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arXiv:1802.06438 · Physical review. B./Physical review. B

Theory of nonlinear microwave absorption by interacting two-level systems

Alexander L. Burin, Andrii Maksymov

Published Jun 27, 2018• 9 citations
arXivHTMLPDF

Abstract

The microwave absorption and noise caused by quantum two-level systems (TLSs) dramatically suppress the coherence in Josephson junction qubits that are promising candidates for quantum information applications. It is a challenge to understand microwave absorption by TLSs because of the spectral diffusion resulting from fluctuations in their resonant frequencies induced by their long-range interactions. Here we treat the spectral diffusion explicitly using the generalized master equation formalism. The proposed theory predicts that the linear absorption regime holds while a TLS Rabi frequency is smaller than their phase decoherence rate. At higher external fields, a nonlinear absorption regime is found with the loss tangent inversely proportional to the intensity of the field. The theory can be generalized to acoustic absorption and lower dimensions realized in superconducting qubits.

DOI
10.1103/physrevb.97.214208

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The microwave absorption and noise caused by quantum two-level systems (TLSs) dramatically suppress the coherence in Josephson junction qubits that are promising candidates for quantum information applications. It is a challenge to understand microwave absorption by TLSs because of the spectral diffusion resulting from fluctuations in their resonant frequencies induced by their long-range interactions. Here we treat the spectral diffusion explicitly using the generalized master equation formalism. The proposed theory predicts that the linear absorption regime holds while a TLS Rabi frequency is smaller than their phase decoherence rate. At higher external fields, a nonlinear absorption regime is found with the loss tangent inversely proportional to the intensity of the field. The theory can be generalized to acoustic absorption and lower dimensions realized in superconducting qubits.
Quantum two-level systems (TLSs) commonly found at low temperature in amorphous and disordered materials are responsible for decoherence in superconducting Josephson junction qubits particularly because they absorb energy of coherent qubit oscillations in the microwave frequency range. In planar Josephson resonators with oxide interfaces this absorption is characterized by an anomalously weak loss tangent dependence on the field in the non-linear regime that conflicts with the theoretical expectations and the observations in amorphous dielectrics. It was recently suggested that this anomalous absorption is due to TLS dynamic interactions. Here we show that such interactions cannot lead to the observed loss-tangent field dependence and suggest the alternative explanation assuming that TLS dipole moments ppp are distributed according to the specific power law P(p)∝1/p3−ηP(p) \propto 1/p^{3-η}P(p)∝1/p3−η (0≤η<10\leq η<10≤η<1). This assumption, indeed, results in the observed loss tangent behavior. The hypothesis of a power law distribution is supported both by the recent measurements of individual TLS dipole moments and the theoretical model of TLS formation due to the long-range dipole-dipole interaction, thus connecting the anomalous absorption with the possible solution of the long-standing problem of the nature of TLSs.
Superconducting circuits are a leading platform for quantum computing. However, their coherence times are still limited and exhibit temporal fluctuations. Those phenomena are often attributed to the coupling between qubits and material defects that can be well described as an ensemble of two-level systems (TLSs). Among them, charge fluctuators inside amorphous oxide layers contribute to both low-frequency 1/f1/f1/f charge noise and high-frequency dielectric loss, causing fast qubit dephasing and relaxation. Moreover, spectral diffusion from mutual TLS interactions varies the noise amplitude over time, fluctuating the qubit lifetime. Here, we propose to mitigate those harmful effects by engineering the relevant TLS noise spectral densities. Specifically, our protocols smooth the high-frequency noise spectrum and suppress the low-frequency noise amplitude via depolarizing and dephasing the TLSs, respectively. As a result, we predict a drastic stabilization in qubit lifetime and an increase in qubit pure dephasing time. Our detailed analysis of feasible experimental implementations shows that the improvement is not compromised by spurious coupling from the applied noise to the qubit.
Two-level system fluctuators (TLS's) in the tunnel barrier of a Josephson junction have recently been demonstrated to cause novel energy splittings in spectroscopic measurements of superconducting phase qubits. With their strong coupling to the Josephson junction and relatively long decoherence times, TLS's can be considered as potential qubits and demonstrate coherent quantum effects. Here, we study the effective interaction between the TLS qubits that is mediated by a Josephson junction resonator driven by an external microwave source. This effective interaction can enable controlled quantum logic gates between the TLS's. Our study can be extended to other superconducting resonators coupling with TLS's.
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.
Two-level systems (TLSs) appear in the insulating layers of microfabricated superconducting circuits and are known to be a source of superconducting qubit decoherence. Here we theoretically analyze the quantum evolution of a TLS bath, which is related to a recent experiment performed with a superconducting resonator. During the application of simultaneous time-varying bias and continuous microwave fields, TLSs pass through resonance with the latter field such that Landau?Zener crossings cause the TLS to remain in the ground (Floquet) state or become inverted. The TLSs are analyzed for insulating films, which convey a distribution of tunneling parameters and associated TLS inversion regimes. Under certain conditions, we indeed find that the TLS population should be inverted over a wide range of frequencies. Discussion is included on how new TLS environments could affect the operation of resonators and qubits.
The analytical solution for the low-temperature 1/f1/f1/f noise in the microwave dielectric constant of amorphous films at frequency ${\ensuremath{\nu}}_{0}\ensuremath{\sim}5\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$ due to tunneling two-level systems (TLSs) is derived within the standard tunneling model including the weak dipolar or elastic TLS-TLS interactions. The 1/f1/f1/f frequency dependence is caused by TLS spectral diffusion characterized by the width growing logarithmically with time. Temperature and field dependencies are predicted for the noise spectral density in typical glasses with universal TLSs. The satisfactory interpretation of the recent experiment by J. Burnett et al. [Nat. Commun. 5, 4119 (2014)] in Pt-capped Nb superconducting resonators is attained by assuming a smaller density of TLSs compared to ordinary glasses, which is consistent with the very high internal quality factor in those samples.