Spin-orbit coupling fluctuations as a mechanism of spin decoherence

We discuss a general framework to address spin decoherence resulting from fluctuations in a spin Hamiltonian. We performed a systematic study on spin decoherence in the compound ${\mathrm{K}}_6\left[{\mathrm{V}}_{15}{\mathrm{As}}_6{\mathrm{O}}_{42}\left({\mathrm{D}}_2\mathrm{O}\right)\right]·8{\mathrm{D}}_2\mathrm{O}$, using high-field electron spin resonance. By analyzing the anisotropy of resonance linewidths as a function of orientation, temperature, and field, we find that the spin-orbit term is a major decoherence source. The demonstrated mechanism can alter the lifetime of any spin qubit and we discuss how to mitigate it by sample design and field orientation.

Figure 1

(a) Ball-and-stick representation of ${\mathrm{V}}_{15}$ (V ions in blue). The $x$ axis is along one side of the triangle, while the $z$ axis is perpendicular to the triangle plane and represents the $c$ axis of the crystal unit cell. (b) Level diagram of the three-spin model in field $\parallel z$, with positions of the three experimental frequencies shown. Dashed lines show the $S=1/2$ doublets with the red dashed arrows indicating those transitions. Lines show the $S=3/2$ quartet with blue arrows indicating the transitions; the resonance fields are averaged in the first moment calculation of $B_{\mathrm{res}}$ at a given frequency.

Figure 2

(a) Typical measurements of the derivative of the absorption ${\chi }^{\prime \prime }$ at 120, 241, and 336 GHz with derivatives of Gaussian (blue dotted line) and Lorentzian (red dashed line) fits. (b) FWHM of Lorentzian fits as a function of field angle $\theta$ measured at three frequencies: 336 GHz (blue triangles), 241 GHz (red circles), and 120 GHz (black squares). The dashed lines are calculated widths as a function of $\theta$; the agreement shows the predicted correlation between the decoherence rate and $g_e-g\left(\theta \right)$. In contrast, the green line (right axis) shows the opposite angular behavior of calculated $g\left(\theta \right)$, leading to $G_g\ll G_{\delta }+G_T$ (see text). (c) FWHM of Lorentzian fits vs temperature/frequency for the three studied frequencies. Dashed lines are calculated $\text{FWHM}\left(T\right)$ for $\theta =0^{\circ }$ and ${90}^{\circ }$.