This paper shows that a carefully chosen laser polarization can cancel unwanted frequency shifts between trapped-ion qubit states. The authors experimentally find the “magic” polarization that suppresses differential light shifts (DLS) in both the 2S1/2 ground and the 2F7/2 metastable clock qubits of 171Yb+. They also calculate the minimum magnetic fields needed to make this cancellation possible for several commonly trapped ion species.

The problem is that high-power, off-resonant laser light used to drive gates can shift the energy difference between the two qubit states. Those differential light shifts map laser intensity noise onto the qubit frequency. That causes dephasing and can make neighboring, idle qubits pick up unwanted phases (crosstalk). In a magnetic field, the laser produces a vector contribution to the shift that depends on the light’s polarization. By choosing a polarization with the right handedness and alignment, that vector part can cancel the usual scalar part, so the two qubit levels shift by the same amount and the qubit frequency is stable against laser intensity changes.

What the researchers did was twofold. Experimentally, they measured this “magic” polarization condition in 171Yb+ for both the ground-state clock qubit and a metastable mF = 0 clock qubit, and developed control methods for the metastable qubit. They report a state preparation and measurement infidelity of 2.9^{+3.0}_{-1.5} × 10^-4 (listed also as −35 ± 4 dB). Theoretically, they derived a simple condition for the required polarization and defined a critical bias magnetic field Bcrit: only fields at or above Bcrit allow the vector contribution to be large enough to cancel the scalar DLS. They computed Bcrit(ωL) for a set of common trapped-ion isotopes — 171Yb+, 173Yb+, 133Ba+, 135Ba+, 137Ba+, 87Sr+, 25Mg+, 43Ca+, and 9Be+ — and found the required fields are below the sizes of bias fields already used in many experiments.