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arXiv:1601.03861 · IEEE Transactions on Applied Superconductivity

Decoherence and Decay of Two-level Systems due to Non-equilibrium Quasiparticles

Sebastian Zanker, Michael Marthaler, Gerd Schön

Published Jan 1, 2016• 6 citations
arXivHTMLPDF

Abstract

It is frequently observed that even at very low temperatures, the number of quasiparticles in superconducting materials is higher than predicted by standard BCS theory. These quasiparticles can interact with two-level systems, such as superconducting qubits or two-level systems (TLS) in the amorphous oxide layer of a Josephson junction. This interaction leads to decay and decoherence of the TLS, with specific results, such as time dependence, depending on the distribution of quasiparticles and the form of interaction. We study the resulting decay laws for different experimentally relevant protocols.

DOI
10.1109/tasc.2016.2519891

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It is frequently observed that even at very low temperatures, the number of quasiparticles in superconducting materials is higher than predicted by standard BCS theory. These quasiparticles can interact with two-level systems, such as superconducting qubits or two-level systems (TLS) in the amorphous oxide layer of a Josephson junction. This interaction leads to decay and decoherence of the TLS, with specific results, such as time dependence, depending on the distribution of quasiparticles and the form of interaction. We study the resulting decay laws for different experimentally relevant protocols.
The quasiparticle density observed in low-temperature superconducting circuits is several orders of magnitude larger than the value expected at thermal equilibrium. The tunneling of this excess of quasiparticles across Josephson junctions is recognized as one of the main loss and decoherence mechanisms in superconducting qubits. Here we present a unified impedance theory that accounts for quasiparticle energy loss in circuit regions both far from and near to (across) junctions. Our theory leverages the recent experimental demonstration that the excess quasiparticles are in quasiequilibrium [Connolly et al., Phys. Rev. Lett. 132, 217001 (2024)] and uses a generalized fluctuation-dissipation theorem to predict the amount of charge and flux noise generated by them. We compute the resulting energy relaxation time T1{T}_{1}T1​ in transmon qubits with and without junction asymmetric gap engineering, and show that quasiparticles residing away from junctions can play a dominant role in the former case. They also may provide an upper limit for resonator quality factors if the density of amorphous two-level systems is reduced. In addition, we show that charge noise from quasiparticles leads to flux noise that is logarithmic in frequency, giving rise to a ``nearly white'' contribution that is comparable to the flux noise observed in flux qubits. This contrasts with amorphous two-level systems, whose associated flux noise is shown to be super-Ohmic. We discuss how this quasiparticle flux noise can limit ${T}_{2}^{\ensuremath{\ast}}$ coherence times in flux-tunable qubits. The final conclusion is that asymmetric gap engineering can greatly reduce noise and increase coherence times in superconducting qubits.
It is important to know the decoherence mechanism of a qubit based on Josephson junctions. At low temperatures, as quasiparticle concentration becomes exponentially small, one needs to consider energy transfer from tunneling electrons to other degrees of freedom to find dissipation in Josephson junctions and decoherence in qubits. Here we discuss the energy transfer to two-level systems, i.e., the transitions between two different configurations of ions inside an insulating layer separated by a potential barrier. We derive a general equation of motion for the phase difference between two superconducting electrodes and we find a retarded dissipation term due to electromagnetic mechanism and also contribution due to electron tunneling mechanism. Using the equation of motion we calculate the decay of Rabi oscillations and frequency shift in qubits due to the presence of the two-level systems. In the long-time limit our results coincide with those obtained by Martinis et al. [Martinis et al., Phys. Rev. Lett. 95, 210503 (2005)] within the Fermi's Golden Rule approach up to a numerical factor.
