Analyzing the collective emission of a Rydberg-blockaded single-photon source based on an ensemble of thermal atoms

An ensemble of rubidium atoms can be excited with lasers such that it evolves into an entangled state with just one collective excitation within the Rydberg-blockade radius. The decay of this state leads to the emission of a single antibunched photon. For a hot vapor of rubidium atoms in a microcell, we numerically study the feasibility of such a single-photon source under different experimental conditions like the atomic density distribution and the choice of electronic states addressed by the lasers. For the excitation process with three rectangular lasers pulses, we simulate the coherent dynamics of the system in a truncated Hilbert space. We investigate the radiative behavior of the moving rubidium atoms and optimize the laser pulse sequence accordingly. We find that the collective decay of the single excitation leads to a fast and directed photon emission and further that a pulse sequence similar to a spin echo increases the directionality of the photon. Finally, we analyze the residual double excitations and find that they do not exhibit these collective decay properties and play only a minor deleterious role.

Figure 1

Setup of the system. (a) ${}^{85}\mathrm{Rb}$ atoms in a vapor cell which get excited by three antiparallel lasers. The cell length as well as the laser beam waist ${\mathsf{\text{w}}}_0$ has the size of the Rydberg-blockade radius. (b) Four-level scheme with the respective Rabi frequencies ${\mathrm{\Omega }}_j$ and atom decay rate $\mathrm{\Gamma }$.

Figure 2

Illustration of the effective description of the low-excitation sector. The oscillations from a state with two excitations, here $|i_n{r}_m\rangle$, to $N-2$ states with a third excitation get combined to one oscillation to an effective state $|i_n{r}_m{i}_{\mathrm{eff}}\rangle$.

Figure 3

Emission properties of the target state: (a) total photon emission after 10 ns into a forward cone up to a $30{}^{\circ }$ angle to the laser direction and (b) photon emission peak position $t_p$ for different $W$-state phases with $N=500$ atoms averaged over ten samples.

Figure 4

Optimized pulses obtained from the simulation of 50 samples, each with $N=30$ atoms each. The atoms were sampled once according to the Boltzmann distribution and once according to the distribution in the LIAD case and the pulses were optimized separately for all four scenarios. The delay between the pulse of the first two lasers and the third one further increases the phases.

Figure 5

Single-photon emission. (a) Photon-population density function from the decay of a single excitation after 10 ns where we excluded the geometrical factor $sin\left(\theta \right)$. (b) Associated emission rate in units of the corresponding single-atom decay rate. Both (a) and (b) also show a comparison between the optimized pulse with the delay of the third laser and without. (c) Linear dependence of the maximal emission rate on the particle number $N$.

Figure 6

Two-photon emission. (a) Photon-population density function for the first photon emitted from the double excitation. (b) Corresponding emission rate in units of the single-atom decay rate. (c) Emission rate of the second photon. The second photon is emitted at a much lower rate and with a peak at larger $t$ compared to the single photon. In the LIAD case we neglected three samples for this plot due to numerical artifacts.