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arXiv:cond-mat/0504449

Single Qubit Rabi Oscillation Decohered by Many Two-Level Systems

Ren-Shou Huang, V. V. Dobrovitski, Bruce N. Harmon

Published Apr 18, 2005• 1 citation
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Abstract

Recent experiments on Josephson junction qubits have suggested the existence in the tunnel barrier of bistable two level fluctuators that are responsible for decoherence and 1/f critical current noise. In this article we treat these two-level systems as fictitious spins and investigate their influence quantum mechanically with both analytical and numerical means. We find that the Rabi oscillations of the qubit exhibit multiple stages of decay. New approaches are established to characterize different decoherence times and to allow for easier feature extraction from experimental data. The Rabi oscillation of a qubit coupled to a spurious resonator is also studied, where we proposed an idea to explain the serious deterioration of the Rabi osillation amplitude.

DOI
10.48550/arxiv.cond-mat/0504449

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Recent experiments on Josephson junction qubits have suggested the existence in the tunnel barrier of bistable two level fluctuators that are responsible for decoherence and 1/f critical current noise. In this article we treat these two-level systems as fictitious spins and investigate their influence quantum mechanically with both analytical and numerical means. We find that the Rabi oscillations of the qubit exhibit multiple stages of decay. New approaches are established to characterize different decoherence times and to allow for easier feature extraction from experimental data. The Rabi oscillation of a qubit coupled to a spurious resonator is also studied, where we proposed an idea to explain the serious deterioration of the Rabi osillation amplitude.
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.
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.
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.
Recent experiments on a range of engineered quantum systems have highlighted the important role of interacting two-level systems (TLSs) in modifying device properties and generating fluctuations. Focusing on the case of an oscillator coupled to a single near-resonant TLS, we explore how interactions between the TLS and lower-frequency thermally activated two-level fluctuators (TLFs) degrade the oscillator's coherence. Depending on the strength of the couplings, a single TLF can give rise to coherence oscillations that appear alongside, or supplant, Rabi oscillations of the oscillator-TLS system. Bath-driven transitions in the TLF cause irreversible coherence decay at a rate that is highly sensitive to both the couplings and the transition rate. For an ensemble of TLFs, we identify and characterise the different regimes of non-exponential phase-averaging-driven coherence decay that the oscillator can display. Using numerical calculations, we examine the extent to which systems with just a few TLFs differ from the limit of a large (continuum) TLF ensemble. Our work provides a theoretical framework for understanding the interplay of coherent TLS interactions and TLF-induced dephasing in quantum devices such as superconducting and phononic resonators.
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.
We consider the problem of a qubit driven by a harmonically oscillating external field while it is coupled to a quantum two-level system (TLS). We perform a systematic numerical analysis of the problem by varying the relevant parameters. The numerical calculations agree with the predictions of a simple intuitive picture, namely one that takes into consideration the four-level energy spectrum, the simple principles of Rabi oscillations and the basic effects of decoherence. Furthermore, they reveal a number of other interesting phenomena. We provide explanations for the various features that we observe in the numerical calculations and discuss how they can be used in experiment. In particular, we suggest an experimental procedure to characterize an environment of TLSs.