Atomic Fock State Preparation Using Rydberg Blockade

We use coherent excitation of 3–16 atom ensembles to demonstrate collective Rabi flopping mediated by Rydberg blockade. Using calibrated atom number measurements, we quantitatively confirm the expected $\sqrt{N}$ Rabi frequency enhancement to within 4%. The resulting atom number distributions are consistent with an essentially perfect blockade. We then use collective Rabi $\pi$ pulses to produce $\mathcal{N}=1$, 2 atom number Fock states with fidelities of 62% and 48%, respectively. The $\mathcal{N}=2$ Fock state shows the collective Rabi frequency enhancement without corruption from atom number fluctuations.

Figure 1

(a) Experimental geometry. Counterpropagating 780 and 480 nm Rydberg excitation lasers, parallel to an applied magnetic field, couple $|a⟩$ or $|b⟩$ to $|r⟩$. Optical pumping and state selective blowaway beams are incident on the ensemble in the perpendicular plane. (b) Two-photon excitation diagram. (c) Fock state generation pulse sequences. Sequential pairs of $A$ and $B$ excitation pulses perform population transfer from $|a⟩\to |r⟩\to |b⟩$. Ideally, the Rydberg blockade mechanism moves a single atom to $|b⟩$ per $A\text{−}B$ pulse pair. After two $A\text{−}B$ pulse pairs, the $B_3$ pulse optionally probes two-atom Fock state dynamics.

Figure 2

Rabi oscillations between $|a⟩$ and $|r⟩$ for various atom number distributions. The single-atom detection probability is shown as a function of the pulse area $\theta ={\mathrm{\Omega }}_{1}t$ of the Rydberg $A$ excitation. (a) The first $2\pi$ rotation for exactly one atom. A $\pi$ pulse takes 670 nsec. (b)–(e) The $|b⟩$ populations show an atom number dependent frequency for ensemble means of, respectively, $\overline{n}=3.0$, 6.5, 9.1, 15.5. The solid black lines are the fits to Eq. (1).

Figure 3

Mean number of atoms in the ensemble, as deduced from collective Rabi oscillations (ordinate) and by fluorescence (abscissa). The red circles are data from Poisson-distributed atom ensembles, the green triangles have exactly 1 or 2 atoms. The solid black line, of slope 1, shows that the collective oscillation frequency closely follows the predicted $\sqrt{N}$ dependence.

Figure 4

(a) Evolution of $N_b=0$, 1, and 2 atom populations using the $A_1{B}_1{A}_2{B}_2(\theta )$ protocol. (b) Output of the $\mathcal{N}=2$ Fock state production as a function of $B_3$ area.

Figure 5

$\mathcal{N}=1$ Fock state production fidelity as a function of mean ensemble number and quantum Monte Carlo simulations. The black dashed line assumes ideal blockade and perfect excitation conditions. The red dot-dashed line adds in realistic experimental imperfections, and the green solid line includes finite blockade strength. The solid green line at the bottom shows the predicted two-atom production.