Bichromatic Tweezers for Qudit Quantum Computing in ${}^{87}$Sr

TL;DR

This paper tackles the problem of tensor light-shift-induced dephasing in qudit implementations using ${}^{87}$Sr in the ${}^{3}P_2$ manifold. It introduces a bichromatic tweezer strategy that uses two wavelengths with opposite tensor polarizabilities and an engineered power ratio to realize both scalar and tensor magic trapping across all hyperfine sublevels, complemented by tuning to the tensor-magic angle at practical magnetic fields. The authors provide two concrete wavelength-pair configurations (891.5/518.0 nm and 813.5/521.3 nm), quantify tolerances to preserve fidelity around 0.999, and assess decoherence channels including Raman, Rayleigh scattering, BBR pumping, and photoionization, showing that the scheme can suppress dephasing and Rayleigh decoherence in realistic experimental settings. The approach promises enhanced loading, cooling, and nuclear-spin coherence, enabling robust qudit-based quantum computing and sensing with ${}^{87}$Sr in the ${}^{3}P_2$ manifold. The work emphasizes operating at modest fields ($ ext{B}\, ext{≲}\,5$ G) and leveraging light-shift engineering over large magnetic-field adjustments to achieve practical, scalable qudit control.

Abstract

Neutral atoms have become a competitive platform for quantum metrology, simulation, sensing, and computing. Current magic trapping techniques are insufficient to engineer magic trapping conditions for qudits encoded in hyperfine states with $J \neq 0$, compromising qudit coherence. In this paper we propose a scheme to engineer magic trapping conditions for qudits via bichromatic tweezers. We show it is possible to suppress differential light shifts across all magnetic sublevels of the $5s5p$ $\mathrm{^{3}P_2}$ state by using two carefully chosen wavelengths (with comparable tensor light shift magnitude and opposite sign) at an appropriate intensity ratio, thus suppressing light-shift induced dephasing, enabling scalar magic conditions between the ground state and $5s5p$ $\mathrm{^{3}P_2}$, and tensor magic conditions for qudits encoded within it. Furthermore, this technique enables robust operation at the tensor magic angle 54.7$^\circ$ with linear trap polarization via reduced sensitivity to uncertainty in experimental parameters. We expect this technique to enable new loading protocols, enhance cooling efficiency, and enhance nuclear spins' coherence times, thus facilitating qudit-based quantum computing in ${}^{87}$Sr in the $5s5p$ $\mathrm{^{3}P_2}$ manifold.

Figures (12)

• Figure 1: Light Shift Engineering in ${}^{87}$Sr via Bichromatic Tweezer. (a) Relevant Energy Levels in ${}^{87}$Sr for this work. (b) Representation of nuclear spins in ${}^{87}$Sr. The nuclear spin $I=9/2$ introduces 10 states in ${}^{1}\mathrm{S}_0$ comprising a qudit. Through a coherent, linearly polarized, excitation at 671 nm (red line), an atom is excited to $5s5p \ \mathrm{^{3}P_2}$ for quantum operations. (c) Experimental concept of Bichromatic tweezers. By aligning the orientation of the quantization axis, defined by the magnetic field $\vec{\mathbf{B}}$, relative to the polarization vector $\epsilon$ by angle $\beta$, differential light shifts between two atomic states can be manipulated.
• Figure 2: Flattening of the Tensor Manifold in $\mathrm{^{3}P_2}$ We illustrate the cancellation of tensor light shift induced by 813.5 nm for a laser power of 1 and a beam waist $w_0$ = 1.0 microns. The red dashed line with triangle markers represents the tensor light shift induced at 813.5 nm. We calculate a quadratic light shift dependency on nuclear spin $m_F$, which is on the scale of 0.3 . The green solid line with filled circular markers represents the light shift induced in $\mathrm{^{3}P_2}$ at 521 nm. The blue unfilled circles represent the light shift present in ${}^{1}\mathrm{S}_0$ at 813 nm. The purple line with cross markers represents the resulting tensor light shift using 813 nm and 521 nm. The combined wavelengths yields a suppressed tensor light shift in $\mathrm{^{3}P_2}$.
• Figure 3: Bichromatic Tweezer Configurations in ${}^{87}$Sr $\mathrm{^{3}P_2}$. (a) Bichromatic tweezer using 891.5 nm and 518.0 nm for ${}^{1}\mathrm{S}_0$ -- $\mathrm{^{3}P_2}$. In this figure $\lambda_1 = 891.5$ nm and $\lambda_2 = 518.0$ nm. The solid blue and the dotted green lines represent the optical potential contributions at 891.5 nm for ${}^{1}\mathrm{S}_0$ and $\mathrm{^{3}P_2}$ respectively. The red dash-dot and the orange dashed lines represent the contributions for 518.0 nm for $\mathrm{^{3}P_2}$ and ${}^{1}\mathrm{S}_0$ respectively. The total potential for ${}^{1}\mathrm{S}_0$ is presented by the purple dashed line with unfilled circles and for $\mathrm{^{3}P_2}$ is presented by brown cross markers. (b) Bichromatic tweezer using 813.5 nm and 521.3 nm for ${}^{1}\mathrm{S}_0$ -- $\mathrm{^{3}P_2}$. In this figure $\lambda_1 = 813.5$ nm and $\lambda_2 = 521.3$ nm. The solid blue and the dotted green lines represent the optical potential contributions at 813.5 nm for ${}^{1}\mathrm{S}_0$ and $\mathrm{^{3}P_2}$ respectively. The red dash-dot and the orange dashed lines represent the contributions for 521.3 nm for $\mathrm{^{3}P_2}$ and ${}^{1}\mathrm{S}_0$ respectively. The total potential for ${}^{1}\mathrm{S}_0$ is presented by the purple line with unfilled circles and for $\mathrm{^{3}P_2}$ is presented by brown cross markers.
• Figure 4: State Infidelity as a Function of Power Ratio Precision for Bichromatic Tweezer using 891.5 nm and 518.0 nm. We estimate the average state fidelity via a Monte Carlo simulation over 1000 trials per base point (5000 points spanning from $\delta x = 10^{-5}$ to $10^{-1}$). The blue line represent estimated state fidelity at $(x_0, \beta_0)$. The orange line represents estimated state fidelity at $(x=x_0, \pi/2)$. The green line represents the state fidelity at $(x=x_0 + x_s, \beta_0)$. The red line represents the state fidelity at $(x=x_0, \, \beta_0)$. The green vertical line represents value for $\delta x$ to yield $\mathcal{F}=0.999$ for $(x=x_0 + x_s, \beta_0)$. The orange vertical dash-dotted line represents $\delta x$ to yield $\mathcal{F}=0.999$ for $(x=x_0 \, , \pi/2)$. Finally, the black horizontal line represents target fidelity $\mathcal{F}=0.999$.
• Figure 5: State Fidelity as Function of Power Ratio and Quantization Axis for 1 ms. State fidelity (a) at $B$ = $0.1$ G, (b) $B$ = $1$ G, (c) $B$ = $5$ G. The dashed horizontal line represents the tensor magic angle while the dotted vertical line represents the optimal power ratio. The region in the center represents the fidelity plateau. The blue contour represents the target fidelity of 0.999.