Surface Dielectric and Quasiparticle Loss in Transmon Qubits Chen Wang

Department of Applied Physics, Yale University

Acknowledgments

Yvonne Gao, Chris Axline,… All members of Schoelkopf lab & Devoret lab & Yale cQED theorists

Workshop on Decoherence in superconducting qubits—JQI, College Park, MD, 2016/4/22 List of Contents

Mechanisms of qubit relaxation (T1) to be discussed: Ø Surface dielectric loss: C. Wang et al. Appl. Phys. Lett. 107, 162601 (2015)

Ø Quasiparticle-induced dissipation: C. Wang et al. Nat. Commun. 5, 5836 (2014)

Ø Seam conduction loss: T. Brecht et al. Appl. Phys. Lett. 107, 192603 (2015) Seamless design: C. Axline et al. (in preparation) Circa 2012

T1 ~ 1-3 µs

e.g. A. Houck et al. (2008)

T1 ~ 50-100 µs JJ

1 mm H. Paik et al. (2011)

Questions: Why, and what’s next? 250 μm 5 Dissipation Channels in Qubit Circuit

environment junction junction environment capacitance capacitance inductance inductance

Transmon: 95% 5% 95% 5% C CE J LJ LE

cap cap ind ind G G Grad E J GJ GE TLS? TLS? QP? QP? radiation Total Loss Rate = ∑ Loss rate contribution from each element = ∑ (Relative weight of element) x (Lossiness of element) Participation ratio 1/Quality factor Lessons Learned “The small Josephson junction is (or can be) very very good.” From fluxonium (I. Pop et al. Nature 2014) and Cooper-pair box (Z. Kim et al. PRL 2011)

“Planar resonators with larger feature size have better Q.” From several studies of resonator Q vs. geometry (H. Wang et al. APL 2009; J. M. Sage et al. JAP 2009; K. Geerlings et al. APL 2012; A. Megrant et al. APL 2012, …)

C CE J LJ LE

cap cap ind G G ind Grad E J GJ GE TLS? TLS? QP? QP? radiation Transmon in 3D Cavity as a Test-bed of Surface Loss Type B ü No uncontrollable radiation (“Gap Capacitor”) loss in a 3D cavity Type A ü Fab together for consistent (“Big pads”) material quality 2 mm 1 mm

Similar idea: O. Dial et al. SuST 29, 044001 (2016) A Tale of Two Transmons Type B Extra filters, Semi-rigid cables, Type A Replace S-S infra-red Teflon-retracted absorbers components couplers s) µ ( 2 mm 1 mm 1 T

4 consecutive cooldowns in 2013 Magnetic Field Dependence of Gap-Capacitor Transmon in Al Cavity

Cooling the qubit in a moderate magnetic field improves T1 !

Field polarity does not matter (zero field point confirmed)

Data from Device B2 (10 µm gap capacitor) 1 mA ~ 8 mG Magnetic Field Dependence of Gap-Capacitor Transmon in Al Cavity

2 Two sharp transitions with applied field Bk ~ Φ0/L

Device B2 Magnetic Field Dependence of Large-Pad Transmon in Al Cavity

“Type A device” Microwave Injection of Quasiparticles

C. Wang et al. Nature Communications 5, 5836 (2014) Similar technique applied to fluxonium qubit: U. Vool et al. PRL 113, 247001 (2014) Measurement of Quasiparticle Decay

Transmon Qubit

t = 0 Measurement of Quasiparticle Decay

Transmon Qubit

T1 = 1.0 µs

Short Time Scale Measurement of Quasiparticle Decay

T1 = 2.3 µs

T1 = 1.0 µs Measurement of Quasiparticle Decay

T1 = 5.5 µs

T1 = 2.3 µs

T1 = 1.0 µs

Earlier experiment on quasiparticle decay in a phase qubit M. Lenander et al. PRB (2011) Demonstration of Quasiparticle Recombination

! !!!! !! = = ! !!" + !!"! Type B transmon !! ℏ!

1/t High QP density Fast QP decay

Low QP density 5 5 Slow QP decay

τss = 18 ms < 3x10-6

Settling !! !" = −!!! + !! !" !" “QP decay time towards a steady-state” τ = 18 ms B = 0 ss Demonstration of Quasiparticle Trapping One decay rate for large range of QP densities ! Type A transmon 250 µm High QP density Fast QP decay

Low QP density Same fast QP decay

τss = 1.5 ms < 3x10-7

!! !" = −!! + !! !" !" Single exponential suggests a single-particle loss mechanism. B = 0 “QP trapping”, trapping rate s = 1/τss = 1/(1.5 ms) Controlling QP Dynamics In-situ by

Magnetic Field Type B Device B1

5 5

QP dynamics crosses over from recombination-dominated to trapping-dominated with increasing cooling magnetic field.

