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arXiv:0906.5169 · Physical Review B

Microscopic model of critical current noise in Josephson-junction qubits: Subgap resonances and Andreev bound states

Rogério de Sousa, K. Birgitta Whaley, T. Hecht, Jan von Delft, Frank K. Wilhelm

Published Sep 18, 2009• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.80.094515

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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.
Intrinsic noise is known to be ubiquitous in Josephson junctions. We introduce a rough tunnel junction model characterized by a very small number of pinholes---transport channels possessing a transmission coefficient close to unity and analyze its transport properties. Although it may still have just a small total leakage current, it can lead to enormous current fluctuations in the low-voltage regime. We show that even fully transparent transport channels between superconductors contribute to shot noise due to the uncertainty in the number of Andreev cycles. We discuss shot-noise enhancement by multiple Andreev reflection in such a junction and investigate whether pinholes might contribute as a microscopic mechanism of two-level current fluctuators. We discuss the connection of these results to the junction resonators observed in Josephson phase qubits.
In addition to the usual superconducting current, Josephson junctions (JJs) support a phase-dependent conductance related to the retardation effect of tunneling quasi-particles. This introduces a dissipative current with a memory-resistive (memristive) character that should also affect the current noise. By means of the microscopic theory of tunnel junctions we compute the complete current autocorrelation function of a Josephson tunnel junction and show that this memristive component gives rise to both a previously noted phase-dependent thermal noise, and an undescribed non-stationary, phase-dependent dynamic noise. As experiments are approaching ranges in which these effects may be observed, we examine the form and magnitude of these processes. Their phase dependence can be realized experimentally as a hysteresis effect and may be used to probe defects present in JJ based qubits and in other superconducting electronics applications.
In this thesis we present theoretical investigations of the effects of Andreev bound states on the current transport in superconducting interferometers. We also investigate the slow dynamics of the Andreev states in a superconducting point contact, and the possible application as a quantum bit. We consider superconductor-normal metal-superconductor (SNS) and normal metalsuperconductor (NS) interferometers, where the contact region is a Y-shaped normal metal wave guide, and the two connection points to the same superconducting electrode can have different phases. The electric current in the interferometer is calculated as a function of the applied voltage and the phase difference . Andreev reflection in SNS and NS interferometers incorporates two features: interference in the arms of the Y-shaped normal region, and interplay with Andreev resonances. The latter feature yields rich phase dependent current structures in the subgap voltage region. The interference effect leads to a suppression of the current structures at . We investigate the effects on the Josephson current in NS interferometers due to current injection from the normal electrode. The two main effects of the nonequilibrium situation are: nonequilibrium population of the Andreev levels, which can result in enhancement, suppression, or even sign reversal of the Josephson current, and an anomalous interference Josephson effect, which gives rise to a long range Josephson effect, increasing with the voltage up to the superconducting gap . The two Andreev states in a superconducting quantum point contact can be accessed for manipulation and measurement by embedding the point contact in a superconducting loop. We calculate an effective Hamiltonian for the slow dynamics of the Andreev two-level system in the ring. Furthermore, we discuss methods of manipulation of the Andreev levels, and coupling of qubits. The state of the Andreev two-level system can be read out by monitoring the macroscopic quantum tunneling in a current biased Josephson junction, which is embedded in the superconducting ring of the qubit. We discuss the effects on the qubit, the readout scheme and the signal-to-noise ratio. THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Coherent processes in Superconducting quantum interferometers and qubits
We explore superconducting quantum circuits where several leads are simultaneously connected beyond the tunneling regime, such that the fermionic structure of Andreev bound states in the resulting multiterminal Josephson junction influences the states of the full circuit. Using a simple model of single-channel contacts and a single level in the middle region, we discuss different circuit configurations where the leads are islands with finite capacitance and/or form loops with finite inductance. We find situations of practical interest where the circuits can be used to define noise-protected qubits, which map to the bifluxon and 0−π qubits in the tunneling regime. We also point out the subtleties of the gauge choice for a proper description of these quantum circuit dynamics. Published by the American Physical Society 2024