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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Stationary and non-stationary noise in superconducting quantum devices

Ivar Martin, Lev N. Bulaevskii, Alexander Shnirman, Y. M. Galperin

Published Jun 7, 2007• 1 citation
Publisher

Abstract

We consider two representative problems that deal with the fluctuator-induced decoherence from two very different perspectives-microscopic and macroscopic. In the first part, we consider an individual two-level system inside a Josephson junction shunted by a resistor. If the TLS modulates the Josephson energy and/or is optically active, it can be Rabi driven by the Josephson oscillation. The Rabi oscillations, in turn, translate into oscillations of current and voltage which can be detected in noise measurements. This effect provides an option to fully characterize the TLS inside Josephson junction and to find the TLS's contribution to the decoherence when the junction is used as a qubit. In the second part, we study the contribution of an ensemble of non-stationary glassy charge fluctuators on qubit decoherence. Low-temperature dynamics of insulating glasses is dominated by a macroscopic concentration of tunneling two-level systems. Due to exponentially broad distribution of their tunneling rates and the finite experimental manipulation timescales, some of the fluctuators are temporarily stuck in high-energy non-thermal states. We find that at low enough temperatures, non-stationary contribution due to these slow non-thermal fluctuators can dominate the stationary (thermal) one, and discuss how this effect can be minimized.

DOI
10.1117/12.725639

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We consider two representative problems that deal with the fluctuator-induced decoherence from two very different perspectives-microscopic and macroscopic. In the first part, we consider an individual two-level system inside a Josephson junction shunted by a resistor. If the TLS modulates the Josephson energy and/or is optically active, it can be Rabi driven by the Josephson oscillation. The Rabi oscillations, in turn, translate into oscillations of current and voltage which can be detected in noise measurements. This effect provides an option to fully characterize the TLS inside Josephson junction and to find the TLS's contribution to the decoherence when the junction is used as a qubit. In the second part, we study the contribution of an ensemble of non-stationary glassy charge fluctuators on qubit decoherence. Low-temperature dynamics of insulating glasses is dominated by a macroscopic concentration of tunneling two-level systems. Due to exponentially broad distribution of their tunneling rates and the finite experimental manipulation timescales, some of the fluctuators are temporarily stuck in high-energy non-thermal states. We find that at low enough temperatures, non-stationary contribution due to these slow non-thermal fluctuators can dominate the stationary (thermal) one, and discuss how this effect can be minimized.
We consider a two-level system (TLS) with energy level separation plankvOmega0 inside a Josephson junction. The junction is shunted by a resistor R and is voltage V biased. If the TLS modulates the Josephson energy and/or is optically active, it is Rabi driven by the Josephson oscillations in the running phase regime near the resonance 2eV=plankvOmega0. The Rabi oscillations, in turn, translate into oscillations of current and voltage that can be detected in noise measurements. This effect provides an option to fully characterize the TLS inside Josephson junction and to find the TLS's contribution to the decoherence when the junction is used as a qubit.
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.
Low-temperature dynamics of insulating glasses is dominated by a macroscopic concentration of tunneling two-level systems (TTLS). The distribution of the switching/relaxation rates of TTLS is exponentially broad, which results in a nonequilibrium state of the glass at arbitrarily long time scales. Due to the electric dipolar nature, the switching TTLS generate fluctuating electromagnetic fields. We study the effect of the nonthermal slow fluctuators on the dephasing of a solid-state qubit. We find that at low enough temperatures nonstationary contribution can dominate the stationary (thermal) one, and we discuss how this effect can be minimized.
Superconducting quantum devices have drawn the attention of physicists greatly in recent years, not only because they are one of the most favorable candidates for developing a solid state quantum computer, but also because they can be employed as test systems for understanding quantum mechanics at nearly macro scale. Superconducting quantum devices can be divided into two groups: the superconducting resonators (linear devices), which have equally spaced discrete energy levels, and the artificial atoms (non-linear devices) consisting of Josephson junctions which have unequally spaced discrete energy levels. By combining these two kinds of devices together, a solid state counterpart of optical cavity quantum electrodynamics (QED) known as circuit QED emerges. Experiments of cavity QED and quantum optics can be reproduced in either circuit QED systems or in bare superconducting artificial atoms. As an example, we have observed the Autler-Townes effect in a three-level artificial atom called phase qutrit. \nMore than one decade has passed since the first experimental demonstration of superconducting two-level artificial atom (qubit). However, to build a practical quantum computer with thousands of superconducting qubits there is still a long way to go (we are at the stage of three qubits now). One of the main obstacles preventing us from scaling up a superconducting quantum computer, as well as some other kinds of quantum computers, has been decoherence, which is believed to be dominated by the low frequency noise due to the two-level system (TLS) fluctuators located inside the Josephson junction barrier. We have experimentally simulated the dynamics of a qubit longitudinally coupled to a randomly fluctuating TLS. A phenomenon known as motional averaging has been observed. \nIn this thesis, theoretical models for decoherence in both resonator and artificial atoms have been established and used for explaining phenomena observed in the experiments performed in our laboratory. The phenomenon of decoherence in coupled bipartite systems has been also studied, and besides the already known entanglement sudden death phenomenon, stable entanglement (robust under decoherence) generated from an arbitrary initial state has been found in these systems.
The electrical noise of mesoscopic devices can be strongly influenced by the quantum motion of electrons. To probe this effect, we have measured the current fluctuations at high frequency (5 to 90 gigahertz) using a superconductor-insulator-superconductor tunnel junction as an on-chip spectrum analyzer. By coupling this frequency-resolved noise detector to a quantum device, we can measure the high-frequency, nonsymmetrized noise as demonstrated for a Josephson junction. The same scheme is used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak is observed in the spectral noise density at the frequency of the coherent charge oscillations.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on the magnetic field dependent crossover temperature TcrT_{cr}Tcr​ between the thermal fluctuation and quantum regimes of switching from the superconducting (the zero-voltage) state to a resistive one. In the absence of two-levels systems the crossover temperature shows a smooth decrease with an applied magnetic field characterized by an external flux ΦΦΦ. Beyond that we predict a narrow peak in the dependence of Tcr(Φ)T_{cr}(Φ)Tcr​(Φ) occurring in the intermediate range of ΦΦΦ. The effect becomes more pronounced as the junction size increases. We explain this effect quantitatively by a strong resonant suppression of a potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.