Anomalous avoided level crossings in a Cooper-pair box spectrum

Kim, Z.; Zaretskey, V.; Yoon, Y.; Schneiderman, Justin F.; Shaw, Matthew D.; Echternach, P. M.; Wellstood, F. C.; Palmer, B. S.

doi:10.1103/physrevb.78.144506

Cited by 49 publications

(54 citation statements)

References 34 publications

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“…Evidence for the existence of TLFs have been found in nearly all known types of superconducting qubits, including phase, 1,2 flux, 3,4 charge, 5 and transmon qubits. 6 Since TLFs are considered to be a source of decoherence, 1,7,8 experiments are usually conducted by biasing the qubit in a frequency range where none of these strongly coupled natural two-level systems are present.…”

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confidence: 99%

Rabi spectroscopy of a qubit-fluctuator system

et al. 2010

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Superconducting qubits often show signatures of coherent coupling to microscopic two-level fluctuators ͑TLFs͒, which manifest themselves as avoided level crossings in spectroscopic data. In this work we study a phase qubit, in which we induce Rabi oscillations by resonant microwave driving. When the qubit is tuned close to the resonance with an individual TLF and the Rabi driving is strong enough ͑Rabi frequency of order of the qubit-TLF coupling͒, interesting four-level dynamics are observed. The experimental data show a clear asymmetry between biasing the qubit above or below the fluctuator's level splitting. Theoretical analysis indicates that this asymmetry is due to an effective coupling of the TLF to the external microwave field induced by the higher qubit levels. and transmon qubits. 6 Since TLFs are considered to be a source of decoherence, 1,7,8 experiments are usually conducted by biasing the qubit in a frequency range where none of these strongly coupled natural two-level systems are present. Alternatively, one can take advantage of the longer coherence times of TLFs as compared to the qubits for using them as a quantum memory. 9 Here we focus on the dynamics of the qubit-fluctuator system on or near resonance.There are at least two possible mechanisms explaining the interaction of the TLFs with the qubit: ͑i͒ the TLF is an electric dipole which couples to the electric field in the qubit's Josephson junction.7,10 Nanoscale dipoles could emerge from metastable lattice configurations in the amorphous dielectric of the junction's tunnel barrier 11 and ͑ii͒ the state of the TLF affects the critical current of the qubit's Josephson junction. 1,12 In this case the TLF could be related, e.g., to the formation of Andreev bound states at the interface between the superconductor and the insulator. 12,13 In this Rapid Communication, we explore the complexity of the dynamical behavior of a driven phase qubit operated in the vicinity of a resonance with a two-level fluctuator. Due to the strong coupling between the qubit and the TLF and equally strong Rabi driving, we observe the dynamics of the resulting four-level hybrid system consisting of the microscopic defect state and the macroscopic phase qubit. Strong microwave driving of the coupled system leads to coherent oscillations, revealing a characteristic beating pattern which we analyze quantitatively. Our experimental data displays a distinct asymmetry of the system response with respect to the detuning between the qubit and the TLF. We argue that this asymmetry is due to Raman-type virtual processes involving higher quantum levels of the qubit, giving rise to an effective driving of the TLF.The sample investigated in this study is a phase qubit, 1 consisting of a capacitively shunted Josephson junction embedded in a superconducting loop. Its potential energy has the form of a double well for suitable combinations of the junction's critical current ͑here, I c = 1.1 A͒ and loop inductance ͑here, L = 720 pH͒. For the qubit states, one uses the two Josephson pha...

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Rabi spectroscopy of a qubit-fluctuator system

et al. 2010

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“…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].…”

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Projected Dipole Moments of Individual Two-Level Defects Extracted Using Circuit Quantum Electrodynamics

et al. 2016

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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...

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“…In addition, comparing microwave loss in plasma-grown aluminum oxide with loss in films fabricated using other methods, i.e. low pressure oxidation 3,12,13 (the standard method for fabrication of Josephson junctions) and deposition of aluminum in a reactive oxygen atmosphere 14 , is relevant for understanding this material. We note that an aluminum oxide growth method similar to the method reported here was demonstrated in ref.…”

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Characterization of low-temperature microwave loss of thin aluminum oxide formed by plasma oxidation

Deng

Otto

Lupaşcu

2014

Applied Physics Letters

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We report on the characterization of microwave loss of thin aluminum oxide films at low temperatures using superconducting lumped resonators. The oxide films are fabricated using plasma oxidation of aluminum and have a thickness of 5 nm. We measure the dielectric loss versus microwave power for resonators with frequencies in the GHz range at temperatures from 54 to 303 mK. The power and temperature dependence of the loss is consistent with the tunneling two-level system theory. These results are relevant to understanding decoherence in superconducting quantum devices. The obtained oxide films are thin and robust, making them suitable for capacitors in compact microwave resonators.Energy loss at microwave frequencies is one of the key aspects of the physics of amorphous dielectrics, a central topic in condensed matter research 1 . In recent years, renewed interest in this topic emerged in the field of superconducting quantum devices 2 . These devices unavoidably contain amorphous dielectrics, which are a significant source of decoherence [3][4][5][6][7] . Reduction of decoherence due to amorphous dielectrics can be achieved by their partial elimination, using suitably modified microwave circuit designs [8][9][10][11] . However, these designs come at the cost of larger space and more difficult fabrication processes. Since the partial elimination of amorphous dielectrics has drawbacks, it is very relevant to investigate the physics of dielectric loss with the aim of reducing the intrinsic loss in these materials.In this letter, we present results on the fabrication and detailed characterization of microwave loss in thin films of amorphous aluminum oxide. This material is highly relevant in superconducting devices, since it forms the tunnel barrier in Josephson junctions. The films, obtained by plasma oxidation of a deposited aluminum layer, have a thickness of 5 nm. We fabricate overlap capacitors formed by the oxidized aluminum layer and a second aluminum layer. Microwave loss is measured based on lumped resonators which contain these overlap capacitors. Our characterization method is complementary to work on two-level spectroscopy using different types of superconducting qubits 3,12,13 and loss measurements based on coplanar waveguide resonators 14 . In addition, comparing microwave loss in plasma-grown aluminum oxide with loss in films fabricated using other methods, i.e. low pressure oxidation 3,12,13 (the standard method for fabrication of Josephson junctions) and deposition of aluminum in a reactive oxygen atmosphere 14 , is relevant for understanding this material. We note that an aluminum oxide growth method similar to the method reported here was demonstrated in ref. temperature and power dependence of microwave loss in plasma grown oxide has not been previously characterized. The small thickness and the robustness of the aluminum oxide layers obtained in our work are relevant for microwave circuits with compact capacitors, especially in applications where relatively large loss can be tolerated, such as pa...

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Anomalous avoided level crossings in a Cooper-pair box spectrum

Cited by 49 publications

References 34 publications

Rabi spectroscopy of a qubit-fluctuator system

Rabi spectroscopy of a qubit-fluctuator system

Projected Dipole Moments of Individual Two-Level Defects Extracted Using Circuit Quantum Electrodynamics

Characterization of low-temperature microwave loss of thin aluminum oxide formed by plasma oxidation

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