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arXiv:0904.2171

Energy Decay in Josephson Qubits from Non-equilibrium Quasiparticles

John M. Martinis, M. Ansmann, José Aumentado

Published Apr 14, 2009• 5 citations
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Abstract

We calculate the energy decay rate of Josephson qubits and superconducting resonators from non-equilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n_qp = 10/um^3, which suggests that non-equilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy. This model also explains a striking feature in Josephson qubits and resonators - a small reduction in decay rate with increasing temperature.

DOI
10.48550/arxiv.0904.2171

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We calculate the energy decay rate of Josephson qubits and superconducting resonators from non-equilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n_qp = 10/um^3, which suggests that non-equilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy. This model also explains a striking feature in Josephson qubits and resonators - a small reduction in decay rate with increasing temperature.
We calculate the energy decay rate of Josephson qubits and superconducting resonators from nonequilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n(qp) = 10/microm(3), which suggests that nonequilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy. This model also explains a striking feature in Josephson qubits and resonators-a small reduction in decay rate with increasing temperature.
Abstract Non-equilibrium quasiparticles are possible sources for decoherence in superconducting qubits because they can lead to energy decay or dephasing upon tunneling across Josephson junctions (JJs). Here, we investigate the impact of the intrinsic properties of two-dimensional transmon qubits on quasiparticle tunneling (QPT) and discuss how we can use quasiparticle dynamics to gain critical information about the quality of JJ barrier. We find the tunneling rate of the non-equilibrium quasiparticles to be sensitive to the choice of the shunting capacitor material and their geometry in qubits. In some devices, we observe an anomalous temperature dependence of the QPT rate below 100 mK that deviates from a constant background associated with non-equilibrium quasiparticles. We speculate that this behavior is caused by high transmission sites/defects within the oxide barriers of the JJs, leading to spatially localized subgap states. We model this by assuming that such defects generate regions with a smaller effective gap. Our results present a unique in situ characterization tool to assess the uniformity of tunnel barriers in qubit junctions and shed light on how quasiparticles can interact with various elements of the qubit circuit.
Superconducting qubits are among the most promising elements for the implementation of the concept of quantum computing. Quasiparticles are an intrinsic sources of qubit decoherence, and are more generally detrimental to the operation of superconducting devices, e.g., Cooper pair pumps. Experiments reveal that quasiparticles fail to equilibrate and their density remains high even at low temperatures. Planting normal-metal traps on a superconducting device offers a way to reduce the quasiparticle density: once a quasiparticle tunnels into the normal metal and relaxes to subgap energy via inelastic processes, it cannot return to the superconductor. This paper presents a theoretical model for the time-resolved dynamics of quasiparticles injected into a qubit, and experiments with transmon qubits validating the model. The authors show that, contrary to expectations, the effective trapping rate depends on temperature, which is a consequence of the strong energy dependence of the quasiparticle density of states in the superconductor. At low temperatures, the relaxation process in the normal metal is the bottleneck limiting the effectiveness of traps. The authors also show that the trapping rate saturates for larger traps. At saturation, the rate is limited by the inverse of the time it takes for quasiparticles to diffuse across the device.
Superconducting qubits hold promise for quantum computing, but their operation is challenged by various sources of noise, including excitations known as quasiparticles. Qubits with gap asymmetry larger than their transition energy are less susceptible to quasiparticle decoherence as the quasiparticles are mostly trapped in the low-gap side of the junction. Because of this trapping, the gap asymmetry can contribute to maintaining the quasiparticles out of equilibrium. Here we address the temperature dependence of the quasiparticle densities in the two sides of the junction. We show that four qualitatively different regimes are possible with increasing temperature: (i) nonequilibrium, (ii) local quasiequilibrium, (iii) global quasiequilibrium, and (iv) full equilibrium. We identify shortcomings in assuming global quasiequilibrium when interpreting experimental data, highlighting how measurements in the presence of magnetic field can aid the accurate determination of the junction parameters, and hence the identification of the nonequilibrium regimes. Quasiparticle poisoning challenges the operation of superconducting qubits, but errors can be suppressed by engineering gap asymmetry between the electrodes of the qubit’s Josephson junction. The authors present a model of the qubit-quasiparticle system valid beyond the low-temperature limit and identify different nonequilibrium regimes, which can affect the interpretation of experimental data.
We analyze the decay of quantum oscillations in a charge qubit consisting of a Cooper pair box connected by a Josephson junction to a finite-size superconductor. We concentrate on the contribution of quasiparticles in the superconductors to the decay rate. Passing of a quasiparticle through the Josephson junction leads to the escape of the qubit out of its Hilbert space, and thus determines the decay rate of quantum oscillations. We find the temperature dependence of the quasiparticle contribution to the decay rate for open and isolated systems. The former case is realized if a normal-state trap is included in the circuit, or if just one vortex resides in the qubit; we find exponential suppression of the rate, $\ensuremath{\Gamma}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\ensuremath{\Delta}∕T)$, at low temperatures (here, $\ensuremath{\Delta}$ is the superconducting gap). In a superconducting qubit isolated from the environment $\ensuremath{\Gamma}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}2\ensuremath{\Delta}∕T)$ if the number of electrons is even, while for an odd number of electrons the decay rate remains finite in the limit $T\ensuremath{\rightarrow}0$. We estimate $\ensuremath{\Gamma}$ for realistic parameters of a qubit.
We study decoherence in superconducting qubits due to quasiparticle tunneling which is enhanced by two known deviations from the equilibrium BCS theory. The first process corresponds to tunneling of an already existing quasiparticle across the junction. The quasiparticle density is increased, e.g., because of an effective quasiparticle doping of the system. The second process is quasiparticle tunneling by breaking of a Cooper pair. This can happen at typical energies of superconducting qubits if there is an extended quasiparticle density inside the gap. We calculate the induced energy decay and pure dephasing rates in typical qubit designs. Assuming the lowest reported value of the nonequilibrium quasiparticle density in Aluminum, we find for the persistent-current flux qubit decay times of the order of recent measurements. Using the typical subgap density of states in Niobium we also reproduce observed decay times in the corresponding Niobium flux qubits.