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

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)

Mechanisms of qubit relaxation (T1) to be discussed:

Circa 2012

JJ

250 μm

1 m

m

T1 ~ 1-3 µs

T1 ~ 50-100 µs

Questions: Why, and what’s next?

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

H. Paik et al. (2011)

environmentcapacitance

junctioncapacitance

junctioninductance

environmentinductance

JCEC JL EL

capEG

QP? QP?TLS? TLS?radG

radiation

indEG

indJG

capJG

Total Loss Rate = Loss rate contribution from each element

= (Relative weight of element) x (Lossiness of element)

Participation ratio 1/Quality factor

∑∑

5 Dissipation Channels in Qubit Circuit

Transmon: 95% 5% 95% 5%

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, …)

JCEC JL EL

capEG

QP? QP?TLS? TLS?radG

radiation

indEGind

JGcapJG

Transmon in 3D Cavity as a Test-bed of Surface Lossü No uncontrollable radiation

loss in a 3D cavityü Fab together for consistent

material quality

1 m

m

Type A(“Big pads”)

2 m

m

Type B(“Gap Capacitor”)

Similar idea: O. Dial et al. SuST 29, 044001 (2016)

A Tale of Two Transmons

T 1(µ

s)

1 m

m

2 m

m

Extra filters,infra-red absorbers

Semi-rigid cables,Teflon-retracted

couplers

4 consecutive cooldowns in 2013

Type AType B

Replace S-Scomponents

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

Two sharp transitions with applied field

Device B2

Magnetic Field Dependence of Gap-Capacitor Transmon in Al Cavity

Bk ~ Φ0/L2

Magnetic Field Dependence of Large-Pad Transmon in Al Cavity

“Type A device”

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

Microwave Injection of Quasiparticles

Measurement of Quasiparticle Decay

Transmon Qubit

t = 0

Measurement of Quasiparticle Decay

T1 = 1.0 µs

Short Time Scale

Transmon Qubit

Measurement of Quasiparticle Decay

T1 = 1.0 µs

T1 = 2.3 µs

Measurement of Quasiparticle Decay

T1 = 2.3 µs

T1 = 5.5 µs

T1 = 1.0 µs

M. Lenander et al. PRB (2011)

Earlier experiment on quasiparticle decay in a phase qubit

Demonstration of Quasiparticle Recombination

“QP decay time towards a steady-state” τss = 18 ms

5 5

Type B transmon

!!!"!" = −!!!"! + !!

High QP densityFast QP decay

Low QP densitySlow QP decay

τss = 18 ms

Settling

1/t

< 3x10-6

!! = !!!= !!!!

ℏ!! !!" + !!" !

B = 0

Demonstration of Quasiparticle Trapping

Single exponential suggests a single-particle loss mechanism.“QP trapping”, trapping rate s = 1/τss = 1/(1.5 ms)

250 µm High QP densityFast QP decay

Low QP densitySame fast QP decay

τss = 1.5 ms

!!!"!" = −!!!" + !!

One decay rate for large range of QP densities !Type A transmon

< 3x10-7

B = 0

5 5

Controlling QP Dynamics In-situ by Magnetic Field

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

Type B Device B1

C. Wang et al. Nat. Commun. 5, 5836 (2014)

Quasiparticle Trapping due to Magnetic Field Penetration

Individual vortices!!

15 µm for B110 µm for B2

15 µm for B110 µm for B2

Previous observation of QP loss in magnetic field of several Gauss:J. N. Ullom et al., Appl. Phys. Lett. (1998)

All vortices are created equal!

Quantized Trapping Rate due to Individual Vortices

• 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

P ≈ 0.06 cm2/s

0

2P ≈ 0.12 cm2/s

Trapping rate x Device areathe macroscopic observable

Total trapping power of N vorticesthe 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 << D0.067 cm2/s 18 cm2/s

Strong: P >> R x0 A

A quasiparticle passing by a vortex is rarely trapped

A vortex is the dominant quasiparticle decay channel compared with weak recombination

0 vortex1 vortex

Improved Qubit Coherence by Vortices!

