Spin Coupling to Superconducting Qubits

Superconducting qubits, equipped with quantum non-demolition (QND) readout and active feedback control, have emerged as powerful tools to probe and manipulate their electromagnetic environment - from intrinsic microscopic defects to engineered spin systems in hybrid architectures. These hybrid systems aim to integrate the fast, versatile control of superconducting circuits with the exceptional coherence of spin systems such as magnetic molecules. However, the magnetic fields required for spin qubit operation present a challenge for superconductors and Josephson junctions, while the commonly used transverse ($\sigma_x$) coupling introduces mode hybridization, compromising QND spin readout.

In this work, we pursue an alternative approach: single-spin readout through a magnetic-field-resilient, longitudinal interaction that avoids mode hybridization and enables frequency-independent QND readout. First, we demonstrate longitudinal coupling between a {Cr$_7$Ni} molecular spin ensemble and a granular aluminum (grAl) resonator, mediated by magnetic-field-induced modulation of the resonator's kinetic inductance. This enables measurement of a full {Cr$_7$Ni} magnetization curve for a $f_\text{spin}=0-26\,\mathrm{GHz}$ spin frequency range ($B=0-1\,\mathrm{T}$) using a fixed readout mode at $f_\mathrm{r}=7.8\,\mathrm{GHz}$.
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To scale this interaction to the single-spin level, we introduce the gralmonium: a fluxonium qubit incorporating a self-structured, lithographically defined $(20\,\mathrm{nm})^3$ granular aluminum junction that replaces the conventional superconductor-insulator-superconductor (SIS) junction. The gralmonium exhibits a fluxonium spectrum indistinguishable from SIS-based devices and maintains microsecond range coherence. Remarkably, its spectrum and coherence remain resilient up to $1.2\,\mathrm{T}$, with only percent-level suppression of the superconducting gap evident in the qubit spectrum.

We further use the gralmonium as a sensitive probe of its magnetic environment. Energy relaxation in magnetic field reveals a paramagnetic spin-$1/2$ ensemble coupled to the qubit, constituting the dominant loss mechanism on resonance. Concomitantly, we observe magnetic-field-induced freezing of fast flux noise, consistent with surface spin polarization. Active reservoir engineering experiments rule out electron-spin-based origins for long-lived two-level systems in the qubit environment, which remain unaffected by magnetic field. Moreover, discrete fluctuations in the qubit frequency confirm the exponential sensitivity of the gralmonium to variations in the junction energy $E_\mathrm{J}$, positioning it as a nanoscale magnetic sensor. Numerical simulations show that a single magnetic molecule placed atop the nanojunction induces a resolvable $\mathrm{kHz}$-scale frequency shift. These results establish a viable path towards longitudinal single-spin readout using superconducting qubits.