Quantum noise spectroscopy of superconducting critical dynamics and vortex fluctuations in a high-temperature cuprate

We use nitrogen-vacancy (NV) centers in diamond as a non-invasive and table-top quantum sensor to study low-energy dynamics in high-T$_c$ cuprate Bi$_2$Sr$_2$CaCu$2$O${8+\delta}$. Our measurements reveal a sharp reduction in NV relaxation time ($T_1$) near the critical temperature ($T_c \approx 90~$K), attributed to supercurrent-fluctuation induced magnetic noise. The temperature scaling of this noise deviates from BCS predictions, allowing us to extract critical exponents. In the presence of a small magnetic field, we observe asymmetric $T_1$ noise spectrum, suggesting a vortex liquid phase. Deep in the superconducting phase, NV decoherence ($T_2$) spectroscopy reveals strong low-frequency magnetic fluctuations, potentially linked to complex vortex dynamics.

We support our findings for the zero magnetic field case with theoretical modeling using the time-dependent Ginzburg-Landau formalism.