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arXiv:0905.2332 · Physical Review B

Relaxation of Josephson qubits due to strong coupling to two-level systems

Clemens Müller, Alexander Shnirman, Yuriy Makhlin

Published Oct 22, 2009• 33 citations
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Abstract

We investigate the energy relaxation $({T}_{1})$ process of a qubit coupled to a bath of dissipative two-level fluctuators (TLFs). We consider the fluctuators strongly coupled to the qubit both in the limit of spectrally sparse single TLFs as well as in the limit of spectrally dense TLFs. We conclude that the avoided level crossings, usually attributed to very strongly coupled single TLFs, could also be caused by many weakly coupled spectrally dense fluctuators.

DOI
10.1103/physrevb.80.134517

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We investigate the energy relaxation (T1)({T}_{1})(T1​) process of a qubit coupled to a bath of dissipative two-level fluctuators (TLFs). We consider the fluctuators strongly coupled to the qubit both in the limit of spectrally sparse single TLFs as well as in the limit of spectrally dense TLFs. We conclude that the avoided level crossings, usually attributed to very strongly coupled single TLFs, could also be caused by many weakly coupled spectrally dense fluctuators.
Spectroscopic analysis of superconducting qubits often shows clear signatures of avoided level crossings, indicating the presence of microscopic two-level fluctuators (TLFs) coupling to the qubit. Within ''direct coherent control'' method it was possible for the first time to investigate coherence times and temperatures properties of single TLFs. Measurements of relaxation time shows unusual behaviour of temperature dependence. Within Bloch Redfield formalism we analyse the influence of higher qubit levels on the resonance shape of relaxation time.
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Temporal fluctuations in the superconducting qubit lifetime, T1T_1T1​, bring up additional challenges in building a fault-tolerant quantum computer. While the exact mechanisms remain unclear, T1T_1T1​ fluctuations are generally attributed to the strong coupling between the qubit and a few near-resonant two-level systems (TLSs) that can exchange energy with an assemble of thermally fluctuating two-level fluctuators (TLFs) at low frequencies. Here, we report T1T_1T1​ measurements on the qubits with different geometrical footprints and surface dielectrics as a function of the temperature. By analyzing the noise spectrum of the qubit depolarization rate, Γ1=1/T1Γ_1 = 1/T_1Γ1​=1/T1​, we can disentangle the impact of TLSs, non-equilibrium quasiparticles (QPs), and equilibrium (thermally excited) QPs on the variance in Γ1Γ_1Γ1​. We find that Γ1Γ_1Γ1​ variances in the qubit with a small footprint are more susceptible to the QP and TLS fluctuations than those in the large-footprint qubits. Furthermore, the QP-induced variances in all qubits are consistent with the theoretical framework of QP diffusion and fluctuation. We suggest these findings can offer valuable insights for future qubit design and engineering optimization.
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 investigate the decoherence and dephasing of two coupled Josephson qubits. With the interaction between the qubits being generated by current–current correlations, two different situations in which the qubits are coupled to the same bath, or to two independent baths, are considered. Upon focussing on dissipation being caused by the fluctuations of voltage sources, the relaxation and dephasing rates are explicitly evaluated. Analytical and numerical results for the coupled qubits dynamics are provided.
Two-level systems (TLS) are widely recognized as a dominant source of energy relaxation in superconducting qubits, limiting coherence times and device performance. While TLS-induced dissipation is often modeled as independent channels, interacting TLS can form finite many-body environments whose dynamical role in qubit relaxation remains insufficiently understood. Building on the information-erasure-based framework for irreversible thermalization developed in our previous work, we present a microscopic model and numerical simulations of a superconducting qubit coupled to a finite interacting many-body TLS environment as a concrete physical realization of this mechanism. We show that effective irreversible energy relaxation can emerge from intrinsic many-body dynamics without invoking external baths or phenomenological dissipation. The introduction of information erasure drives a transition from coherent oscillatory energy exchange to nonoscillatory exponential relaxation of the qubit. The relaxation times exhibit the scaling T1,T2∝Jq,τ−2T_1, T_2 \propto J_{q,τ}^{-2}T1​,T2​∝Jq,τ−2​ with respect to the qubit-TLS coupling strength, consistent with Fermi's golden rule and Lindblad-type descriptions. Importantly, both exponential decay and its scaling behavior arise directly from microscopic many-body dynamics. These results provide quantitative insight into TLS-induced decoherence mechanisms and establish a microscopic link between information erasure, many-body thermalization, and irreversible relaxation in superconducting quantum systems.