Quantum defects from single surface exhibit strong mutual interactions

Two-level system (TLS) defects constitute a major decoherence source of quantum information science, but they are generally less understood at material interfaces than in deposited films. Here we study surface TLSs at the metal-air interface, by probing them using a quasi-uniform field within vacuum-gap (VG) capacitors of resonators. The VG capacitor has a nano-gap which creates an order-of-magnitude larger contribution from the metal-air interface than typical resonators used in circuit QED. We measure three phenomena and find qualitative agreement with an interacting TLS model, where near-resonant TLSs experience substantial frequency jitter from the state switching of far-detuned low-frequency TLSs. First, we find that the loss in all of our VG resonators is weakly or logarithmically power dependent, in contrast to data from deposited dielectric films. Second, we add a saturation tone with power $P_{in}$ to a transmission measurement and obtain the TLS Rabi frequency $\Omega_{0}$. These data show a substantially weaker $P_{in}$ dependence of $\Omega_{0}$ than the prediction from the standard non-interacting TLS model. Lastly, we increase the temperature and find an increased TLS jitter rate and dephasing rate from power-dependent loss and phase noise measurements, respectively. We also anneal samples, which lowers the low-frequency TLS density and jitter rate, but the single-photon loss is found to be unchanged. The results are qualitatively consistent with a fast-switching interacting-TLS model and they contrast the standard model of TLSs which describes TLSs independently.