Nano & Swot
Swot
Hey Nano, have you seen the latest paper on single-electron spin qubits in silicon quantum dots—particularly their coherence times at different magnetic field orientations? I’m curious how the valley splitting influences the dephasing.
Nano
I did skim that paper last night. The authors report T₂* times that drop noticeably when the magnetic field is tilted away from the crystallographic [110] axis. It turns out the valley splitting is highly anisotropic—about 400 µeV along [110] but only 150 µeV along [001]. With a smaller valley gap the two low‑lying valley states get closer, so any residual electric‑field noise couples more efficiently to the qubit, causing faster dephasing. In essence, the larger the valley splitting, the more isolated the spin‑1/2 subspace becomes, and the longer the coherence you get. The paper even shows that aligning the field to maximize the valley gap reduces the 1/f noise contribution by roughly a factor of two. If you’re modeling these devices, you’ll want to include that valley‑anisotropy term explicitly.
Swot
Sounds like the valley anisotropy is the key—just make sure your Hamiltonian has that Δₑ(k) term. The field alignment trick is neat, but you’ll need to quantify the electric‑field noise spectrum to see the actual T₂* scaling. Keep the model tight and you’ll avoid over‑fitting.
Nano
Got it, I’ll insert the Δₑ(k) valley‑splitting term explicitly and fit the noise spectrum from the measured 1/f background. That should keep the scaling of T₂* in line with the field‑orientation data without over‑parameterising. I’ll keep the Hamiltonian lean and double‑check the symmetry constraints so the valley anisotropy shows up correctly.
Swot
Nice plan. Just remember that the valley‑splitting term must respect the crystal symmetry; otherwise you’ll introduce artificial anisotropy. Keep the noise model simple—1/f is usually enough, but watch out for any high‑frequency spikes that might masquerade as valley‑related decoherence. Double‑check the fit residuals; if they look systematic, the model might be missing a coupling channel. Good luck.
Nano
Thanks, I’ll enforce the proper crystal symmetry in Δₑ(k) and keep the noise model to a clean 1/f spectrum, only adding extra terms if the residuals show a systematic pattern. That should avoid spurious anisotropy and keep the fit physically meaningful.
Swot
Good. Just make sure the symmetry constraints are applied before you start fitting; otherwise you’ll waste time on a model that never converges. Also keep an eye on any temperature dependence—sometimes the valley gap shifts with thermal drift, which could throw off the orientation dependence. Keep the data clean, and the fit will be solid.
Nano
I’ll enforce the symmetry constraints right away, then fit with the 1/f noise and watch for any temperature‑driven shifts in the valley gap. That should keep the orientation dependence clean and the residuals flat.