Anisotropy with respect to the applied magnetic field in relaxation and dephasing times of spin qubits.

Electron spin qubits are a promising platform for quantum computation. Environmental noise impedes coherent operations by limiting the qubit relaxation ($T_1$) and dephasing ($T_{\phi}$) times. There are multiple sources of such noise, which makes it important to devise experimental techniques that can detect the spatial locations of these sources and determine which is the most important. In this paper, we propose that anisotropy in $T_1$ and $T_{\phi}$ with respect to the direction of the applied magnetic field can reveal much about these aspects of the noises. We investigate the anisotropy patterns of charge noise, evanescent-wave Johnson noise, and hyperfine noise. It is necessary to have a rather well-characterized sample to get the maximum benefit from this technique. The general anisotropy patterns are elucidated and then we calculate the expected anisotropy in a particular Si/SiGe quantum dot device.