Abstract
Material-based two-level systems (TLSs), appearing as defects in low-temperature devices including superconducting qubits and photon detectors, are difficult to characterize. In this study we apply a uniform dc electric field across a film to tune the energies of TLSs within. The film is embedded in a superconducting resonator such that it forms a circuit quantum electrodynamical system. The energy of individual TLSs is observed as a function of the known tuning field. By studying TLSs for which we can determine the tunneling energy, the actual , dipole moments projected along the uniform field direction, are individually obtained. A distribution is created with 60 . We describe the distribution using a model with two dipole moment magnitudes, and a fit yields the corresponding values and . For a strong-coupled TLS the vacuum-Rabi splitting can be obtained with and tunneling energy. This allows a measurement of the circuit’s zero-point electric-field fluctuations, in a method that does not need the electric-field volume.
- Received 25 March 2015
DOI:https://doi.org/10.1103/PhysRevLett.116.167002
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