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arXiv:cond-mat/0601556 · Physical Review B

Loss of quantum coherence due to nonstationary glass fluctuations

Ivar Martin, Y. M. Galperin

Published May 3, 2006• 10 citations
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Abstract

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.

DOI
10.1103/physrevb.73.180201

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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.
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.
Several experiments have shown qubit coherence decay of the form $exp[\ensuremath{-}{(t/{T}_{2})}^{\ensuremath{\alpha}}]$ due to environmental charge-noise fluctuations. We present a microscopic description for temperature dependencies of the parameters T2{T}_{2}T2​ and $\ensuremath{\alpha}$. Our description is appropriate to qubits in semiconductors interacting with spurious two-level charge fluctuators coupled to a thermal bath. We find distinct power-law dependencies of T2{T}_{2}T2​ and $\ensuremath{\alpha}$ on temperature depending on the nature of the interaction of the fluctuators with the associated bath. We consider fluctuator dynamics induced by first- and second-order tunneling with a continuum of delocalized electron states. We also study one- and two-phonon processes for fluctuators in either GaAs or Si. These results can be used to identify dominant charge-dephasing mechanisms and suppress them.
Two-level systems (TLSs) are a dominant decoherence mechanism in superconducting qubits, microwave kinetic inductance detectors, and quantum dots. TLSs are tunneling states commonly found in amorphous materials and interfaces, which interact electromechanically, leading to energy loss. Fluctuations in the frequency of the TLSs are a significant problem for qubit operation and force recalibration every few hours. In this study, we probe the effect of alternating bias at cryogenic temperatures on TLSs in a purpose-built LC oscillator. When an alternating bias is applied, the steady-state spectra of the TLSs disappear. Spectroscopy reveals transient behavior, in which the TLS frequency fluctuates on the order of minutes. Thermal cycling above 10 K reverses these effects, restoring the TLS spectrum to its original state. Importantly, the intrinsic loss tangent of the LC oscillator remains unchanged before and after the application of the alternating bias. We propose that the disappearance of the steady-state spectrum is caused by nonequilibrium energy buildup from strain in the oxide film introduced by the pulsed voltage-bias sequence. Understanding this nonequilibrium energy could shed light on TLS fluctuations and reduce the calibration requirements for qubits.
A major issue for the implementation of large-scale superconducting quantum circuits is the interaction with interfacial two-level system (TLS) defects that lead to qubit parameter fluctuations and relaxation. Another major challenge comes from nonequilibrium quasiparticles (QPs) that result in qubit relaxation and dephasing. Here, we reveal a previously unexplored decoherence mechanism in the form of a new type of TLS originating from trapped QPs, which can induce qubit relaxation. Using spectral, temporal, thermal, and magnetic field mapping of TLS-induced fluctuations in frequency tunable resonators, we identify a highly coherent subset of the general TLS population with a low reconfiguration temperature ∼300 mK and a nonuniform density of states. These properties can be understood if the TLS are formed by QPs trapped in shallow subgap states formed by spatial fluctutations of the superconducting order parameter. This implies that even very rare QP bursts will affect coherence over exponentially long time scales.
We study the effect of external driving on the two-level systems (TLSs) assumed to be a major obstacle in increasing the coherence time of solid-state Josephson junction qubits. We find, by use of a Bloch-Redfield approach, that external driving has two major effects on the TLS. The first is increased fluctuations between the two states of the TLS; the significance of this effect compared to thermal fluctuations depends on the energy splitting of the TLS compared to temperature. The second effect is a reduction in the intensity of the noise spectrum at low frequencies, and at the same time an increase in intensity around the renormalized Rabi frequency of the TLS and the driving frequency and at beatings between these two frequencies. Finally, we study the ensemble-averaged noise spectrum for a typical distribution of TLSs known to give origin to 1/f1/f1/f noise. We find that strong driving leads to reduced noise at low frequencies, and therefore to an increased dephasing time T2Q{T}_{2}^{Q}T2Q​ of the qubit. However, this effect is exponentially suppressed when the driving frequency is large compared to temperature, as we typically find for Josephson qubits. We suggest that external driving at frequencies much lower than the qubit frequency might be used in order to enhance the the qubit coherence time.
Quantum two-level systems (TLSs) intrinsic to glasses induce decoherence in many modern quantum devices, such as superconducting qubits. Although the low-temperature physics of these TLSs is usually well-explained by a phenomenological standard tunneling model of independent TLSs, the nature of these TLSs, as well as their behavior out of equilibrium and at high energies above 1 K, remain inconclusive. Here we measure the non-equilibrium dielectric loss of TLSs in amorphous silicon using a superconducting resonator, where energies of TLSs are varied in time using a swept electric field. Our results show the existence of two distinct ensembles of TLSs, interacting weakly and strongly with phonons, where the latter also possesses anomalously large electric dipole moment. These results may shed new light on the low temperature characteristics of amorphous solids, and hold implications to experiments and applications in quantum devices using time-varying electric fields.