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arXiv:2209.07677 · AVS Quantum Science

Dynamic phases induced by two-level system defects on driven qubits

Yanxiang Wang, Ziyang You, Hou Ian

Published Sep 1, 2023• 1 citation
arXivHTMLPDF

Abstract

Recent experimental evidences point to two-level defects, located in the oxides and on the interfaces of the Josephson junctions, as the major constituents of decoherence in superconducting qubits. How these defects affect the qubit evolution with the presence of external driving is less well understood since the semiclassical qubit-field coupling renders the Jaynes–Cummings model for qubit-defect coupling undiagonalizable. We analyze the decoherence dynamics in the continuous coherent state space induced by the driving and solve the master equation endowed with an extra decay-cladded driving term via a Fokker–Planck equation. The solutions for diffusion propagators as Gaussian distributions show four distinct dynamic phases: four types of convergence paths to limit cycles of varying radius by the distribution mean, which are determined by the competing external driving and the defect decays. The qubit trajectory resulted from these solutions is a super-Poissonian over displaced Fock states, which reduces to a Gibbs state of effective temperature decided by the defect at zero driving limit. Furthermore, the Poincare map shows the dependence of the rate of convergence on the initial state. In other words, the qubit evolution can serve as an indicator of the defect coupling strength through the variation of the driving strength as a parameter.

DOI
10.1116/5.0159488

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Recent experimental evidences point to two-level defects, located in the oxides and on the interfaces of the Josephson junctions, as the major constituents of decoherence in superconducting qubits. How these defects affect the qubit evolution with the presence of external driving is less well understood since the semiclassical qubit-field coupling renders the Jaynes–Cummings model for qubit-defect coupling undiagonalizable. We analyze the decoherence dynamics in the continuous coherent state space induced by the driving and solve the master equation endowed with an extra decay-cladded driving term via a Fokker–Planck equation. The solutions for diffusion propagators as Gaussian distributions show four distinct dynamic phases: four types of convergence paths to limit cycles of varying radius by the distribution mean, which are determined by the competing external driving and the defect decays. The qubit trajectory resulted from these solutions is a super-Poissonian over displaced Fock states, which reduces to a Gibbs state of effective temperature decided by the defect at zero driving limit. Furthermore, the Poincare map shows the dependence of the rate of convergence on the initial state. In other words, the qubit evolution can serve as an indicator of the defect coupling strength through the variation of the driving strength as a parameter.
[EN] Two-level system (TLS) defects constitute a major source of noise and decoherence in superconducting qubits, particularly due to microscopic defects located in Josephson junctions and their surrounding materials, limiting coherence times and the performance of quantum information devices. While extensive experimental evidence of TLS-induced noise exists, establishing a microscopic theoretical description that consistently connects quantum defect dynamics, open-system theory, and experimental observations remains an open challenge. The objective of this Master s thesis is to study the impact of TLS defects on superconducting qubits using a fully quantum, open-system framework. Starting from a microscopic Hamiltonian description of a qubit coupled to TLS defects in Josephson junctions, the project aims to derive and analyze a Bloch-Redfield master equation that captures the correlated dynamics between a qubit, a quantum TLS, and a dissipative environment. This approach enables the investigation of coherence decay, population dynamics, and qubit-TLS correlations beyond phenomenological Lindblad models. The work will combine analytical methods with numerical simulations implemented in the Julia programming language. In addition to master-equation techniques, tensor-network methods based on Matrix Product States (MPS) will be employed as a scalable framework to extend the analysis to multiple interacting TLS, allowing the explicit treatment of quantum correlations and non-Markovian effects in many-body defect environments. Simple effective noise models, such as random telegraph noise, will be considered for comparison in order to assess their range of validity relative to microscopic descriptions. The theoretical analysis will be discussed in connection with recent experimental observations in superconducting circuits, particularly those reported in the work of Christopher Eichler and Andreas Wallraff, with the goal of contributing to a unified microscopic understanding of TLS-induced noise in Josephson-junction-based superconducting qubits.
Decoherence is a quantum-mechanical phenomenon severely limiting quantum information processing and storage capability in quantum computers. Decoherence refers to mechanisms that cause transfer of information from a quantum system to its bath. Typically, in theoretical and experimental considerations of different systems containing superconducting qubits, the coupling strength between a qubit and its bath has been assumed to be constant in time. In this case, many standard results in the dynamics of two-level systems follow. For example, due to decoherence, driven Rabi oscillations in a qubit have a characteristic decay time. In addition, the oscillations may take place at any phase. However, by considering time-dependent coupling to the bath, these phenomena may be absent. In this thesis, we demonstrate with numerical simulations of a time-dependent Lindblad master equation persistent Rabi oscillations in a qubit driven by a coherent drive tone. The persistent Rabi oscillations are induced by modulating the coupling of the qubit to the bath with a sinusoidal temporal shape. We observe that the temporal modulation enforces a limit cycle on the evolution of the dressed qubit state with a fixed phase relative to the phase of the sinusoidal modulation regardless of the initial state of the system. Through a synchronization-like phenomenon, the frequency of the Rabi oscillation adapts to match the frequency of the modulation. We determine the effect of different system parameters on the limit cycle and study how the amplitude of the persistent oscillation depends on the coupling modulation parameters. We also observe a similar effect in the freely evolving qubit precession. In addition, the qubit acts as a non-linear mixer, resulting in different linear combinations of the original modulation waveform appearing in the bath-induced Rabi oscillations. We also introduce a design for a physical system where our simulations can be verified experimentally.
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.
Synchronizing a few-level quantum system is of fundamental importance to the understanding of synchronization in the deep quantum regime. We investigate quantum phase synchronization of a two-level system (qubit) driven by a semiclassical laser field, in the presence of a general non-Markovian dissipative environment. The phase preference of the qubit is demonstrated through Husimi Q-function, and the existence of a limit cycle is also shown in our system. Synchronization of the qubit is quantified using the shifted phase distribution. The signature of quantum phase synchronization viz the Arnold tongue is obtained from the maximal value of the shifted phase distribution. Two distinct types of qubit dynamics is considered depending on the reservoir correlation time being very short and a situation when bath correlation time is finite. In the Markov regime of the environment, the phase preference of the qubit goes away in the long time limit, whereas the long-time phase localization persists in the non-Markovian regime. We also plot the maximum of the shifted phase distribution in two ways: (a) by varying the detuning and laser driving strength, and (b) by varying the system-bath coupling and laser driving strength. Various system-environment parameters determine the synchronization regions and the qubit phase synchronization is shown to be enhanced in the non-Markov regime.
One of the key problems facing superconducting qubits and other Josephson junction devices is the decohering effects of bistable material defects. Although a variety of phenomenological models exist, the true microscopic origin of these defects remains elusive. For the first time we show that these defects may arise from delocalization of the atomic position of the oxygen in the oxide forming the Josephson junction barrier. Using a microscopic model, we compute experimentally observable parameters for phase qubits. Such defects are charge neutral but have nonzero response to both applied electric field and strain. This may explain the observed long coherence time of two-level defects in the presence of charge noise, while still coupling to the junction electric field and substrate phonons.
Identifying the microscopic origins of decoherence sources prevalent in Josephson junction (JJ) based circuits is central to their use as functional quantum devices. Focussing on so called ‘strongly coupled’ two-level defects, we construct a theoretical model using the atomic position of the oxygen which is spatially delocalized in the oxide forming the JJ barrier. Using this model, we investigate which atomic configurations give rise to two-level behaviour of the type seen in experiments. We compute experimentally observable parameters for phase qubits and examine defect response under the effects of applied electric field and strain.