24.11.2016 Mario Palma

Motivation Quasiparticles (QPs) poisoning : Counting error in Superconducting Qubit Decrease the coherence of Superconducting Qubit Decoherence of Majorana Qubit Gap engineering Vortex trap Normal metal trap J. Aumentado et al., PRL 92,066802 (2004). M. Taupin et al., Nat. Commun. 7,10977 (2016)

Model NIS system electrons in N with energy ξn Tunneling Hamiltonian QPs in S with energy 𝜖 𝑛 = 𝜉 𝑛 2 + Δ 2 QPs tunneling from S into N Electrons escape from N into S c electron in the normal metal and d the electron in the superconductor, which is related by the Bogoliubov’ s transformation to the quasi-particles operators. Γ 𝑡𝑟 =2𝜋| 𝑡 | 2 𝜈 𝑠0 / Ω 𝑠 Γ 𝑒𝑠𝑐 𝜖 =2𝜋| 𝑡 | 2 𝜈 𝑠0 𝜈 𝑠 (𝜖)/ Ω 𝑁 BCS density of the states Energy independent

Model 𝜖≫∆ Γ 𝑒𝑠𝑐 (𝜖)→ Γ 𝑒𝑠𝑐 𝑑 𝑠 ≈ 𝑑 𝑁 𝜈 𝑠0 ≈ 𝜈 𝑁0 Γ 𝑒𝑠𝑐 ≈ Γ 𝑡𝑟 Γ tr ~8𝑥 10 6 𝑠 −1 𝜖≥∆ Γ 𝑟 relaxation rate of the electron in the normal metal due to electron-electron interaction or electron-phonon interaction 𝑇≫Δ Γ r →0 𝑇≪Δ There are many unoccupied state below ∆ in N Γ 𝑟 ≠0

Model Rate equations for the probability density in normal metal and in the superconductor Assuming steady-state distribution of the electrons in the normal metal Normalize QPs density 𝑝 𝑁 =0 We have to compare the relaxation rate with the escape rate They normalize the density to V_s0 Fast relaxation rate Slow relaxation Excitation in the normal metal fast relax at energy below the gap and cannot return in the super conductor

Real case Assume that the diffusion time is bigger than 1/Γr The QPs density distribution can be describe through a diffusion equation: The trap component Pair breaking mechanisms The scale over which the density decay due to the trapping Source of QPs tinj =time that the source is on t = time after the source is switched off

Device and experimental set up 3D transmon qubit Josephson junction Al/AlOx /Al Superconductive cavity Cu trap 20 µm<d<400 µm Reference Antenna C. Wang et al., Nat.Commun. 5,5836 (2014)

Decay rate w/o trap T1 = 19 µs 10 µs<T1 <22µs 22µm < d < 80 µm T1 is qualitative the same T1 =5 µs →d = 200 µm & T1 =7 µs →d = 400 µm T1 is reduce The time dependent part of the qubit si directly proportional to the QPs density at the junction 𝑡> 𝑡 𝐿

short & long trap Long trap Short trap the model predict: linear dependence of the characteristic time scale 1/𝜏 𝑤 on the trap length Short trap Long trap saturation behavior 1/ 𝑡 𝐿 ~1/ 𝜏 𝑤 Tfr =13 mK 𝑙 0 =41.2±17.1𝜇𝑚 𝑡 𝐿 =184±29 𝜇𝑠 Γeff =2.42x105 s-1 Tfr =50 mK 𝑙 0 =45.8±16.7𝜇𝑚 𝑡 𝐿 =125±29 𝜇𝑠 Γeff =3.74x105 s-1

Conclusion Γeff is energy dependent for time scale shorter than electron relaxation rate Evacuation time depend linearly on the length of trap and saturated for long trap The decay rate increase with length of the trap For short trap Γeff increases with temperature indicating back flow of QPs

Gap engineering