Vortices reduce QP lifetime

Background QP density is reduced

Less dissipation due to QP tunneling

T2E

T1

τss

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)

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

Improved Qubit Coherence by Vortices!

Vortices reduce QP lifetime

Background QP density is reduced

Less dissipation due to QP tunneling

T2E

T1

τss

Also show field-cool improvement: Fluxonium: U. Vool et al. PRL (2014); CPW resonator: I. Nsanzineza et al., PRL (2014)

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

Short live the quasiparticles, long live the qubit!

Analysis of QP Induced Qubit Dissipation and QP Generation Rate

1) Stray QP generation rate: g ~ 1 x 10-4 /s2) Relaxation rate due to other mechanisms: Γex = 1 / (26 µs) for B1, 1 / (17 µs) for B2

Geometry Dependence of Transmon T1

250 µm

Type A

A1 A2 A375 µs 66 µs 95 µs

B4 (x=3) B2 (x=10) B1 (x=15) B3 (x=30)7.5 µs 19 µs 25 µs 31 µs

x x

Type B

Measured with B ~ 30 mG

Pi =energy stored in element i

total energy1Qcap

=PiQi

∑

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

Surface Dielectric Participation Ratio

E Energy in vacuum:

Uvac =12ε0 Evac

2 Vvac =12Evac2 Ad

E Energy in MA interface:

UMA =12εrε0 EMA

2 VMA =121εrEvac2 2AtMA

Pi =1εMA

2tMAd

≈1102×3nm5mm

=1.2×10−7

Example: Coplanar waveguide

Surface Dielectric Participation Ratio

Cross-sectional (2D) numerical simulation: (assuming translation symmetry)

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):

PMS ,PSA ~εr102tg~ 10−2

(g / µm)

J. Wenner, Appl. Phys. Lett. 99, 113513 (2011)M. Sandberg, Appl. Phys. Lett. 100, 262605 (2012)

PMA ~110εr

2tg~ 10−4

(g / µm)

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

Design A(Big-pads)

Or maybe not?

Design B(Gap-Capacitor)

CBB

Some other designs

Design C

Design D

Proportionality of 1/T1 vs Surface Participation

Design A

1T1=ω

PMStanδMS

+Γ0

⇒ tanδMS = 2.6×10−3,Γ0 ≈1/ (300µs)

CBB C

B

Participation of the Three Interfaces Scale Similarly

So we can not pinpoint which interface (MS, SA or MA) is responsible for loss

1T1=ω

PMStanδMS

∑ +Γ0

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

Summary on the Coherence of 3D Transmons*

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:g ~ 1.0 x 10-4 , τss ~ 1 ms: xqp = 1 x 10-7 à Γ ~ 1/(250 µs)

Ø We have a bound on the sapphire substrate quality:Q > 12 M or Γ < 1/(300 µs)

* of the “big-pad style” (Paik, et al. PRL 2011)

Can We Further Reduce Surface Participation?

Design A(Big-pads)

Design C(Gap-Capacitor)

By making bigger, more separated electrodes?

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

CBB

Can be Achieved with Suspended Josephson Junction

100 µm

500 nm

XeF2 etch

A few attempts with qubits on silicon substrate

ü Suspension improves T1

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

DRIE (Bosch process)

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 *

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

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.

L. D. Burkhart et al. APS March Meeting 2016

Normal-Metal Quasiparticle Traps on Transmon Devices

Coherence of 3D “Vertical (Bridge) Transmon”

T1 = 10 µs G. Kirchmair et al. Nature (2013)T1 = 8 µs L. Sun et al. Nature (2014)

Field-cool improvement of T110 µs à 20 µs

Evidence of Quasiparticle Dissipation in Vertical Transmons

Metal trace width = 50 µm

The Seam Loss

Our cavity is cut along a symmetry plane to avoid seam loss

Sapphire chip breaks symmetryà Seam loss in both cavity mode and

transmon modeBigger tunnel à better T1 for vertical transmonsT1 ~ 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 OutlookØ 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!