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arXiv:cond-mat/0510554 · Physical Review Letters

Quantum Two Level Systems and Kondo-Like Traps as Possible Sources of Decoherence in Superconducting Qubits

Lara Faoro, L. B. Ioffe

Published Jan 31, 2006• 69 citations
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Abstract

We discuss the origin of decoherence in Josephson junction qubits. We find that two level systems in the surrounding insulator cannot be the dominant source of noise in small qubits. We argue that electron traps in the Josephson barrier with large Coulomb repulsion would emit noise that agrees both in magnitude and in temperature dependence with experimental data.

DOI
10.1103/physrevlett.96.047001

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We discuss the origin of decoherence in Josephson junction qubits. We find that two level systems in the surrounding insulator cannot be the dominant source of noise in small qubits. We argue that electron traps in the Josephson barrier with large Coulomb repulsion would emit noise that agrees both in magnitude and in temperature dependence with experimental data.
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.
We propose a microscopic model of critical current noise in Josephson junctions based on individual trapping centers in the tunnel-barrier hybridized with electrons in the superconducting leads. We calculate the noise exactly in the limit of no on-site Coulomb repulsion. Our result reveals a noise spectrum that is dramatically different from the usual Lorentzian assumed in simple models. We show that the noise is dominated by sharp subgap resonances associated to the formation of pairs of Andreev bound states, thus providing a possible explanation for the spurious two-level systems (microresonators) observed in Josephson-junction qubits [R. W. Simmonds et al., Phys. Rev. Lett. 93, 077003 (2004).]. Another implication of our model is that each trapping center will contribute a sharp dielectric resonance only in the superconducting phase, providing an effective way to validate our results experimentally. We derive an effective Hamiltonian for a qubit interacting with Andreev bound states, establishing a direct connection between phenomenological models and the microscopic parameters of a Fermionic bath.
We analyze the impact of trap states in the oxide layer of a superconducting tunnel junction on the fluctuation of the Josephson critical current, thus on coherence in superconducting qubits. Two mechanisms are usually considered: the current blockage due to repulsion at the occupied trap states and the noise from electrons hopping across a trap. We extend previous studies of noninteracting traps to the case where the traps have onsite electron repulsion inside one ballistic channel. The repulsion not only allows the appropriate temperature dependence of 1/f1/f1/f noise, but also the control of the coupling between the computational qubit and the spurious two-level systems inside the oxide dielectric. We use second-order perturbation theory, which allows to obtain analytical formulas for the interacting bound states and spectral weights, limited to small and intermediate repulsions. Remarkably, it still reproduces the main features of the model as identified from the numerical renormalization group. We present analytical formulations for the subgap bound state energies, the singlet-doublet phase boundary, and the spectral weights. We show that interactions can reverse the supercurrent across the trap. We finally work out the spectrum of junction resonators for qubits in the presence of onsite repulsive electrons and analyze its dependence on microscopic parameters that may be controlled by fabrication.
Although Josephson junction qubits show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. Improving the operation of a Josephson junction based phase qubit has revealed microscopic two-level systems or resonators within the tunnel barrier that cause decoherence. We report spectroscopic data that show a level splitting characteristic of coupling between a two-state qubit and a two-level system. Furthermore, we show Rabi oscillations whose "coherence amplitude" is significantly degraded by the presence of these spurious microwave resonators. The discovery of these resonators impacts the future of Josephson qubits as well as existing Josephson technologies.
Dielectric loss from two-level states is shown to be a dominant decoherence source in superconducting quantum bits. Depending on the qubit design, dielectric loss from insulating materials or the tunnel junction can lead to short coherence times. We show that a variety of microwave and qubit measurements are well modeled by loss from resonant absorption of two-level defects. Our results demonstrate that this loss can be significantly reduced by using better dielectrics and fabricating junctions of small area . With a redesigned phase qubit employing low-loss dielectrics, the energy relaxation rate has been improved by a factor of 20, opening up the possibility of multiqubit gates and algorithms.
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.