Hot Nonequilibrium Quasiparticles in Transmon Qubits

K. Serniak, M. Hays, G. de Lange, S. Diamond, S. Shankar, L. D. Burkhart, L. Frunzio, M. Houzet, and M. H. Devoret

Phys. Rev. Lett. 121, 157701 – Published 10 October 2018

Abstract

Nonequilibrium quasiparticle excitations degrade the performance of a variety of superconducting circuits. Understanding the energy distribution of these quasiparticles will yield insight into their generation mechanisms, the limitations they impose on superconducting devices, and how to efficiently mitigate quasiparticle-induced qubit decoherence. To probe this energy distribution, we systematically correlate qubit relaxation and excitation with charge-parity switches in an offset-charge-sensitive transmon qubit, and find that quasiparticle-induced excitation events are the dominant mechanism behind the residual excited-state population in our samples. By itself, the observed quasiparticle distribution would limit $T_{1}$ to $\approx 200 μ s$ , which indicates that quasiparticle loss in our devices is on equal footing with all other loss mechanisms. Furthermore, the measured rate of quasiparticle-induced excitation events is greater than that of relaxation events, which signifies that the quasiparticles are more energetic than would be predicted from a thermal distribution describing their apparent density.

Received 2 April 2018
Revised 27 July 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.157701

Physics Subject Headings (PhySH)

Quantum information with solid state qubits

Superconducting devices Superconducting qubits

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

K. Serniak^1,*, M. Hays¹, G. de Lange^1,2, S. Diamond¹, S. Shankar¹, L. D. Burkhart¹, L. Frunzio¹, M. Houzet³, and M. H. Devoret^1,†

¹Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
²QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
³Univ. Grenoble Alpes, CEA, INAC-Pheliqs, F-38000 Grenoble, France

^*kyle.serniak@yale.edu
^†michel.devoret@yale.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 121, Iss. 15 — 12 October 2018

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
QP-induced transitions in transmon qubits. (a) Density of states $ν_{s}$ versus the reduced energy $ϵ / Δ$ in the leads of a superconductor-insulator-superconductor (SIS) JJ, in the excitation representation. Gray arrows represent tunneling processes of QPs, shown as purple dots. Dashed, dotted, and solid lines correspond to relaxation, excitation, and interband transitions of the qubit, respectively, with associated inelastic QP scattering. (b) The two lowest energy levels of an offset-charge-sensitive transmon qubit (vertical axis not to scale) as a function of offset charge $n_{g}$ , in units of $2 e$ . These levels are shifted depending on the charge parity (even or odd) of the qubit, and $\bar{E_{0}}$ and $\bar{E_{1}}$ are time-averaged energies of the ground and first-excited states, respectively, assuming ergodic fluctuations of $n_{g}$ and/or charge parity. Arrows correspond to those in (a).
Reuse & Permissions
Figure 2
Monitoring slow fluctuations of $δ f_{01} (n_{g})$ . (a) Depiction of the Ramsey sequence. High-fidelity qubit measurements $M_{1}$ and $M_{2}$ have thresholded outcome 0 or 1, corresponding to the ground and first-excited states of the qubit, respectively. (b) Ramsey fringes of $⟨ M_{1} M_{2} ⟩$ oscillate at $δ f_{01} (n_{g})$ , which is measured every $\sim 4 s$ (c). The gray dashed line marks the frequency fit from (b). The right-hand side $y$ axis shows the conversion from $δ f_{01} (n_{g})$ to $n_{g}$ , where $n_{g}^{n . m .}$ is the value of $n_{g}$ corresponding to the nearest maximum of $δ f_{01} (n_{g})$ .
Reuse & Permissions
Figure 3
Detecting fast charge-parity switches in an offset-charge-sensitive transmon qubit. (a) Charge-parity-mapping pulse sequence, which results in an effective charge-parity-conditioned $π$ pulse, $π_{e, o}$ . Inset (b): A 1-ms snapshot of a $\sim 600 − ms$ -long charge-parity jump trace. Main: Power spectrum of charge-parity fluctuations, with a Lorentzian fit (orange curve) corresponding to $T_{P} = 77 \pm 1 μ s$ .
Reuse & Permissions
Figure 4
Correlating charge-parity switches with qubit transitions. (a) Inset: Pulse sequence depicting the charge-parity correlation measurement. The charge-parity conditioning of the state-mapping sequence is varied between measurements to balance mapping-dependent errors. Main: Conditioned probabilities $\tilde{ρ} (j, p p^{'} | i) (τ)$ with and without a charge-parity switch ( $p p^{'} = + 1$ or $- 1$ , respectively). The relative amplitudes of curves with and without parity switches (triangles and squares, respectively) indicate the likelihood that those transitions were correlated with quasiparticle-tunneling events. Theory lines are obtained from a least-squares fit to the master equation described in the main text. (b) Probabilities plotted in (a) after rescaling $τ$ by $Γ_{i j}$ , the overall decay rate governing each curve at large $τ$ . The crossing of curves with $p p^{'} = - 1$ (black dashed line) indicates a negative effective temperature of the quasiparticle bath. (c) Transition rates extracted from the master equation, in units of $μ s^{- 1}$ . Note that rates are invariant under exchange of even and odd charge-parity states. (d) Charge-parity autocorrelation function $⟨ P P^{'} ⟩$ conditioned on the outcomes $m_{2} = i$ and $m_{3} = j$ .
Reuse & Permissions
Figure 5
Temperature dependence of qubit-state-conditioned parity-switching rates. (a) Above $\sim 140 mK$ , all rates begin to increase, and $Γ_{01}^{e o} / Γ_{10}^{e o} \leq 1$ suggests that thermally generated QPs begin to outnumber nonequilibrium QPs. (b) $1 / Γ_{10}^{e o}$ normalized by its base-temperature value $1 / {Γ_{10}^{e o}}^{0}$ , as a function of temperature. The solid black line is a fit to the thermal dependence of $x_{QP}^{0} / x_{QP}$ , which gives $x_{QP}^{0} \approx 1 \times 10^{- 7}$ . (c) $Γ_{01}^{e o} / Γ_{10}^{e o}$ compared to predictions from detailed balance, assuming QPs are thermalized with the cryostat. Gray dashed line indicates the value above which $T_{eff}^{QP} \leq 0$ .
Reuse & Permissions

Physical Review Letters