Deterministic single-atom excitation via adiabatic passage and Rydberg blockade

We propose to use adiabatic rapid passage with a chirped laser pulse in the strong dipole blockade regime to deterministically excite only one Rydberg atom from randomly loaded optical dipole traps or optical lattices. The chirped laser excitation is shown to be insensitive to the random number $N$ of the atoms in the traps. Our method overcomes the problem of the $\sqrt{N}$ dependence of the collective Rabi frequency, which was the main obstacle for deterministic single-atom excitation in the ensembles with unknown $N$, and can be applied for single-atom loading of dipole traps and optical lattices.

Figure 1

(a) The time dependence of the amplitude and detuning from the resonance with atomic transition for a chirped pulse. (b) Scheme of the deterministic single-atom excitation from ground state $g$ to Rydberg state $r$ in a blockaded Rydberg ensemble. (c–e) Scheme of the adiabatic rapid passage. The energies of the dressed states are shown for laser detunings (c) $\Delta <0$, (d) $\Delta \sim 0$, and (e) $\Delta >0$. The laser frequency is rapidly chirped across the resonance. The population is transferred from state $g_{-}$ to state $r_{-}$ independently of the Rabi frequency.

Figure 2

(a) Envelope and (b) spectrum of the chirped Gaussian laser pulses with the chirp rates $\alpha /\left(2\pi \right)=0.5$ THz/s (solid line) and $\alpha /\left(2\pi \right)=1$ THz/s (dashed line) used in numerical calculations. The spectrum of the unchirped laser pulse of the same duration is shown for reference (dash-dotted line, height rescaled for clarity).

Figure 3

Time dependence of the probability $P_1$ to excite a single Rb($37P_{3/2}$) atom in a trap containing (a, b) one atom, (c, d) two atoms, (e, f) five atoms, and (g, h) seven atoms by chirped Gaussian laser pulses. In the left-hand panels the chirp rate is $\alpha /\left(2\pi \right)=1$ THz/s and the Rabi frequency is ${\Omega }_1/\left(2\pi \right)=2$ MHz. In the right-hand panels the chirp rate is $\alpha /\left(2\pi \right)=0.5$ THz/s and the Rabi frequency is ${\Omega }_1/\left(2\pi \right)=0.5$ MHz. The calculations have been done for the exact Stark-tuned F$\ddot{\mathrm{o}}$rster resonance $37P_{3/2}+37P_{3/2}\to 37S_{1/2}+38S_{1/2}$ with zero energy defect. The atoms are randomly placed in the cubic interaction volume of size $L=1$ $\mu \mathrm{m}$.

Figure 4

(a) Scheme of the three-level ladder system interacting with the two laser fields with Rabi frequencies ${\Omega }_s$ and ${\Omega }_c$ and detuning from the intermediate state $\delta$. (b) Time sequence of pulses for STIRAP. The delay between the two pulses is $\Delta T$. (c) Time dependencies of the probabilities $P_{gg}$, $P_{ee}$, and the probability to excite a single Rydberg atom, $P_1$, for on-resonant STIRAP with $\delta =0$. (d) Time dependencies of the probabilities $P_{gg}$, $P_{ee}$, and the probability to excite a single Rydberg atom, $P_1$, for off-resonant STIRAP with $\delta =10$ MHz.

Figure 5

(a) Dependencies of the probability $P_1$ to excite a single Rb($37P_{3/2}$) atom on the size $L$ of the cubic interaction volume for two (squares), three (circles), four (triangles), and five (diamonds) randomly positioned atoms at the chirp rate $\alpha /\left(2\pi \right)=1$ THz/s and Rabi frequency ${\Omega }_1/\left(2\pi \right)=2$ MHz. (b) The same dependencies at the chirp rate $\alpha /\left(2\pi \right)=0.5$ THz/s and Rabi frequency ${\Omega }_1/\left(2\pi \right)=0.5$ MHz. (c) Dependence of $P_1$ on Rabi frequency and chirp rate for the two frozen atoms in the full-blockade regime. (d) Monte Carlo simulation of the same dependence for the two interacting atoms, randomly placed in the cubic volume with $L=4$ $\mu$m. The calculations have been done for the exact Stark-tuned F$\ddot{\mathrm{o}}$rster resonance $37P_{3/2}+37P_{3/2}\to 37S_{1/2}+38S_{1/2}$ with zero energy defect.