Filtering single atoms from Rydberg-blockaded mesoscopic ensembles

We propose an efficient method to filter out single atoms from trapped ensembles with unknown numbers of atoms. The method employs stimulated adiabatic passage to reversibly transfer a single atom to the Rydberg state which blocks subsequent Rydberg excitation of all the other atoms within the ensemble. This triggers the excitation of Rydberg-blockaded atoms to short-lived intermediate states and their subsequent decay to untrapped states. Using an auxiliary microwave field to carefully engineer the dissipation, we obtain a nearly deterministic single-atom source. Our method is applicable to small atomic ensembles in individual microtraps and in lattice arrays.

Figure 1

Level scheme of atoms driven by a pair of laser fields with Rabi frequencies ${\Omega }_{ge}$ and ${\Omega }_{er}$ on the transitions $|g\rangle \to |e\rangle$ and $|e\rangle \to |r\rangle$. The atoms in the ground state $|g\rangle$ are confined within a volume of linear dimension $L\simeq 2\mu \mathrm{m}$ smaller than the blockade distance $d_{\mathrm{b}}$ determined by the interaction ${\mathcal{V}}_{\mathrm{aa}}$ between their Rydberg states $|r\rangle \equiv n{S}_{1/2}$ with large principal quantum number $n$ $\left(\simeq 50\right)$ and small decay ${\Gamma }_{re}$ $\left(\simeq 3\mathrm{kHz}\right)$ and dephasing ${\gamma }_r$ $\left(\lesssim 0.1\mathrm{MHz}\right)$ rates. In (a) the ground state of ${}^{87}\mathrm{Rb}$ atoms is $|g\rangle \equiv 5S_{1/2}|F=1,m_F=1\rangle$ while the intermediate state $|e\rangle \equiv 5P_{1/2}|F=2,m_F=2\rangle$ decays back to $|g\rangle$ with the rate ${\Gamma }_{eg}=\frac{1}{2}{\Gamma }_e$ $\left({\Gamma }_e=36\mathrm{MHz}\right)$ and to other untrapped states $|s\rangle \equiv 5S_{1/2}|F=2,m_F=1,2\rangle$ with the rate ${\Gamma }_{es}=\frac{1}{2}{\Gamma }_e$ (branching ratio ${\Gamma }_{es}/{\Gamma }_{eg}=1)$. In (b) the transition between the ground $|g\rangle \equiv 5S_{1/2}|F=2,m_F=2\rangle$ and intermediate $|e\rangle \equiv 5P_{3/2}|F=3,m_F=3\rangle$ states is closed $(|e\rangle$ decays only to $|g\rangle$ with rate ${\Gamma }_e=38\mathrm{MHz})$, but a microwave field coupling $|e\rangle$ to, e.g., $|e^{\prime }\rangle \equiv 5P_{1/2}|F=2,m_F=2\rangle ,$ with Rabi frequency ${\Omega }_{e{e}^{\prime }}$ can open a weak decay channel ${\Gamma }_{es}=\frac{8|{\Omega }_{e{e}^{\prime }}{|}^2}{3{\Gamma }_{e^{\prime }}}\simeq 2.4\mathrm{MHz}$ $\left(\ll {\Gamma }_{eg}={\Gamma }_e+\frac{4|{\Omega }_{e{e}^{\prime }}{|}^2}{{\Gamma }_{e^{\prime }}}\right)$ to the untrapped states $|s\rangle \equiv 5S_{1/2}|F=1,2,m_F=1\rangle$. The hyperfine and/or Zeeman shifts of states $|s\rangle$ suppress their coupling to the ${\Omega }_{ge}$ field, while facilitating selective interaction with a pushing laser of appropriate frequency and polarization.

Figure 2

Dynamics of the system, as obtained from $M=200$–500 independent realizations (trajectories) of the numerical experiment for each number $N$ of atoms with the level scheme of Fig. 1, irradiated with two resonant fields, ${\Delta }_e=0$, of Rabi frequencies ${\Omega }_{ge}$ and ${\Omega }_{er}$ shown in the upper panel. Main panel shows the mean number $\langle n\rangle$ of surviving atoms in the trap, starting with $N=1$–10 (from bottom to top) ground-state atoms, for ${\gamma }_r=0$. Inset shows the corresponding probabilities $P_N\left(n\right)$ of finding $n$ trapped atoms in state $|g\rangle$ at the end of the process (open bars), while the black $\left({\gamma }_r=0\right)$ and gray $\left({\gamma }_r\ne 0\right)$ circles denote the $P\left(n\right)$ averaged over the initial Poisson number distribution $P_{\mathrm{init}}\left(N\right)$ of the trapped atoms with the mean $\overline{N}=5$.

Figure 3

Same as in Fig. 2, but with finite detuning ${\Delta }_e$ and slightly different optimized pulse shape of ${\Omega }_{ge}$.

Figure 4

Same as in Figs. 2 and 3, but for the scheme of Fig. 1 with resonant fields, ${\Delta }_e=0$, and weaker decay to $|s\rangle$ (notice the longer time scale of the process). Thin dotted lines in the main panel show single trajectories for the corresponding initial number of atoms $N=1$–10.