Superconducting films are inherently limited by losses due to two-level system (TLS) defects within the amorphous oxide layers surrounding them and from quasiparticles in the film. In this thesis I will discuss novel theoretical and experimental methods toward understanding superconducting resonator loss from deleterious surface TLS defects as well as a loss transition from non-equilibrium quasiparticles in granular TiN. I will show using finite element solver software that a resonator with submicron linewidth and linespacing can be used to better characterize and simulate surface TLS as part of a circuit QED system. I have observed individual surface TLS and found coupling values in the range of g/2π =50 kHz -280 kHz with a maximum dipole moment pz-max = 4.5 Debye (.93 eÅ). I have found in in simulation of experiment that over 80% of the strongly coupled TLS reside within 50 nm of the corner between the Metal-Substrate (MS) and Substrate-Air (SA) interface. Additionally I have studied a loss transition from non-equilibrium quasiparticles in TiN films. These films exhibit an anomalous loss dependence on substrate treatment and film thickness. The films of interest are ones grown thin on oxidized substrates, which exhibit an order of magnitude decrease in internal quality factor (Qi) relative to either thicker ˝films or films grown without the oxidized substrate. These films additionally exhibit a grain size on average of 7.5 nm, a higher inhomogeneous gap, a transition to lower stress and a preference for the [111] crystal growth. The temperature dependence of the conductivity is fit and a factor of two difference in quasiparticle lifetime is found between the two films where the thinner film has a shorter lifetime. A two gap quasiparticle trapping model is fit to the temperature dependent loss data. The data is consistent with a model where non-equilibrium quasi-particles are trapped in low gapped grains on the inside of the films. From these works and others presented in my thesis the understanding of TLSs on surfaces and non-equilibrium quasiparticles in TiN has improved. This will help illuminate some of the most important absorption mechanisms plaguing superconducting qubits and resonators.
The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an Al/AlOx\mathrm{Al}/{\mathrm{AlO}}_{x}Al/AlOx​/Al Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating AlOx{\mathrm{AlO}}_{x}AlOx​ barrier. We control the density of quasiparticles in the junction electrodes either by the sample temperature or by injecting them using an on-chip dc superconducting quantum interference device driven to its resistive state. The decoherence rates were measured by observing the two-level system's quantum state evolving under application of resonant microwave pulses and were found to increase linearly with quasiparticle density, in agreement with theory. This interaction with electronic states provides a noise and decoherence mechanism that is relevant for various microfabricated devices such as qubits, single-electron transistors, and field-effect transistors. The presented experiments also offer a possibility to determine the location of the probed two-level systems across the tunnel barrier, providing clues about the fabrication step in which they emerge.
A major issue for the implementation of large scale superconducting quantum circuits is the interaction with interfacial two-level system defects (TLS) that leads to qubit relaxation and impedes qubit operation in certain frequency ranges that also drift in time. Another major challenge comes from non-equilibrium quasiparticles (QPs) that result in qubit dephasing and relaxation. In this work we show that such QPs can also serve as a source of TLS. Using spectral and temporal mapping of TLS-induced fluctuations in frequency tunable resonators, we identify a subset of the general TLS population that are highly coherent TLS with a low reconfiguration temperature ∼\sim∼ 300 mK, and a non-uniform density of states. These properties can be understood if these TLS are formed by QPs trapped in shallow subgap states formed by spatial fluctutations of the superconducting order parameter Δ\DeltaΔ. Magnetic field measurements of one such TLS reveals a link to superconductivity. Our results imply that trapped QPs can induce qubit relaxation.
Abstract Non-equilibrium quasiparticles are possible sources for decoherence in superconducting qubits because they can lead to energy decay or dephasing upon tunneling across Josephson junctions (JJs). Here, we investigate the impact of the intrinsic properties of two-dimensional transmon qubits on quasiparticle tunneling (QPT) and discuss how we can use quasiparticle dynamics to gain critical information about the quality of JJ barrier. We find the tunneling rate of the non-equilibrium quasiparticles to be sensitive to the choice of the shunting capacitor material and their geometry in qubits. In some devices, we observe an anomalous temperature dependence of the QPT rate below 100 mK that deviates from a constant background associated with non-equilibrium quasiparticles. We speculate that this behavior is caused by high transmission sites/defects within the oxide barriers of the JJs, leading to spatially localized subgap states. We model this by assuming that such defects generate regions with a smaller effective gap. Our results present a unique in situ characterization tool to assess the uniformity of tunnel barriers in qubit junctions and shed light on how quasiparticles can interact with various elements of the qubit circuit.