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Two-level system (TLS) defects constitute a major decoherence source ofquantum information science, but they are generally less understood at materialinterfaces than in deposited films. Here we study surface TLSs at the metal-airinterface, by probing them using a quasi-uniform field within vacuum-gap (VG)capacitors of resonators. The VG capacitor has a nano-gap which creates anorder-of-magnitude larger contribution from the metal-air interface thantypical resonators used in circuit QED. We measure three phenomena and findqualitative agreement with an interacting TLS model, where near-resonant TLSsexperience substantial frequency jitter from the state switching of far-detunedlow-frequency TLSs. First, we find that the loss in all of our VG resonators isweakly or logarithmically power dependent, in contrast to data from depositeddielectric films. Second, we add a saturation tone with power $P_{in}$ to atransmission measurement and obtain the TLS Rabi frequency $\Omega_{0}$. Thesedata show a substantially weaker $P_{in}$ dependence of $\Omega_{0}$ than theprediction from the standard non-interacting TLS model. Lastly, we increase thetemperature and find an increased TLS jitter rate and dephasing rate frompower-dependent loss and phase noise measurements, respectively. We also annealsamples, which lowers the low-frequency TLS density and jitter rate, but thesingle-photon loss is found to be unchanged. The results are qualitativelyconsistent with a fast-switching interacting-TLS model and they contrast thestandard model of TLSs which describes TLSs independently.

Quantum defects from single surface exhibit strong mutual interactions