Application of superconducting

Resonators for Study of Two Level Defect

States in DielectricsSergiy Gladchenko

Collaborators: Moe Khalil, Micah Stoutimore, K. D. Osborn (LPS)

F.C. Wellstood, C.J.Lobb (UMD)

Laboratory for Physical Sciences, Maryland

Outline:

Common problems of superconducting quantum computing

Two-level defect states in dielectric is a powerful source of decoherence in superconducting qubit

Resonance methods of study of defect states in dielectric.

Experimental observation of TLS-TLS interaction

Resonance absorption of dielectric in the swept DC field

Relaxation and Dephasing

T1 = Relaxation time T2 = Dephasing time

10

1/T1 - radiation to the environment

1/T2 - parameter fluctuations

phonons

photons

magnetic-field noise

charge fluctuations

fluctuatingspins

trapped vortices

quasiparticletunneling

charge/Josephson-energy fluctuations

A short decoherence time: the qubits are strongly affected by local noises (such as critical current fluctuations, charge noise, flux noise and quasiparticle poisoning).

Sapphire

Al

AlSiNX

Trialayer JJ ~ mm

AlOX Josephson Junction Barrier(thermally grown,in almost all qubits, 2 nm thick)

Interfaces/Surfaces*

Interlayer Dielectric (stores energy, 250 nm thick, a-Si is also used)

Source of dielectric loss in superconducting qubit

a

f

cb d

e

Two-level defect states in Josephson qubit

Loss in the amorphous dielectric arise from resonant absorption from two level system (TLS) defects with a dipole moment coupling to the electric field .

dielectric

Defect in dielectric capacitor

dr

Al

Al

h

V

ac electric field: E=V/d moment from modified D: p=qr

Li-Chung Ku and Clare C. Yu PRB 72, 024526 (2005)R.W.Simmonds et al. PRL 93, 077003 (2004)

The Hamiltonian can be diagonalized to give the

eigenenergies

Interaction Hamiltonian

Hamitonian of TLS in the electric problem

of a spin 1/2 system in a magnetic fieldHamitonian

Correspondence between TLS and spin system:

Resonant TLS contribution to the (isotropic) dielectric function:

Rabi frequency

TLS contribution to the dielectric function

We

Field Dependence of TLS Loss

Approximations of strong and weak fields

Weak field

TLS TLS

Dilution Refrigerator

30mK

1.4K

T=4K

RF setup for |S12| measurement

RF Source RF Analyzer

-20 dB

-20 dB

T=300K

4K

1.4K

30mK

Z0

Pin Pout

Z0

Resonator + Sample Box

Experimental setup

C

L

waveguide center

Resonance dielectric studies

Quasi-lumped element coplanar resonators

Lumped element resonators with parallel plate capacitor

C

L

Equivalent model of the experimental device

aZbZ

iV

oV

0000 /21

~1/

QiQQcVVS e

ii

)(/10 TCCL

voltage wave amplitudes:

Resonance Lineshape

ML

Norton Equivalent

NI

CC

L1

C V

CL CT RT V

ba

Cba

ba

ZZLMC

ZZZZ

22

LRRQ T 0111

...)( 01

0

ab

abCT ZZ

ZZLMCiRL

FWHM= 1/Q

]CIm[i

Resonance Frequency

)~Re(:parametersfitwith

/qualityinternalObtain111

0

ei

i

QQQ

LRQ

incident wave

Compact C-CPS

Compact L-CPS

~450mm

CL ~350mm

2

00

22

0 /21

~1/

QiQQcVV e

i

Coplanar resonators

sapphire substrate

Al AlALD AlOx

Process sequence during one ALD cycle

Monolayergrowth

SUBSTRATEOH OH OH

M LLL

L

OH OH O

M LLL

L

M LLL

LH

M LLL

M LLL

M LLL

M LLL

M LMOH

OH OH

H2O

MMOH OH

O O O

O O OO O OO O M

OH

Initial surface

Metal precursorexposure

Purge

Reactant B exposure

Purge

O

LHH2O

H2O

ALD dielectric research with coplanar resonators

Coplanar Strip (CPS)

