OD}}_{\text{eff}}$ due to the creation of impurities. (b) Dependence of $R_{\mathrm{OD}}$ on $R_{\text{in}}$ for different Rabi frequencies $\mathrm{\Omega }$. Parabolic fits (solid lines) determine the rate constant $\mathcal{C}(\mathrm{\Omega })$ for each data set. The vertical dashed lines correspond to mean photon numbers inside the medium exceeding 2 where the quadratic dependence breaks down. (c) Rate constants $\mathcal{C}$ for different $\mathrm{\Omega }$. For the different principal quantum numbers $n$ we observe the same scaling according to Eq. (3) with $k=1.67(4)$. Dashed lines are fits to the data.

Figure 3

Calculated pair state potentials of (a) $|80D_{5/2};80D_{5/2}⟩$ and (b) $|100D_{5/2};100D_{5/2}⟩$ pair states (gray lines). The color shading represents the projection of the $|m_{J1,2}=5/2,5/2⟩$ state with respect to the light propagation direction onto the new eigenstates in the presence of interaction for an angle of $\theta =60°$ between the interatomic axis and the coupling laser beam.

Figure 4

(a) We model the anisotropic DD interaction between two polaritons as an effective potential $V(\mathbf{r}=\{z,r_{\perp }\})$ capturing the interaction-induced blockade effect and a position dependent dephasing rate $\mathrm{\Gamma }(\mathbf{r})$ out of the pair state coupled by the EIT control laser. (b) Example plot showing the anisotropic blockaded volume and the dephasing rate outside this region for $n=80$ and $\mathrm{\Omega }/2\pi =25\mathrm{MHz}$. (c) Numerical simulations showing for $z>0$ the probability distribution associated with two Rydberg excitations $|{\psi }_{dd}(z,R){|}^2$ and, for $z<0$, the product $\mathrm{\Gamma }(z)|{\psi }_{dd}(z,R){|}^2$, where $R=(z_1+z_2)/2$ is the center of mass coordinate. Both quantities are presented in arbitrary units for $r_{\perp }=4.2\mu \mathrm{m}$, $\mathrm{\Omega }/2\pi =12\mathrm{MHz},n=80$, and probe-beam waist $w_{\mathrm{eff}}=7\mu \mathrm{m}$. (d) Comparison of $\mathcal{C}(\mathrm{\Omega })$ from numerical simulations (markers) with fits to experimental data from Fig. 2 (dashed lines).