Electro-optic control of atom-light interactions using Rydberg dark-state polaritons

We demonstrate a multiphoton Rydberg dark resonance where a $\Lambda$ system is coupled to a Rydberg state. This $\mathcal{N}$-type level scheme combines the ability to slow and store light pulses associated with long-lived ground-state superpositions with the strongly interacting character of Rydberg states. For the $n{d}_{5/2}$ Rydberg state in ${}^{87}\text{R}\text{b}$ (with $n=26$ or 44) and a beam size of 1 mm, we observe a resonance linewidth of less than 100 kHz in a room-temperature atomic ensemble limited by transit-time broadening. The resonance is switchable with an electric field of order $1\text{V}{\text{cm}}^{-1}$. Applications in electro-optic switching and photonic phase gates are discussed.

Figure 1

(Color online) (a) Level scheme used for the experimental demonstration of a four-photon Rydberg dark resonance: The $\Lambda$ system $\left(|1⟩\to |2⟩\to |3⟩\right)$ is coupled to a Rydberg state $|5⟩$ using a two-photon transition via an intermediate state $|4⟩$. The absorption or dispersion of the medium is detected on the transition $|1⟩\to |2⟩$ using a probe beam with Rabi frequency ${\Omega }_{21}$. (b) Schematic of the experimental setup. The $\Lambda$-system beams [light solid (green) and dashed (orange)] copropagate with the second step of the Rydberg excitation [dark solid (red)]. The first step of the Rydberg excitation [dark dashed (purple)] is counterpropagating.

Figure 2

(Color online) Experimental measurement of the change in transmission, $\Delta T$, associated with (a) the $\Lambda$ system $|1⟩\to |2⟩\to |3⟩$ and (b) the Rydberg dark-resonance signal corresponding to the difference between the $\Lambda$-system resonance with Rydberg coupling $\left(n=26\right)$ on and off. The Rydberg dark resonance (normalized relative to the $\Lambda$-system resonance) is measured using a lock-in amplifier and is over two orders of magnitude smaller than the $\Lambda$-system resonance.

Figure 3

(Color online) Absorption $\alpha$ (proportional to the imaginary part of the density matrix component ${\sigma }_{21}$) experienced by the probe beam as a function of detuning for a four-photon Rydberg dark resonance with the Rydberg coupling (a) off and (b) on. In (c) we show the difference between (a) and (b) $\left(\times 10\right)$, which corresponds to the effect of coupling to the Rydberg state as observed in the experiment, Fig. 2b. The specific parameters are ${\Omega }_{21}=0.02{\gamma }_2$, ${\Omega }_{32}=0.2{\gamma }_2$, ${\Omega }_{43}=0.8{\gamma }_2$, ${\Delta }_{43}={\Delta }_{54}=0$, ${\gamma }_4={\gamma }_2$, and ${\gamma }_5=0.01{\gamma }_2$. (a) ${\Omega }_{54}=0.0{\gamma }_2$ and (b) ${\Omega }_{54}=0.8{\gamma }_2$. The thin lines show velocities in the range $-10{\gamma }_2{\lambda }_1$ to $+10{\gamma }_2{\lambda }_1$ in steps of $0.5{\gamma }_2{\lambda }_1$. The thick light (green) lines indicates the absorption of the zero-velocity-class atoms. The thick black line indicates the total absorption obtained by summing over velocity. The curves for each velocity class are multiplied by 5 so that they can be plotted on the same scale as the sum.

Figure 4

(Color online) Electric field dependence of the Rydberg dark resonance (RDR) amplitude for $n=44$. The RDR signals at $0\text{V}{\text{cm}}^{-1}$ [light (green)] and $1.1\text{V}{\text{cm}}^{-1}$ [dark (blue)] are shown inset. Note that the relative height of the central peak and the wings is smaller for $n=44$ than $n=26$, Fig. 2b, due to the lower value of ${\Omega }_{54}$.