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Transcript of Application of superconducting Resonators for Study of Two Level Defect States in Dielectrics Sergiy...
Application of superconducting
Resonators for Study of Two Level Defect
States in Dielectrics
Sergiy 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
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/
QiQQ
cVVS eii
)(/10 TCCL
voltage wave amplitudes:
Resonance Lineshape
ML
Norton Equivalent
NI
CC
L1
C V
CL CT RT V
ba
Cba
ba
ZZ
LMC
ZZ
ZZ
22
LRRQ T 0111
...)( 01
0
ab
abCT ZZ
ZZ
L
MCiRL
FWHM= 1/Q
]CIm[i
Resonance Frequency
)~
Re(:parametersfitwith
/qualityinternalObtain111
0
ei
i
QQQ
LRQ
incident wave
Compact C-CPS
Compact L-CPS
~450m
CL ~350m
2
00
22
0 /21
~1/
Qi
QQcVV e
i
Coplanar resonators
sapphire substrate
Al Al
ALD AlOx
Process sequence during one ALD cycle
Monolayergrowth
SUBSTRATE
OH 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 O
O 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
w
w
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-AlOx
CPS, H-AlOx
Compact L - CPS, D-AlOx
Compact C - CPS, D-AlOx
CPS, 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-AlOx
CPS, H-AlOx
Compact L - CPS, D-AlOx
Compact C - CPS, D-AlOx
CPS, 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
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
Si
OH 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
Co
mp
res
siv
e s
tre
ss (
GP
a)
[N2]/[SiH4] flow rate ratio (%)
2.5
2
1.5
1
0.5
0
-0.5
Co
mp
ressive stress (GP
a)
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 temperature
Sample #1
Sample #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 contributionto dielectric susceptibility has
been found
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 ~0 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 0.
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
10-4
10-5
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
10-4
4.674
4.6745
4.675
4.6755
4.676x 10
9
VRMS
(V)
f 0(G
Hz)
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