Improving Single Excitation Fidelity in Rydberg Superatoms for Efficient Single Photon Emission

Abstract

Deterministic single photon emission from a Rydberg ensemble coupled to an optical cavity requires high-fidelity preparation of collective single excitations. In such a setup imperfect Rydberg blockade can lead to unwanted double excitations, which degrade photon indistinguishability. In this work we adapt the Derivative Removal by Adiabatic Gate (DRAG) technique, originally developed for superconducting qubits, to shape optical pulses that suppress double excitations in this atomic platform. By combining analytical modeling with numerical optimization, DRAG provides an improvement over conventional sine-squared pulses. Further optimization of pulse duration and atomic ensemble size identifies a parameter regime, distinct from that used in [Nature Photonics 17, 688 (2023)], that enhances the single excitation probability from the previous theoretical benchmark of 77% to 91.9%, approaching the fundamental limits set by decoherence in the system. Benchmarking against GRAPE (Gradient Ascent Pulse Engineering) confirms that DRAG operates close to the optimal control limit, while maintaining smooth, experimentally feasible pulse shapes. These results demonstrate the effectiveness and cross platform adaptability of DRAG for a high-fidelity single photon source.

Figures (9)

• Figure 1: Schematic representation of the experimental setup. (a) An atomic ensemble confined within an optical cavity, where the yellow shaded region denotes the Rydberg blockade sphere. (b) Two-photon excitation scheme in which a red drive ($\Omega_r$) and a blue drive ($\Omega_b$) coherently couple the ground state $\ket{g}$ to the Rydberg state $\ket{r}$ via a far-detuned intermediate state $\ket{e}$. The gray dashed arrow indicates the effective two-photon Rabi coupling. Following excitation, a blue read pulse drives a de-excitation process that results in the emission of a single photon into a well-defined cavity mode.
• Figure 2: Schematic representation of the system dynamics. The ground state $G$ couples to the singly-excited symmetric Rydberg state $R_0$ with Rabi frequency $\Omega$ (yellow arrow). The state $R_0$ sequentially couples to a series of singly-excited asymmetric Rydberg states $R_1, R_2, \!\ldots\!, R_j, \!\ldots\!, R_{n_{\text{max}}}$ (blue arrows), capturing memory effects arising from thermal atomic motion, and subsequently undergoes irreversible exponential decay (red arrow) into a continuum of these states $M_{\mathrm{th}}$ with a decay rate $\gamma_{n_{\text{max}}}$Covolo_2025_Optica. Each singly-excited asymmetric state further couples to the doubly-excited Rydberg states $S_0, S_1, \!\ldots\!, S_k, \!\ldots\!, S_{n_{\text{max}-1}}$ with corresponding Rabi frequencies $\beta_{jk}\Omega$ (yellow arrow). Each doubly-excited state is detuned by $\delta_{S_k}$ (green arrow) and irreversibly couples to the interaction-induced continuum $M$ with decay rate $\gamma_{S_k}$ (red arrow). All singly- and doubly-excited states share a common dephasing rate, $\gamma$ and $2\gamma$, respectively (purple arrows). This effective model explains the system dynamics while remaining computationally efficient.
• Figure 3: Identifying the dominant leakage channels. (a) The system dynamics for $T = 0.25~\mu\mathrm{s}$ and $\sigma = 4.6~\mu\mathrm{m}$, corresponding to the experimental parameters of Ref. magro_nature_photonics_2023 for a sine-squared $\pi$ pulse. Populations in the relevant states are shown: ground state $G$ (blue), singly-excited symmetric state $R_0$ (green), all singly-excited asymmetric states and the associated thermal continuum $R + M_{\mathrm{th}}$ (yellow), leakage dominated doubly-excited state $S_3$ (purple), remaining doubly-excited states $S_{\mathrm{other}}$ (orange), and the associated interaction-induced continuum $M$ (pink). Final populations are highlighted with matching colors. (b) Population difference between $S_3$ and $S_4$ as a function of the ensemble radius $\sigma$ and total pulse duration $T$, illustrating the dominant doubly-excited leakage state for different parameters. Colors indicate the sign of the difference; $S_3>S_4$ in red and $S_4>S_3$ in blue. The black and white stars mark the experimental and optimized parameters, respectively. For the experimental