Discrimination and estimation for dephasing sources of trapped ion qubits

In this paper, we propose a handy method to discriminate and estimate the dephasing noise sources of trapped ion qubits, which are mainly magnetic field noise and laser frequency noise. In our method, the conventional Ramsey experiment is used to measure the dephasing time $T_2^{\ast }$ and calculate the total linewidth of dephasing noise. Transitions with different magnetic field sensitivities and error propagation theory are employed to quantitatively estimate the linewidth of each noise. We experimentally demonstrated this method by taking advantage of five magnetically sensitive transitions of single trapped ${}^{40}$Ca${}^{+}$, and the linewidth of the laser frequency noise and magnetic field noise is determined to be 493.3 ± 8.1 Hz and 181.4 ± 3.5 $\mu$G, respectively, in our system. This method also can be used to separate magnetic field noise and other dephasing noise in other atomic system such as neutral atoms.