C. Wang et al. Nat. Commun. 5, 5836 (2014) Quasiparticle Trapping due to Magnetic Field Penetration

15 µm for B1 15 µm for B1 10 µm for B2 10 µm for B2

Individual vortices!!

Previous observation of QP loss in magnetic field of several Gauss: J. N. Ullom et al., Appl. Phys. Lett. (1998) Quantized Trapping Rate due to Individual Vortices

All vortices are created equal!

• Subtract a “background trapping rate” (yet to be understood) • Multiply by total device area (A)

Single vortex “trapping power”: P

C. Wang et al. Nat. Commun. 5, 5836 (2014) Single Vortex Trapping Power

2P ≈ 0.12 cm2/s

P ≈ 0.06 cm2/s

0

Trapping rate x Device area Total trapping power of N vortices the macroscopic observable the microscopic intrinsic property Interplay of QP Trapping and Diffusion

For high magnetic field:

• Enough trapping power to deplete QP in the pad • Trapping rate limited by diffusion through the lead • QP diffusion constant at 20 mK measured: D = 18 cm2/s Single Vortex as a Quasiparticle Trap is Both Weak and Strong

Weak: P << D A quasiparticle passing by a vortex is rarely trapped 0.067 cm2/s 18 cm2/s

A vortex is the dominant quasiparticle decay Strong: P >> R x A 0 channel compared with weak recombination

0 vortex 1 vortex Improved Qubit Coherence by Vortices!

Unambiguous evidence of non-equilibrium quasiparticles limiting T1 of a transmon

Vortices reduce QP lifetime T2E

T 1 Background QP density is reduced

τss Less dissipation due to QP tunneling

Short live the quasiparticles, long live the qubit!

Also show field-cool improvement: Fluxonium: U. Vool et al. PRL (2014); CPW resonator: I. Nsanzineza et al., PRL (2014) Improved Qubit Coherence by Vortices!

Unambiguous evidence of non-equilibrium quasiparticles limiting T1 of a transmon

Vortices reduce τss QP lifetime T2E

Background QP density is reduced

T1

Less dissipation due to QP tunneling

Short live the quasiparticles, long live the qubit!

Also show field-cool improvement: Fluxonium: U. Vool et al. PRL (2014); CPW resonator: I. Nsanzineza et al., PRL (2014) Analysis of QP Induced Qubit Dissipation and QP Generation Rate

1) Stray QP generation rate: g ~ 1 x 10-4 /s

2) Relaxation rate due to other mechanisms: Γex = 1 / (26 µs) for B1, 1 / (17 µs) for B2 Geometry Dependence of Transmon T1

Type A 250 µm Type B

x x

Measured with B ~ 30 mG

A1 A2 A3 B4 (x=3) B2 (x=10) B1 (x=15) B3 (x=30) 75 µs 66 µs 95 µs 7.5 µs 19 µs 25 µs 31 µs Surface Dielectric Participation Ratio

energy stored in element i 1 P P = = i i total energy cap ∑ Q Qi

Example: Metal-air interface for a rectangular 3D cavity (TE101)

E Energy in vacuum: 1 1 U = ε E 2 V = E 2 Ad vac 2 0 vac vac 2 vac

E Energy in MA interface:

1 2 1 1 2 U MA = εrε0 EMA VMA = Evac 2AtMA 2 2 εr

1 2tMA 1 2×3nm −7 Pi = ≈ =1.2×10 εMA d 10 5mm Surface Dielectric Participation Ratio

Example: Coplanar waveguide

The participation ratio for all three types of interfaces scale inversely with the “pitch” size (w or g, assuming w/g is a constant or order unity): ε 2t 10−2 1 2t 10−4 r P ~ ~ PMS , PSA ~ ~ MA 10 g (g / µm) 10εr g (g / µm)

Cross-sectional (2D) numerical simulation: (assuming translation symmetry) J. Wenner, Appl. Phys. Lett. 99, 113513 (2011) M. Sandberg, Appl. Phys. Lett. 100, 262605 (2012) The Challenge of Computing Surface Participation in 3D Qubits

E&M simulation of 3D qubits:

Have to discretize to < t ~ 3 nm for energy in surface layer to converge (Computationally infeasible)

Surface charge distribution of a half-infinite metal plane: ++ + + + x A Two-Step Approach for Computing Surface Participation in 3D Qubits

Assumption: Field scaling near the edge is independent of far-away boundary conditions

Perimeter Area Energy = Line Energy x Scaling Factor

C. Wang et al. Appl. Phys. Lett. 107, 162601 (2015) A Two-Step Approach for Computing Surface Participation in 3D Qubits

C. Wang et al. Appl. Phys. Lett. 107, 162601 (2015) The Near-Junction Region Matters for Surface Participation Or maybe not?

