# Two-Level-System Noise & Qubit Decoherence Theory
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**Anchor paper:** K. Agarwal, I. Martin, M.D. Lukin, E. Demler, "Polaronic model of two-level systems in amorphous solids," *Phys. Rev. B* 87, 144201 (2013). [arXiv:1212.3299]
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## Background
Since the 1970s, low-temperature anomalies in amorphous solids (anomalous heat capacity, acoustic/dielectric loss) have been explained by the standard tunneling model: a defect tunneling between two nearly-degenerate configurations forms a two-level system (TLS). The same picture explains decoherence in superconducting qubits, where TLSs in the amorphous oxide barrier couple strongly to the qubit. But the two settings implied wildly different microscopics — bulk measurements implied atomic tunneling over eV-scale barriers, while the strong TLS-qubit coupling matched what a single-electron tunneling a few angstroms would produce — a six-order-of-magnitude energy-scale mismatch the standard model couldn't reconcile.
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## New results
The authors show that when an electronic TLS is strongly coupled to phonons, a polaron transformation exponentially suppresses the bare tunneling amplitude, naturally converting eV-scale microscopic parameters into the GHz-scale TLS energies actually observed in Josephson-junction experiments. In the polaron frame nearly all bath coupling acts diagonally, so pure dephasing is suppressed by the same exponential factor as tunneling — and for energy relaxation (T1), the super-ohmic strain coupling predicts a counterintuitive, testable signature: T1 is *maximized* exactly where the TLS energy is minimized by applied strain, opposite the naive expectation.
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![TLS energy and relaxation time vs. applied strain](https://arxiv.org/html/1212.3299v2/strain.svg)
*Fig. 2 — TLS energy E and relaxation time T1 vs. applied strain ε: E is minimized at ε=ε0, where T1 simultaneously reaches its maximum.*
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## Related work in this direction
- K. Agarwal, E. Demler, I. Martin, "1/f noise and generalized diffusion in random Heisenberg spin systems," PRB 92, 184203 (2015) — scales this single-defect picture up to collective many-body dynamics, showing random TLS-like impurity networks generate 1/f noise.
- K. Agarwal, T. Martin, I. Martin, "Effect of quasiperiodic and random noise on many-body dynamical decoupling protocols," PRB 106, 134306 (2022) — examines how such noise environments limit dynamical-decoupling protocols meant to combat exactly this decoherence.
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# Parents
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* Noise Magnetometry as a Probe of Correlated Electron Dynamics⏎