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 (cQED) 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 pz, dipole moments projected along the uniform field direction, are individually obtained. A distribution is created with 60 pz. We describe the distribution using a model with two dipole moment magnitudes, and a fit yields the corresponding values p = p1 = 2.8 ± 0.2 Debye and p = p2 = 8.3 ± 0.4 Debye. For a strong-coupled TLS the vacuum-Rabi splitting can be obtained with pz 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.PACS numbers: 03.67.-a, 03.67. Pp, 33.15.Kr, 66.35.+a Dielectric two-level systems (TLSs) have attracted the attention of the quantum computing community ever since they were identified as a major source of decoherence in superconducting qubits [1]. Subsequent studies found that TLSs were also a performance-limiting source of noise in photon detectors used for astronomy [2,3]. This motivation has led to quantum characterization of TLSs in the tunneling barrier of superconducting qubits [1,4] and both noise and loss characterization in high quality superconducting resonator circuits. Thus TLSs are found as defects in various dielectric structures: deposited insulating films [1,5,6], Josephson Junction (JJ) tunneling barriers [1,7,8], imperfect interfaces between superconducting films with crystalline substrates [9], and the native oxides on materials [10]. Recent modeling has predicted possible structures and values for the TLS dipole moment [11][12][13]. While these TLSs are generally known to be charged atomic configurations that spatially tunnel, their microscopic structure and elemental composition are generally unknown.In a qubit made from an anharmonic oscillator the interaction energy is observed as a spectroscopic splitting in the qubit state. However, this quantity is not only dependent on circuit element parameters, but also on the thickness of the tunneling barrier [1]. The barrier has a thickness variation of 1-2 nm [14], such that this lack of accuracy is also present in the electric field amplitude and the measured TLS dipole moment. In general, individual measurements of TLSs within JJs find the transition dipole moment p tr = p z ∆ 0 /E, where p z ≡ |p z | is the absolute value of the dipole moment projected in the field direction, and the TLS tunneling energy over the total energy ∆ 0 /E is generally unknown. As a result only a lower bound of p z is determined from those measurements (∆ 0 /E ≤ 1). However, in studie...

Transmission-line resonators for the study of individual two-level tunneling systems

“…Only recently, strong coupling to individual TLS was observed using a superconducting lumped element LC-resonator which featured electric field tuning of TLS. 13 Here, we present an alternative approach of addressing single TLS: We terminate a k/2 transmission line resonator with an overlap capacitor that hosts TLS in its dielectric, and we tune TLS by mechanical strain rather than by an electric field. This setup constitutes a circuit-QED system with the dynamics described by the JaynesCummings model, 14 in which the coupling strength between a TLS and the resonator is given by g ¼ ðD=EÞ p k jE RMS j, where p k is the component of the TLS' dipole moment that is parallel to the oscillating electric field of amplitude jE RMS j in the capacitor, E is the TLS' excitation energy, and D is the tunneling energy between states.…”

Towards understanding two-level-systems in amorphous solids: insights from quantum circuits

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Possible Hundredfold Enhancement in the Direct Magnetic Coupling of a Single-Atom Electron Spin to a Circuit Resonator

“…Over the last two decades, superconducting microwave resonators have had extensive applications that range from superconducting qubit initialization, manipulation and readout [11,12], and inter-qubit coupling [13] to dielectric characterization [14]. One of the most commonly used superconducting quantum computing architectures is one based on cavity quantum electrodynamics (cQED) [15], in which a 2D (circuit based) or 3D cavity is employed to initialize, manipulate and readout the superconducting qubit.…”