title: Projected Dipole Moments of Individual Two-Level Defects Extracted Using Circuit Quantum Electrodynamics.
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 p_{z}, dipole moments projected along the uniform field direction, are individually obtained. A distribution is created with 60 p_{z}. We describe the distribution using a model with two dipole moment magnitudes, and a fit yields the corresponding values p=p_{1}=2.8±0.2  D and p=p_{2}=8.3±0.4  D. For a strong-coupled TLS the vacuum-Rabi splitting can be obtained with p_{z} 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.
authors.affiliation: Laboratory for Physical Sciences, College Park, Maryland 20740, USA.|Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: B
authors.initials: B
authors.lastname: Sarabi
authors.affiliation: Laboratory for Physical Sciences, College Park, Maryland 20740, USA.|Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: A N
authors.initials: AN
authors.lastname: Ramanayaka
authors.affiliation: Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, USA.
authors.forename: A L
authors.initials: AL
authors.lastname: Burin
authors.affiliation: Department of Physics, University of Maryland, College Park, Maryland 20742, USA.|Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: F C
authors.initials: FC
authors.lastname: Wellstood
authors.affiliation: Laboratory for Physical Sciences, College Park, Maryland 20740, USA.|Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: K D
authors.initials: KD
authors.lastname: Osborn