Atomic Quadrupole Moment Measurement Using Dynamic Decoupling

Abstract

We present a method that uses dynamic decoupling of a multi-level quantum probe to distinguish small frequency shifts that depend on $m_j^2$, where $m_j^2$ is the angular momentum of level $|j⟩$ along the quantization axis, from large noisy shifts that are linear in $m_j$, such as those due to magnetic field noise. Using this method we measured the electric quadrupole moment of the $4D_{\frac{5}{2}}$ level in ${}^{88}S{r}^{+}$ to be $2.973_{-0.033}^{+0.026}e{a}_0^2$. Our measurement improves the uncertainty of this value by an order of magnitude and thus helps mitigate an important systematic uncertainty in ${}^{88}S{r}^{+}$ based optical atomic clocks and verifies complicated many-body quantum calculations.

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