Programmable Adiabatic Rapid Passage laser pulses for Ultra-fast Gates on trapped ions

TL;DR

This work addresses the challenge of achieving ultrafast, high-fidelity entangling gates in trapped-ion systems by proposing a programmable pulsed-laser source based on a continuous-wave seed modulated by high-speed arbitrary waveform generators and broadband electro-optic modulators. By implementing adiabatic spin-dependent-kick protocols—ARP, STIRARP, and DE—via flexible pulse shaping, the authors show that STIRARP yields the highest fidelity and robustness against pulse-intensity fluctuations and single-photon detuning, with simulated gate fidelities exceeding $99.99\%$. Critical to practical performance are timing precision and bandwidth: achieving $1-F_{s}\lesssim 2\times10^{-4}$ requires timing resolution below about $120$ ps (and below $20$ ps for $1-F_s\lesssim 1\times10^{-4}$), corresponding to bandwidths in the 10–50 GHz range. The framework enables fast entangling gates without the repetition-rate constraints of mode-locked lasers and is compatible with current high-bandwidth modulators, offering a scalable route toward robust, ultra-fast trapped-ion quantum gates.

Abstract

Scaling of quantum gates remains a central challenge in quantum information science. Ultrafast gates based on spin-dependent kicks provide a promising approach for trapped-ion systems. However, these gates require laser pulses with both high temporal tunability and stability, which are difficult to achieve with existing pulsed sources. Here, we propose a programmable pulsed source that allows flexible control of pulse intensity, waveform, and phase profiles. This enables precise manipulation of pulse sequences, thereby improving the fidelity of entangling gates. Furthermore, since the pulse parameters can be conveniently tuned, various coherent population-transfer schemes can be implemented adiabatic SDKs, thereby improving both the fidelity and robustness of fast quantum gate. Simulation results show that our programmable pulse system can achieve gate fidelities above 99.99% with strong robustness against variations in pulse intensity and single-photon detuning using stimulated Raman adiabatic rapid passage (STIRARP) protocols.

Figures (8)

• Figure 1: Spin-dependent kick on $^{171}\mathrm{Yb}^{+}$ ion. (a) Energy level of $^{171}\mathrm{Yb}^+$ and stimulated Raman transition process. Qubit states are encoded onto the hyperfine energy levels of $^{171}\mathrm{Yb}^{+}$ ion ($\left|0\right\rangle$ and $\left|1\right\rangle$). The ions will absorb a photon to reach a virtual level and emit another photon which gives the spin-dependent momentum transfer of $\pm\hbar (\mathbf{k}_{\hat{x}} - \mathbf{k}_{\hat{y}} )$ where the subscripts $\hat{x}$ and $\hat{y}$ represent the polarization directions. The two Raman pulses have a large single-photons detuning $\Delta$ and a two-photons detuning $\delta$. Pulses with horizontal ($|H\rangle$) and vertical ($|V\rangle$) polarizations couple the hyperfine energy levels. (b) spin-dependent momentum kick. Depends on both the ion's initial spin state and the propagation directions of the laser pulses, the direction of the momentum kick will be different. (c) SDK pulse diagram. The two Raman pulses alternately incident from opposite directions and are incident along the ion axis direction. Here, the sign convention for optical field intensity represents the propagation direction of the pulses. (d) The evolution of the qubit state during the SDK process.
• Figure 2: The pulse sequences and SDK performances for different protocols. (a–d) illustrate various adiabatic SDK schemes. (a) In the SRT scheme, a large single-photon detuning is employed to ensure that the population in the intermediate state remains negligible. (b) In ARP, the system evolves along the instantaneous eigenstate by sweeping the two-photon detuning $\delta$. (c) In STIRARP, two Raman pulses are applied with a temporal separation $t_d$; by arranging the Stokes pulse to precede the pump pulse, the system is likewise guided to follow the instantaneous eigenstate. (d) In DE, the electric fields of the two pulses are modulated at a high frequency $\omega_e$ to generate zero-area pulses, and their relative phase is offset by $\pi$, ensuring that the intermediate state remains unpopulated. (e-h) The fidelity of SDK under different techniques when the pulse duration $\tau = 1~\text{ns}$. For (e, g, h), the two-photon detuning is set to $\delta = 0$; for (e,f), the single-photon detuning is set to $\Delta = 400~\text{GHz}$; and for (g, h), $\Delta = 0$.
• Figure 3: Comparison of the fast gate error $1-F_s$ caused by the unperfect SDK for different protocols: SRT (blue), ARP (red), STIRARP (green), and DE (purple). (a) Dependence on relative laser intensity. (b) Dependence on relative single-photon detuning. STIRARP shows the lowest sensitivity to both intensity and detuning variations.
• Figure 4: The gate infidelity $1-F_s$ for the STIRARP protocols is plotted as a function of the deviation in delay time $t_d$, with a pulse duration of $\tau = 1~\text{ns}$.
• Figure 5: Trajectories of the COM and SM phonon modes in phase space under the rotating frame for the (a, b)GZC scheme and (c, d) FRAG scheme. (a, c) The trajectory of the COM mode in phase space traces a closed path during the entire gate duration, ensuring that the entanglement gate leaves the phonon modes unaffected, ultimately decoupling the spin state from the phonon state. The blue curve represents the simulation results for a pulse repetition rate of 1 GHz, whereas the orange curve corresponds to the results simulated at a 100 MHz repetition rate. (c, d) Corresponding trajectory of the SM mode.