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arXiv:1609.06173 · Physical review. B./Physical review. B

Electronic decoherence of two-level systems in a Josephson junction

Alexander Bilmes, Sebastian Zanker, Andreas Heimes, Michael Marthaler, Gerd Schön, Georg Weiss, Alexey Vladimirovich Ustinov, Jürgen Lisenfeld

Published Aug 3, 2017• 31 citations
arXivHTMLPDF

Abstract

The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an $\mathrm{Al}/{\mathrm{AlO}}_{x}$/Al Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating ${\mathrm{AlO}}_{x}$ 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.

DOI
10.1103/physrevb.96.064504

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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.
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.
Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two-level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two-level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two-level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two-level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two-level systems in the oxide barrier produce fluctuations and 1∕f1∕f1∕f noise in the Josephson junction critical current I0{I}_{0}I0​. This in turn leads to fluctuations in the qubit energy splitting that degrade the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.
Two-level system fluctuators (TLS's) in the tunnel barrier of a Josephson junction have recently been demonstrated to cause novel energy splittings in spectroscopic measurements of superconducting phase qubits. With their strong coupling to the Josephson junction and relatively long decoherence times, TLS's can be considered as potential qubits and demonstrate coherent quantum effects. Here, we study the effective interaction between the TLS qubits that is mediated by a Josephson junction resonator driven by an external microwave source. This effective interaction can enable controlled quantum logic gates between the TLS's. Our study can be extended to other superconducting resonators coupling with TLS's.
We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc superconducting quantum interference device phase qubit with a $16\text{ }\ensuremath{\mu}{\text{m}}^{2}$ area Al/AlOx/Al\text{Al}/{\text{AlO}}_{x}/\text{Al}Al/AlOx​/Al junction. Applying microwaves in the 10--11 GHz range, we found eight avoided level crossings with splitting sizes from 10 to 200 MHz and spectroscopic lifetimes from 4 to 160 ns. Assuming the transitions are from the ground state of the composite system to an excited state of the qubit or an excited state of one of the TLS states, we fit the location and spectral width to get the energy levels, splitting sizes, and spectroscopic coherence times of the phase qubit and TLSs. The distribution of splittings is consistent with noninteracting individual charged ions tunneling between random locations in the tunnel barrier and the distribution of lifetimes is consistent with the AlOx{\text{AlO}}_{x}AlOx​ in the junction barrier having a frequency-independent loss tangent. To check that the charge of each TLS couples independently to the voltage across the junction, we also measured the spectrum in the 20--22 GHz range and found tilted avoided level crossings due to the second excited state of the junction and states in which both the junction and a TLS were excited.
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.
In structurally disordered solids, some atoms or small groups of atoms are able to quantum mechanically tunnel between two nearly equivalent sites. These atomic tunneling systems have been identified as the cause of various low-temperature anomalies of bulk glasses and as a source of decoherence of superconducting qubits where they are sparsely present in the disordered oxide barrier of Josephson junctions. We demonstrated experimentally that minute deformation of the oxide barrier changes the energies of the atomic tunneling systems, and we measured these changes by microwave spectroscopy of the superconducting qubit through coherent interactions between these two quantum systems. By measuring the dependence of the energy splitting of atomic tunneling states on external strain, we verify a central hypothesis of the two-level tunneling model for disordered solids.