parameters ($T=0.25~\mu\mathrm{s}$, $\sigma=4.6~\mu\mathrm{m}$), leakage is dominated by $\ket{S_3}$; for the optimized parameters ($T=0.5~\mu\mathrm{s}$, $\sigma=4.3~\mu\mathrm{m}$), it is dominated by $S_4$. (c) Final population distribution among the leakage states, normalized to the total leakage, for parameters in (a). The leakage into the doubly-excited state $S_3$ exceeds that into other doubly- and singly-excited asymmetric states, indicating $S_3$ as the dominant leakage channel and showing that interaction-induced dephasing dominates over thermal dephasing on short timescales. Population in $S_3$ irreversibly decays into the continuum $M$, and the difference between them quantifies the rapid Markovian dephasing.
• Figure 4: System dynamics with the optimized pulses. (a) Optimized control pulses for the detuning-aided sine-squared (solid), perturbative DRAG (dashed), and non-perturbative DRAG (dotted) schemes, showing the corresponding fields $\Omega_x$ (black), $\Omega_y$ (dark green), and $\Omega_z$ (dark red), which represent the in-phase (primary) drive, the out-of-phase (counterdiabatic) drive, and the constant laser detuning, respectively, for $T = 0.25~\mu\mathrm{s}$ and $\sigma = 4.6~\mu\mathrm{m}$. The optimized parameters for each pulse are: detuning-aided sine-squared: $A = 3.79$, $\Delta_d = -0.28$; perturbative DRAG: $A = 1.95$, $\Delta_d = -2.92$, $\alpha = -1.21$; and non-perturbative DRAG: $A = 2.00$, $\Delta_d = -2.87$, $\alpha = -1.20$. (b) Difference in the population dynamics relative to the initial sine-squared $\pi$ pulse for the optimized pulse shapes of panel (a) indicated with the same line code. Populations in the relevant states are shown; the singly-excited symmetric state $R_0$ (green), all singly-excited asymmetric states and the associated thermal continuum $R + M_{\mathrm{th}}$ (yellow), the leakage-dominated doubly excited state $S_3$ (purple), and the interaction-induced dephasing continuum $M$ (pink). Positive differences indicate the desired increase in the $R_0$ population with the optimized pulses, while negative differences indicate the targeted reduction in the population of $M$. The improvement provided by the DRAG pulses is higher than that obtained with the detuning-aided sine-squared pulse. (c) Final populations in all the relevant states for the optimized control pulses.
• Figure 5: Identification of a parameter regime that minimizes dephasing. Population distributions as functions of the atomic ensemble radius $\sigma$ and total pulse duration $T$, shown before DRAG optimization (first row) and after DRAG optimization (second row), together with their difference (third row), for (a) the leakage-dominated doubly excited state $\ket{S_3}$, (b) the interaction-induced dephasing continuum $M$, (c) the asymmetric singly-excited states and associated thermal continuum $\ket{R_{1,\ldots,8}} + M_{\mathrm{th}}$, and (d) the symmetric singly-excited target state $\ket{R_0}$. The color scale represents the final population after a complete pulse sequence, with red (dark blue) indicating high (low) population. These maps identify parameter regimes that minimize irreversible dephasing and highlight the effectiveness of DRAG in suppressing leakage. Leakage into $\ket{S_3}$ and $M$ increases with the ensemble size [see panels (a) and (b)] but is strongly suppressed by DRAG as indicated by the green regions in the third row, with optimal performance occurring to the left of the dashed contour curves. DRAG significantly enlarges the parameter space in which the leakage into $M$ remains below the $5.4\%$ threshold. In contrast, the population in $\ket{R_{1,\ldots,8}} + M_{\mathrm{th}}$ increases for longer pulse durations [see panel (c)] and is only weakly affected by DRAG. The population in the target state $\ket{R_0}$ is maximized for small ensemble radii and short pulses, a regime that is unfavorable due to collisional losses. The white star in the DRAG-optimized plot of panel (d) marks an optimal intermediate operating point that balances these competing constraints. For a lower bound of $\sigma = 4.3~\mu\mathrm{m}$, high-fidelity transfer to $\ket{R_0}$ is achieved at $T = 0.5~\mu\mathrm{s}$, as indicated by the dotted contour levels. For a threshold of $89.8\%$ population in $\ket{R_0}$, the accessible parameter space is again larger with DRAG.