{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"4ba8fd7efc57f6266157c49d154ddd1219929479934c488cec16ff7266c55901","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"66bc627f24d6f5e9225978cf625bd4edbacba4503b1de13bbcc870d52db42b76","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"cm.qubit-decoherence-defects.resonator-loss-power-law","kind":"phenomenon","literature_status":"open","n":"1","parents":[],"plain":"The standard tunneling model predicts that defect losses in superconducting resonators fall steeply once the microwave drive is strong enough to saturate the defects, but measured losses fall much more slowly. Whether interactions between the defects explain this is not established.","posed_since":"","precise":"The non-interacting standard tunneling model gives a two-level-system loss tangent $\\tan \\delta = \\tan \\delta_0 \\tanh(\\hbar \\omega/2T)(1 + n/n_c)^{-1/2}$, i.e. $\\tan \\delta \\sim n^{-1/2}$ at photon number $n >> n_c$, while resonators typically show a much weaker power dependence. Faoro and Ioffe (Physical Review Letters 109, 157005, 2012) proposed that interacting two-level systems with spectral diffusion give a logarithmic dependence on n. Determine whether this or another mechanism accounts quantitatively for $\\tan \\delta(n, T)$ in a given resonator with the defect density and interaction strength fixed independently.","problem_ref":null,"references":"","settled_by":"$\\operatorname{tan}\\delta$ measured over many decades of photon number and temperature on resonators whose defect density and spectral-diffusion rates are measured independently (for example by two-tone spectroscopy), compared with the interacting-defect prediction without free parameters.","status_note":"Fits of Nb resonator loss continue to invoke interacting defects (Gorgichuk, Junginger and de Sousa, Physical Review Applied 19, 024006, 2023); a parameter-free test is lacking.","title":"Why does defect loss in superconducting resonators depend weakly on power?","topic_ref":"228b58abc42aea116ba49a5712e2571d336009d0276f52a950ef3939fbb3059f"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"34553c68ac470cacd01fccc3d77e5486116f77e9c846d299f9d59191836c61c5","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"d03bee4e11e47b6eead8d0821e9be82efa127d0d4b141ce25e54a69cf0c7cc85","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"4hsu9NbuixqrkyRY_RwgqkCG2sPKHyuuSDKCowuool8TUx-FSKxf133zdmhioJKohFXZ_DSy6LF_25-8UpkeDw"},"schema":"pubphys.envelope/1"},"record_hash":"34553c68ac470cacd01fccc3d77e5486116f77e9c846d299f9d59191836c61c5","leaf_index":1140}