Protection of Atomic Coherence in the Geomagnetic Environment

In the Earth's field range, the nonlinear Zeeman (NLZ) effect and magnetic field gradient are dominated decoherence sources. Dynamic decoupling (DD) is a method to cancel out the decoherence effects, which is usually realized by pulsed microwave fields. While, global applied microwave fields have a lot of drawbacks to the atomic system, e.g., crosstalk between adjacent samples, which is essential to multi-sensors detection. We demonstrate an all-optical DD scheme to suppress the NLZ effect and magnetic field gradient at the same time. We design an all-optical control sequence 90°y - τ/2 - 180°y - τ/2 90°y via Raman processes. The NLZ effect can be canceled out by the quadrupolar echo 90°y- τ - 90°y. There are two ways to set the free evolution time τ. One is to set τ to half of the-Larmor precession period, which can be realized by self-oscillating. The other is to use arbitrary τ with quadrature detection. For the F = 1 system, the NLZ effect can be completely removed by both methods. For the F = 2 system, the 90°y pulses are added at every half time of the Larmor precession period. Due to the greater amount of NLZ splitting in the F = 2 system, the NLZ effect cannot be completely canceled out, and the decoupling results rely on the ratio of the revival frequency to the Larmor precession frequency. By analyzing the fidelity of the atomic spin state with and without DD, we find that the fidelity is maintained as high as 99.99% in a wide range η < 1 10^-3 after five DD cycles, where most atomic systems are located. The magnetic field gradient× can be completely eliminated by inserting Hahn echo 180°y pulses into the quadrupolar echo.