J/m3

x (µm)

z (µ

m)

Electric Energy Density Distribution

vacuum

sapphire substrate

50 nm thick ALD AlOx film

CPS

Simulation of electric field distribution

Resonatorin StoredEnergy Total

VolumeLossy in StoredEnergy 2

2

e

eh

V

V h

ww

rdrE

rdrEF h

sS

FQ

tan1

10-6

10-5

10-4

10-3

10-2

10-6

10-5

10-4

10-3

VRMS (V)

1/Q

i

Coplanar resonators on 50nm of ALD AlOx

Compact L - CPS, H-AlOxCompact C - CPS, H-AlOxCPS, H-AlOxCompact L - CPS, D-AlOxCompact C - CPS, D-AlOxCPS, D-AlOxCompact LC, D-AlOx

10-6

10-5

10-4

10-3

10-2

10-4

10-3

10-2

VRMS (V)

tand

Coplanar resonators on 50nm of ALD AlOx

Compact L - CPS, H-AlOxCompact C - CPS, H-AlOxCPS, H-AlOxCompact L - CPS, D-AlOxCompact C - CPS, D-AlOxCPS, D-AlOxCompact LC, D-AlOx

10-2

10-3

10-4

10-4

10-3

10-5

10-210-310-410-510-610-210-310-410-510-6

d3r

d3r

Loss tangent of ALD AlOx

VRMS (V) VRMS (V)

Loss

tan

1/Q

i

Al(200nm)

SiNx (250nm)

Wave guide

Capacitor(bottom plate)

Inductor

Al (100nm)

Sapphiresubstrate

Fabrication of the parallel plate capacitor superconducting resonator

capacitor

waveguide

inductor

groundplane

20mm

Fabrication of the superconducting resonator

No

CL

LC

Coupling strength of the microwave resonators

Qe describes interaction of resonator with the transmission line and inversely proportional to square of coupling coefficient.

Internal quality factor is defined by and attributed to the dielectric loss in capacitor.

VQi tan1

“Classic” TLS model: OH rotor (point defect)(Phillips, 1981; Hutt, Phillips, Butcher, 1989)θ

SiO

H C. Musgrave (CU):similar to a Al(OH)3 defect model for AlOx:H

3 SiH4 + 4 NH3 → Si3N4 + 12 H2

Oxygen concentration is correlated with loss.UCSB a-Si has similar O concentration as Si-rich SiNx.

-0.5

0

0.5

1

1.5

2

2.5

0.8 0.9 1 1.1 1.2 1.3 1.4

n C

ompr

essi

ve s

tres

s (G

Pa)

[N2]/[SiH4] flow rate ratio (%)

2.5

2

1.5

1

0.5

0

-0.5

Com

pressive stress (GPa)

n @

633

nm

Si3N4 Al Si

TLS in amorphous SiNx

10-6

10-4

10-5

10-4

10-3 High vs Low Stress

VRMS (V)

tan

Low StressHight StressN-richSi-rich

Raw experimental data

-75-73-71-69-67-65-63-61

Pin , dBmT=100 mK

-75-73-71-69-67-65-63-61

T=40 mKPin , dBm

Dielectric loss versus microwave voltage

Lyo S.K: Phys.Rev.Lett. 48, 688 (1982)

Sample #1

Dielectric loss versus temperature

Sample #1Sample #2

Crossover temperature: T(SiO2) ~ 30mK T(SiOx) ~ 100mK

VRMS = 2*10-7 V

A.L.Burin JLTP 100, 309 (1995)

Delocalized collective excitation

Energy transport is not efficient in the off resonance (A) case where the energy Level mismatch exceeds the resonant interval. For resonant pair (B) interaction induce flip-flop transition.

