Precision Polarization Tuning for Light Shift Mitigation in Trapped-Ion Qubits

Abstract

Trapped-ion qubits are among the most promising candidates for quantum computing, quantum information processing, and quantum simulation. In general, trapped ions are considered to have sufficiently long coherence times, which are mainly characterized under laser-free conditions. However, in reality, essential laser fields for quantum manipulation introduce residual light shift, which seriously degrades the coherence due to power fluctuations. Here, we present a comprehensive study of AC Stark shifts in the hyperfine energy levels of the $^{171}\mathrm{Yb}^+$ ion, revealing an asymmetric light shift between two circular polarizations in the clock qubit and pronounced vector light shifts in the Zeeman qubits. By precisely tuning these polarizations, a remarkable enhancement in coherence time is observed, reaching over a hundredfold for the clock qubit and more than tenfold for the Zeeman qubits, when comparing conditions of maximum and minimum shifts. These findings advance the practical realization of scalable trapped-ion quantum processors, enabling deep quantum circuit execution and long duration adiabatic operations.

Figures (7)

• Figure 1: (a) Energy level diagram of the $^{171}\text{Yb}^{+}$ ion. The 355 nm laser operates at a frequency between the $^2P_{1/2}$ and $^2P_{3/2}$ levels, thereby inducing a second-order AC Stark shift in the four hyperfine sub-levels of the $^2S_{1/2}$ ground state. This laser is pulsed with a repetition rate $\nu_\text{rep}$ in the picosecond regime, enabling spectral components that span the hyperfine splitting and drive two-photon Raman transitions. These Raman processes result in fourth-order AC Stark shifts, with detunings of $\Delta\omega_k = \omega_{\mathrm{hf}} - 2\pi k \nu_{\mathrm{rep}}$, which is described in detail in (b). In the experiment, the laser polarization is chosen to exclude any $\pi$-polarized components, thereby preventing fourth-order AC Stark shifts among the Zeeman sub-levels. (b) The clock states are modified by an external magnetic field $\mathbf{B}$, leading to the dressed state $\ket{F,m_F}_\text{d}$, which is the mixture of clock states and $R = \mu_{B}B/w_{\mathrm{hf}}$.
• Figure 1: Polarization-dependent differential shift of the clock qubit. The asymmetry induced by the external magnetic field shifts the position of the overall minimum (blue star) away from the fourth-order minimum (red square). The purple-filled circle indicates the offset of the second-order AC Stark shift in the absence of the magnetic field. The inset highlights the displacement of the minimal point due to magnetic-field-induced asymmetry.
• Figure 2: (a) Diagram of the optical path. HWP and QWP are used to adjust the polarization of the laser via the motorized rotation, and $\theta$ is the relative angle between the HWP and QWP. The 355 nm laser is focused onto the ion with a waist radius ($\omega_{0}$) of approximately $7~\mathrm{\mu m}$. (b) The Ramsey measurement sequence for the AC Stark shift measurement is realized by scanning the time interval $\tau$ between two $\pi$/2 microwave pulses.
• Figure 2: Calculated AC Stark shift as a function of the relative angle under different magnetic field strengths. The calculation assumes a wavelength of 355 nm, an optical power of 52.1 mW, and a beam waist of 7 $\mathrm{\mu m}$. The solid lines represent the theoretical shifts for various magnetic fields, while the filled circles, squares, and triangles mark the corresponding zero-crossing points. No zero-crossing is observed when the magnetic field is below 15.557 Gauss, indicating that the light shift cannot be fully canceled. In contrast, for fields exceeding 15.557 Gauss, zero-crossing points emerge, allowing for perfect cancellation of the AC Stark shift via magic polarization.
• Figure 3: Differential AC Stark shift as a function of relative angle $\theta$ between the HWP and QWP. (a) The clock qubit $\Delta m_F=0$ (filled circles) exhibits a pronounced asymmetry in AC Stark shifts between $\sigma_+$ and $\sigma_-$ polarizations, with the shift induced by $\sigma_-$ being larger than that of $\sigma_+$. The solid, dotted, and dashed lines represent total, second- and fourth-order differential shifts, respectively, calculated using Eqs. \ref{['equ:total ac Stark shift']}, \ref{['equ:clock qubit 2nd order']} and \ref{['equ:clock qubit 4th order']}. (b) The Zeeman qubit $\Delta m_F=+1$ (triangles) and $\Delta m_F=-1$ (squares) exhibit shifts over an order of magnitude larger than those observed in the clock states. These shifts demonstrate a clear vector‑Stark‑shift behavior: $\Delta m_F=+1$ ($-1$) states experience positive (negative) shifts under $\sigma_-$ polarization and negative (positive) shifts under $\sigma_+$ polarization. The solid curves show theoretical predictions from Eq. \ref{['equ:Zeeman qubits ac Stark shift']}, with beam width $\omega_0$ fitted to experimental data. Each data point was extracted via Ramsey interferometry. Error bars (standard error) were calculated from 2000 bootstrap resamples, which are smaller than the marker size and thus not visible.