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Superconductor Science and Technology

Quantum coherent manipulation of two-level systems in superconducting circuits

Alexander L. Burin, Andrii Maksymov, Kevin D. Osborn

Published Jul 2, 2014• 5 citations
Publisher

Abstract

Two-level systems (TLSs) appear in the insulating layers of microfabricated superconducting circuits and are known to be a source of superconducting qubit decoherence. Here we theoretically analyze the quantum evolution of a TLS bath, which is related to a recent experiment performed with a superconducting resonator. During the application of simultaneous time-varying bias and continuous microwave fields, TLSs pass through resonance with the latter field such that Landau?Zener crossings cause the TLS to remain in the ground (Floquet) state or become inverted. The TLSs are analyzed for insulating films, which convey a distribution of tunneling parameters and associated TLS inversion regimes. Under certain conditions, we indeed find that the TLS population should be inverted over a wide range of frequencies. Discussion is included on how new TLS environments could affect the operation of resonators and qubits.

DOI
10.1088/0953-2048/27/8/084001

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Two-level systems (TLSs) appear in the insulating layers of microfabricated superconducting circuits and are known to be a source of superconducting qubit decoherence. Here we theoretically analyze the quantum evolution of a TLS bath, which is related to a recent experiment performed with a superconducting resonator. During the application of simultaneous time-varying bias and continuous microwave fields, TLSs pass through resonance with the latter field such that Landau?Zener crossings cause the TLS to remain in the ground (Floquet) state or become inverted. The TLSs are analyzed for insulating films, which convey a distribution of tunneling parameters and associated TLS inversion regimes. Under certain conditions, we indeed find that the TLS population should be inverted over a wide range of frequencies. Discussion is included on how new TLS environments could affect the operation of resonators and qubits.
Increasing and stabilizing the coherence of superconducting quantum circuits and resonators is of utmost importance for various technologies, ranging from quantum information processors to highly sensitive detectors of low-temperature radiation in astrophysics. A major source of noise in such devices is a bath of quantum two-level systems (TLSs) with broad distribution of energies, existing in disordered dielectrics and on surfaces. Here we study the dielectric loss of superconducting resonators in the presence of a periodic electric bias field, which sweeps near-resonant TLSs in and out of resonance with the resonator, resulting in a periodic pattern of Landau–Zener transitions. We show that at high sweep rates compared to the TLS relaxation rate, the coherent evolution of the TLS over multiple transitions yields a significant reduction in the dielectric loss relative to the intrinsic value. This behavior is observed both in the classical high-power regime and in the quantum single-photon regime, possibly suggesting a viable technique to dynamically decouple TLSs from a qubit.
Quantum two-level systems (TLSs) limit the performance of superconducting qubits and superconducting and optomechanical resonators breaking down the coherence and absorbing the energy of oscillations. TLS absorption can be suppressed or even switched to the gain regime by inverting TLS populations. Here we theoretically explore the regime where the full inversion of TLS populations is attained at energies below a pump field quantization energy by simultaneously applying the pump field and the time varying bias. This regime is attained changing the bias sufficiently slowly to fully invert TLS populations when their energies cross resonance with the pump field and sufficiently fast to avoid TLS relaxation between two resonance crossing events. This population inversion is accompanied by a significant red shift of cavity resonance due to quantum level repulsion. The red-shift in frequency serves as a signature of the population inversion, as its re-entrant behavior as function of bias sweep rate and of the magnitude of the pump field allows the determination of the TLSs dipole moment and relaxation time. The predicted behavior is qualitatively consistent with the recent experimental observations in Al superconducting resonators.
Abstract Increasing and stabilizing the coherence of superconducting quantum circuits and resonators is of utmost importance for various technologies, ranging from quantum information processors to highly sensitive detectors of low-temperature radiation in astrophysics. A major source of noise in such devices is a bath of quantum two-level systems (TLSs) with broad distribution of energies, existing in disordered dielectrics and on surfaces. Here we study the dielectric loss of superconducting resonators in the presence of a periodic electric bias field, which sweeps near-resonant TLSs in and out of resonance with the resonator, resulting in a periodic pattern of Landau–Zener transitions. We show that at high sweep rates compared to the TLS relaxation rate, the coherent evolution of the TLS over multiple transitions yields a significant reduction in the dielectric loss relative to the intrinsic value. This behavior is observed both in the classical high-power regime and in the quantum single-photon regime, possibly suggesting a viable technique to dynamically decouple TLSs from a qubit.
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.
Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.
One significant source of decoherence in superconducting circuits is known as two-level systems (TLSs), found in amorphous oxide layers. These circuits can, however, also be utilized as spectral and temporal TLS probes. Comprehensive investigations on the physics of TLSs are now possible thanks to recent advancements in superconducting qubits. Here, we simultaneously measure the tunable Xmon qubit decoherence time as well as the resonance frequency for more than 3 days to investigate stochastic fluctuations. Time-domain Allan deviation and frequency-domain power spectral density analysis indicate that two TLSs in near resonance with the qubit are responsible for the fluctuations. From the extracted oscillation in T1 decay, we locate the two TLSs near the junctions.