Lattice-Renormalized Tunneling Models for Superconducting Qubit Materials

TL;DR

The paper introduces a lattice-renormalized formalism for configurational tunneling two-level systems by coupling hydrogen defects to a composite lattice coordinate Q, derived from the nuclear Hamiltonian. By sampling a multidimensional potential V(q,Q) and solving a 4D Schrödinger problem, it avoids unstable symmetrized structures and minimum-energy-path biases, providing tunnel-splitting predictions that bound experimental values for H and D defects in bcc Nb. The study reveals strong anharmonic H–lattice couplings and a direct link between TLS dynamics and phonon-mediated strain, while generalizing to multi-level systems to illuminate defect-induced decoherence in superconducting qubits and inform materials design to suppress TLS-related loss. It also demonstrates that lattice mass and higher-dimensional phonon couplings can significantly modify TLS spectra, underscoring the need for strain engineering and structural control in quantum devices. The framework thus offers a predictive, extensible tool for understanding and mitigating TLS effects in superconducting materials.

Abstract

We present a lattice-renormalized formalism for configurational tunneling two-level systems (TLS) that overcomes limitations of minimum-energy-path and light-particle models. Derived from the nuclear Hamiltonian, our formulation introduces composite phonon coordinates to capture lattice distortions between degenerate potential wells. This approach resolves deficiencies in prior models and enables accurate computation of tunnel splittings and excitation spectra for hydrogen-based TLS in bcc Nb. Our results bound experimental tunnel splittings and reveal strong anharmonic couplings between tunneling atoms and lattice phonons, establishing a direct link between TLS dynamics and phonon-mediated strain interactions. The formalism further generalizes to multi-level systems (MLS), providing insight into defect-induced decoherence in superconducting qubits and guiding strategies for materials design to suppress TLS-related loss.

Figures (2)

• Figure 1: (left) Schematic of lattice order parameters. Nb (green) and degenerate H tetrahedral sites (white) are shown; offset Nb atoms indicate lattice distortions. Atoms with solid borders lie in the same plane; the dashed Nb is body-centered. Order parameter $Q$ transforms singly-degenerate H configurations ($l$ or $r$) into a two-fold degenerate configuration ($s$); $S$ and $T$ produce a four-fold degenerate configuration ($f$). (a-f) Potential energy ($V$), ground ($\psi_0$) and first-excited ($\psi_1$) state wavefunctions for an O-H defect along the path connecting adjacent, degenerate H sites. $V$, $\psi_0$, and $\psi_1$ are shown at three fixed values of the composite phonon coordinate ($Q_l$, $Q_{s}$, $Q_r$). (g, h) $V$ and $\psi_0$ are shown along the composite phonon coordinate $Q$ at fixed hydrogen coordinates ($\mathbf{q_1}$, $\mathbf{q_2}$).
• Figure 2: Exponential dependence of the computed tunnel splitting ($J$) for O-H and O-D defects on the mass-scaled phonon coordinate $Q'=Q\sqrt{m/m_\mathrm{Nb}}$ using a 4D Hamiltonian. Markers indicate $m=m_\mathrm{V}$ (circles), $m=m_\mathrm{Nb}$ (squares), and $m=m_\mathrm{Ta}$ (triangles). Experimental (exp) data from Wipf1984p2.