APS March Meeting 2020.

1. T1 of transmons with electrodes that have
different gaps
Kungang Li
S. K. Dutta, R. Zhang, D. Poppert, S. Keshvari, C. J. Lobb
and F. C. Wellstood
University of Maryland – College Park
Department of Physics
Kungang Li F16.000013/6/2020 1

2.  Motivation:
Produce transmons with long relaxation time T1
 Approach:
Use gap engineering to suppress quasiparticle loss
 Basic idea:
Quasiparticles cause loss when they tunnel across the transmon junction. If
electrodes have different superconducting gaps, tunneling from the low-gap
side to high-gap side is suppressed.
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Introduction

3. Configuration of the two transmons
Sapphire
Oxygen doped Al
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∆2
∆3
∆1
∆1
Transmon 1
(gap engineered)
Transmon 2
Sapphire
Nominally pure Al
Nominally pure Al
Nominally pure Al

4. Transmon design
Left transmon Right transmon
Left Right
Junction (nm2
) 200 × 220 200 × 200
𝑓𝑔𝑒 (GHz) 2.929780 3.773817
ℎ𝑓𝑔𝑒 (μeV) 12 16
𝐸𝐽 ℎ (GHz) 5.549344 9.950487
𝐸 𝐶 ℎ (MHz) 224.050 198.192
Δ1 (μeV) 200.0 200.0
Δ2 / Δ3 (μeV) 227.7 191.1
Δ2 − Δ1 (μeV) 27.7 -8.9
Ω2 Ω1 2.75 2.32
Two transmons deposited in same pump down.
Left transmon has oxygen-doped upper layer and pure Al lower layer.
Right transmon has both layers of pure Al.
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500 μm
3 μm
Gaps from separate measurements on
co-deposited films

5. Measurement setup
Al Cavity
Two
Transmons
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Input pin Output pin
Input line
Output line

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Al ∆1=200 μeV
Al ∆3=191 μeV
Al ∆1= 200 μeV
Al (O2 doped) ∆2=227 μeV
T1 vs Temperature for two transmons
Run 1↓ Run 2↑ Run 3↑ Run 4 ↓
Left transmon Right transmon

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Al ∆1=200 μeV
Al ∆3=191 μeV
Al ∆1= 200 μeV
Al (O2 doped) ∆2=227 μeV
T1 vs Temperature for two transmons
Run 1↓ Run 2↑ Run 3↑ Run 4 ↓
Left transmon Right transmon
Left transmon

8. 3/6/2020 8
Low gap limit : Δ2 − Δ1 < ℎ𝑓01
)()( 4
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𝑛 𝑡ℎ =
3𝑛 𝑒
𝜀 𝐹
Δ + 𝑧0 𝑘 𝐵 𝑇 𝜋𝑘 𝐵 𝑇
2Δ + 𝑧0 𝑘 𝐵 𝑇
𝑒−Δ 𝑘 𝐵 𝑇
𝑛1𝐿 =
𝑛 𝑛𝑒,1L
1+
Ω2
Ω1
Δ2
Δ1
𝑒− Δ2−Δ1 𝑘 𝐵 𝑇
+𝑛 𝑡ℎ,1𝐿
𝑛2𝑅 =
𝑛 𝑛𝑒,1R
Δ1
Δ2
𝑒− Δ1−Δ2 𝑘 𝐵 𝑇 +
Ω2
Ω1
+𝑛 𝑡ℎ,2𝑅
Model of loss due to Non-equilibrium quasiparticles
Fitting parameters: ∆1 , ∆2
𝑛 𝑛𝑒,1𝐿
𝑛 𝑛𝑒,1𝑅
Density parameter for nonequilibrium quasiparticles on left side in layer 1
Density parameter for nonequilibrium quasiparticles on right side in layer 1

9. Comparison between measurement and model
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Left transmon Right transmon
𝑛 𝑛𝑒 = 0
Δ1 = 200 𝜇eV
Δ2 = 227 𝜇eV
𝑛 𝑛𝑒 = 0
Δ1 = 200 𝜇eV
Δ3 = 191 𝜇eV
Gaps from separate measurements on
co-deposited films

10. Comparison between measurement and model
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Left transmon Right transmon
Δ1 = 225.3 𝜇eV
Δ2 = 230.9 𝜇eV
𝑛 𝑛𝑒.1𝐿 = 2.0 𝜇𝑚−3
; 3.8 𝜇𝑚−3
; 7.0 𝜇𝑚−3
𝑛 𝑛𝑒.1𝑅 = 10 𝜇𝑚−3
; 13 𝜇𝑚−3
; 18 𝜇𝑚−3
Δ1 = 190.5 𝜇eV
Δ2 = 179.6 𝜇eV
𝑛 𝑛𝑒.1𝐿 = 7.6 𝜇𝑚−3
; 7.1 𝜇𝑚−3
; 4.7 𝜇𝑚−3
𝑛 𝑛𝑒.1𝑅 = 6.7 𝜇𝑚−3
; 8.3 𝜇𝑚−3
; 11 𝜇𝑚−3

11. Conclusion
 Used gap engineering to build 2 Al/AlOx/Al
transmons with electrodes that have different gaps
 High gap-low gap device produced T1 up to 300 μs
 T1 vs T data consistent with non-equilibrium
quasiparticle model
 See Talk L08.00002 tomorrow morning at Room 104
for more information about T1 fluctuations
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