C Design B B (Gap-Capacitor) B

Design A (Big-pads) Some other designs

Design C

Design D Proportionality of 1/T1 vs Surface Participation

C B B C B

Design A

1 PMS = ω + Γ0 T1 tanδMS

−3 ⇒ tanδMS = 2.6 ×10 , Γ0 ≈ 1/ (300µs) Participation of the Three Interfaces Scale Similarly So we can not pinpoint which interface (MS, SA or MA) is responsible for loss

1 PMS = ω∑ + Γ0 T1 tanδMS −3 ⇒ tanδMS +1.2tanδSA + 0.1tanδMA = 2.6 ×10 , Γ0 ≈ 1/ (300µs)

Summary on the Coherence of 3D Transmons* * of the “big-pad style” (Paik, et al. PRL 2011)

Ø The major limiting factor is still surface dielectric loss !

Ø We have a good estimate of vortex microwave loss: B = 100 mG : Γ ~ 1/(100 µs) à Γ < 1/(1 ms) at B < 10 mG

Ø We have a good estimate of quasiparticle dissipation: -4 -7 g ~ 1.0 x 10 , τss ~ 1 ms: xqp = 1 x 10 à Γ ~ 1/(250 µs)

Ø We have a bound on the sapphire substrate quality: Q > 12 M or Γ < 1/(300 µs) Can We Further Reduce Surface Participation? By making bigger, more separated electrodes?

It’s harder than you think… because of the junction leads

C Design C B (Gap-Capacitor) B

Design A (Big-pads) Can be Achieved with Suspended Josephson Junction A few attempts with qubits on silicon substrate

XeF2 etch DRIE (Bosch process)

100 µm

500 nm ü Suspension improves T1

✖ But on Si substrate, our surface loss tangent is much worse

Y. Chu et al. (in preparation) Is Non-equilibrium Quasiparticle a Problem to be Solved?

Quasiparticle trapping is already needed at current state-of-art level of T1 (10’s – 100 µs) g ~ 1 x 10-4/s *

1/2 -6 Recombination steady state xqp = (g/r) ~ 1-3 x 10

T1~ 8-25 µs ! Is Non-equilibrium Quasiparticle a Problem to be Solved?

For the moment, unintentional trapping is often taking care for you!

Ø Vortices (in large extended region, e.g. ground plane). Ø Gap variation (between superconductors from different steps) Ø Residual trapping yet to be understood -- Possibly due to defects or gap imhomogeneity

-- Strongly dependent on fabrication recipe, can make τss < 1 ms -- Stronger at higher temperature (15 mK vs 50 mK)

Kinetic inductance detector people: watch out… For qubits: more controllable traps are needed for the future. Normal-Metal Quasiparticle Traps on Transmon Devices

L. D. Burkhart et al. APS March Meeting 2016 Coherence of 3D “Vertical (Bridge) Transmon”

T1 = 10 µs G. Kirchmair et al. Nature (2013)

T1 = 8 µs L. Sun et al. Nature (2014) Evidence of Quasiparticle Dissipation in Vertical Transmons Metal trace width = 50 µm

Field-cool improvement of T1 10 µs à 20 µs The Seam Loss

Sapphire chip breaks symmetry à Seam loss in both cavity mode and transmon mode

Our cavity is cut along a Bigger tunnel à better T1 for vertical symmetry plane to avoid transmons

seam loss T1 ~ 35 µs: R. Heeres, et al. PRL (2015) N. Ofek, et al. arXiv: 1602.04768 (2016) T. Brecht et al. APL 107, 192603 (2015) A Seamless (and More Scalable) Solution of 3D cQED C. Axline et al. APS March meeting 2015 (manuscript in preparation)

Transmon T1 ~ 50-120 µs

Implementation in more complex experiments: 3 cavity 1 transmon: C. Wang et al. arXiv:1601.05505 (2016)

Transmon T1 = 70 µs (partially suppressed by Purcell) 2 cavity 4 transmon: J. Blumoff et al. (APS MM 2016, manuscript in preparation)

Transmon T1 = 86 µs, 87 µs, 58 µs, 23 µs (Purcell limited) Conclusions and Outlook

Ø The bottleneck for transmon coherence in 3D cQED appears to be surface dielectric loss -- Implementation of better surface treatment is very important -- Further reduction of surface participation is possible using suspension

Ø Other factors are often in play, but are curable by good design -- Non-equilibrium quasiparticles (mitigated by field-cool or other “natural” trapping, but requiring new solutions soon) -- Purcell effect -- Seam conduction loss

Ø We see no evidence of additional (unidentified) mechanisms at the level of T1 ~1 ms

Thank you!