Measurement of an atomic quadrupole moment using dynamic decoupling

Some of the best clocks today are ion-based optical clocks. These clocks are referenced to a narrow optical transition in a trapped ion. An example for such a narrow transition is the electric quadrupole $E2$ transition between states with identical parity. An important systematic shift of such a transition is the quadrupole shift resulting from the electric field gradient inherent to the ion trap. We present a new dynamic decoupling method that rejects magnetic field noise while measuring the small quadrupole shift of the optical clock transition. Using our sequence we measured the quadrupole moment of the $4D_{\frac{5}{2}}$ level in a trapped $^{88}Sr^{+}$ ion to be $2.973^{+0.026}_{-0.033}\, ea_{0}^{2}$, where $e$ is the electron charge and $a_{0}$ is the Bohr radius. Our measurement improves the uncertainty of this value by an order of magnitude and thus helps mitigate an important systematic uncertainty in $^{88}Sr^{+}$ based optical atomic clocks and verifies complicated many-body quantum calculations. (Ref: arXiv:1511.07277 2015)