A.L.Burin, L.A.Maksimov, and I.Ya. Polischuk JETP Lett.80, 513 (2004)

Fluctuation of the dielectric loss in non-saturated TLS regime

Measurements of conductance fluctuations in amorphous metals Indicate that TLS interact

G.A.Garfunkel et al. Phys. Rev. B 40, 8049 (1989)

Sample #2

Low temperature dielectric response of glasses to DC electric field

The relaxation and resonance responseof dielectric susceptibility expected

Instantaneous rise with log relaxation of the density of states insures the same behavior for AC dielectric constant. The logarithmic character of relaxation contribution described by logarithm spectrum of TLS relaxation times.

The second contribution caused by relaxation of TLS population differences, there is a resonance component with relaxation time proportional to 1/t. No resonance contribution

to dielectric susceptibility hasbeen found

Superconducting resonator with DC bias

L

VDC

C1

C2

C3

C4

SiNxCapacitorsInductor

DC Bias

DC pulse amplitude = 20V ~ 40MV/m

S21

Time, s

Freq., GHz

0

20

UD

C,V

Resonant relaxation Non-resonant relaxation

Two observed relaxation behaviors : power and logarithmic.

First process caused by excitation of resonant TLSs with energy ~D0 leading to a large state population difference. This process can be described as lowering the effective temperature for the resonant TLSs analogous to the effect of adiabatic demagnetization. Theoretical prediction for relaxation time is ~1/t[2] .

Logarithmic relaxation caused by relaxation of non-resonant TLSs. This law can be explained by logarithmically uniform distribution of TLS tunneling amplitudes D0.

Response of resonance absorption of SiNx in the presence of swept DC field

Dielectric loss for different delay time after DC pulse application

10-7

10-6

10-5

10-410

-5

10-4

10-3

VRMS (V)

tan

0V (0 V/m)25V (50 MV/m) 50V (100 MV/m) 75V (150 MV/m) 100V (200 MV/m)

10-7

10-6

10-5

10-44.674

4.6745

4.675

4.6755

4.676x 109

VRMS (V)

f 0(GH

z)

Pulse turned on at t=0 (rise time~20ms) Steady state measurement

Loss tangent increases at sudden DC voltage step then decays as 1/t and logarithmically. The dielectric permittivity (~ f-2) changes instantaneously to the steady state value, which is shown to the left, after the step.

1 H. Paik and K. D. Osborn, Appl. Phys. Lett. 96, 072505 (2010).2A.L.Burin JLTP 100, 309 (1995)

Summary

We studied sources of decoherence in the superconducting qubits mainly focusing on the two level defect states in amorphous dielectrics.

1. We measured the dielectric loss of ALD deposited AlOx. That is the same order of magnitude as the loss found for another amorphous oxides.

2. The dominant contribution of the native oxide loss has been found for the coplanar resonator deposited on the crystalline sapphire.

3. We have demonstrated that the OH rotor is the main source of loss in amorphous SiNx.

4. We found evidence of interaction between two-level defects states in amorphous SiNx. We suppose this interactions can lead to delocalized collective excitation at sufficiently low energy.

5. We measured AC susceptibility response on the DC field and found the clear proof of the both relaxation and resonant TLSs contribution to dielectric function.

6. The discrepancy between theory and experiment found in the behavior of real component of dielectric function.

E-beam evaporation

Sputtering

l – mean free pathd - thickness

0 >> d,l

Effective penetration depth

LCfres 2

1

10-7

10-6

10-5

10-4

10-3

10-2

10-6

10-5

<V2>1/2

1/Q

i

sputtered and evaporated films

Compact LC sputteredCPS sputteredCompact C - CPS sputteredCompact L - CPS sputteredCompact LC evaporatedCPS evaporatedCompact C - CPS evaporatedCompact L - CPS evaporated

6.4%

6.59%

5.65%

6.05%

Superconductor loss

Effect of TLS-TLS interaction