Quantum two-level systems (TLSs) commonly found at low temperature in amorphous and disordered materials are responsible for decoherence in superconducting Josephson junction qubits particularly because they absorb energy of coherent qubit oscillations in the microwave frequency range. In planar Josephson resonators with oxide interfaces, this absorption is characterized by an anomalously weak loss-tangent dependence on the field in the nonlinear regime that conflicts with the theoretical expectations and the observations in amorphous dielectrics. It was recently suggested that this anomalous absorption is caused by TLS dynamic interactions. Here, we show that such interactions cannot lead to the observed loss-tangent field dependence and suggest the alternative explanation assuming that TLS dipole moments $p$ are distributed according to the specific power law $P\left(p\right)\propto 1/p^{3-\eta }$ ($0\le \eta <1$). This assumption, indeed, results in the observed loss-tangent behavior. The hypothesis of a power-law distribution is supported both by the recent measurements of individual TLS dipole moments and the theoretical model of TLS formation because of the long-range dipole-dipole interaction, thus connecting the anomalous absorption with the possible solution of the longstanding problem of the nature of TLSs.

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• Dielectric properties
• Electric polarization
• Josephson effect
• Lifetimes & widths
• Open quantum systems & decoherence
• Optical & microwave phenomena
• Quantum coherence & coherence measures
• Quasiparticles & collective excitations