Flux Noise McDermott - jqi.umd.edu · (NEC, NTT) Delft flux qubit Phase qubit Flux qubit Universal...
Transcript of Flux Noise McDermott - jqi.umd.edu · (NEC, NTT) Delft flux qubit Phase qubit Flux qubit Universal...
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Origin and Suppression of 1/f Magnetic Flux Noise
Robert McDermott University of Wisconsin
DiSQ2 College Park, MD
April 21, 2016
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Personnel
PD Pradeep KumarGS Matt BeckGS Steve Sendelbach (now at Northrop Grumman)
Clare Yu, Ruqian Wu; PDs Hui Wang, Zhe Wang (UC Irvine)
John Freeland (Argonne National Lab)
David Pappas (NIST Boulder)
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Outline
• 1/f flux noise in superconducting circuits (SQUIDs, qubits)
• Evidence for surface magnetic defects
• XAS and XMCD: magnetism from adsorbed O2
• Suppression of surface magnetism: susceptibility and flux noise
• Recent theoretical progress
• Some details (geometry, materials dependence of noise)
• Future directions
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1/f Flux Noise in SQUIDs [Wellstood et al., APL 50 772 (‘87)]
“universal” 1/f flux noise
no clear dependence on materials
mechanism unknown
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Dephasing from 1/f Noise
Sλ
ω
Ramsey fringes
tπ/2 π/2
time (ns)
T2* = 90 ns
P 1
ωλAS =
ωλAS =
(not a rate)
Gaussian decay envelope
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1/f Flux Noise in SC Qubits
50 µm
L = 720 pHSΦ
1/2 (1 Hz) = 2-4 µΦ0/Hz1/2
(UCSB)
L = 3 - 5 pHSΦ
1/2 (1 Hz) = 1 µΦ0/Hz1/2
(NEC, NTT)
Delft flux qubit
Phase qubit Flux qubit
Universal flux noise? Compatible with earlier SQUID measurements
Also: • Investigations of dressed dephasing (Siddiqi et al.): probe to 100s MHz• Evidence for magnetic loss at GHz frequencies (Lincoln, Google)
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Surface Magnetism in SC Devices
Bcool 0Φ≈ cool
vortexB
σ
T > Tc T < Tc
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Temperature-dependent flux scales linearly with density of vortices
Temperature (mK)0 200 400 600 800
Flux
(Φ0)
0
0.5
1
-0.5
-1
Bfc (µT)-600 -300 0 300 600
-0.8
-0.4
0.4
0.8
0
Bfc = 500 µT
Bfc = -500 µT
Sendelbach et al., PRL 100 227006 (08)
Surface Magnetism in SC Devices
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Interpretation: Polarization of Unpaired Spins in Vortex
decrease temperature
• Circulating current decreases due to flux quantization• Flux coupled to vortex by polarization of spins ~ 10 µΦ0• Substantial fraction of the vortex current couples to the SQUID
1: Calculate flux coupled to SQUID from vortex
2: Calculate flux coupled to vortex from uniform density of spins
[Sendelbach et al. arXiv:0802.1511 (08)]
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Interpretation of Field Cool DataPolarization of unpaired spins in vortex
Implies:
Bfc (mT)-600 -300 0 300 600
ΔΦ
(Φ0)
-0.8
-0.4
0.4
0 ASQ = SQUID Area
LV = Vortex Self Inductance
ΔPeff = Change in effective spin polarization
σS = Spin Density
0.8
compatible with Bluhm et al.
Rogachev et al.
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Theoretical Models
• disordered metal-insulator interface• Localized metal-induced gap states (MIGS); density σ ~ 5x1017 m-2
Choi et al. [PRL 103, 197001 (09)]
L. Faoro and L.B. Ioffe [PRL 100, 227005 (08)]
• spins at S-I interface (surface density of spins σ ~ 1016-1017 m-2)• RKKY interaction, spin diffusion in nonuniform current distribution of SQUID
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Investigations of Surface Spin Susceptibility
Rich, history-dependent structure in ΔL(T)
Correlated fluctuationsof L and Φ (susceptibilityand magnetization)
40
0 0.5 1 1.5 20
10
20
30
40
0
10
20
30
Temperature (K)
Indu
ctan
ce (f
H)
ΔL' (f 0 = 10Hz)
≈≈ΔL' (f 0= 100Hz)
ΔL''(f0= 100Hz)
x5
ΔL''(f = 10Hz)010x
Sendelbach et al.,PRL 103 117001 (09)
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X-ray Magnetic Circular Dichroism (XMCD)
User proposal to Argonne National Lab [co-PIs Pappas (NIST); Yu, Wu (Irvine); Freeland (ANL)]
Argonne beamline 4-ID-C:7 T field at 4.2 K (unique in the US)
Look at native Nb, Al, SiOx/SiNx encapsulated Nb, Al
• Element-specific spectroscopic probe of magnetism• Good sensitivity to surface/interfacial spins
• Absorption of LHCP and RHCPX-rays by polarized sample
•Total Electron Yield (TEY): sensitive to surface magnetism
•Total Fluorescence Yield (TFY): sensitive to bulk magnetism
www-ssrl.slac.stanford.edu/stohr/xmcd.htm
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X-ray Magnetic Circular Dichroism (XMCD)
Al-K Nb-L O-K
No signature of magnetism on native samples cooled in the UHV cryostat of the end station!
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X-ray Magnetic Circular Dichroism (XMCD)
Strong XMCD signal from O K-edge following adsorption of air on the sample at low temperature (1e-6 Torr for ~1 min.)
Significant modification of O K-edge at ~ 45 K in O2 partial pressure around 1e-8Torr
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O2 Magnetism
paramagnetic O2
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O2 Magnetism
Long range AFM order
Helicoidalorder
Freiman and Jodl,Phys. Rep. 401, 1 (2004)
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Evolution of UHV Cell
• Commercial SS conflat parts, coated with TiN inside and out• Commercial welded SMA feedthrus
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Evolution of UHV Cell
• Welded Al box• Explosively-joined Al-SS bimetal
for CF flanges
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Evolution of UHV Cell
• Machined enclosure from grade 5 titanium• Single conflat gasket• Weld-in hermetic SMA feedthrus• Copper pinch tube for pumpout
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UHV Sample Cell
Investigated treatments:
• UHV bake (120 C)• UHV + UV irradiation (365 nm)• UHV bake + NH3 backfill (~100 Torr)
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Suppression of Static Susceptibility
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2 x Al shielding
Madison SQUID Noise Measurements
Al/AlOx/Al
Nb/AlOx/Nb
typ. flux gain: 40-80
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• 2 layers SC shielding• 1 layer cryogenic mu-metal• Powder filters on all leads• RC filters on bias leads of DUT
Madison SQUID Noise Measurements
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Fit to form A/f α + B; extract A, α
Madison SQUID Noise Measurements
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Madison SQUID Noise Measurements
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Madison SQUID Noise Measurements
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surface-treated devices
oxide encapsulation
nitride encapsulation
UHV
UHV+NH3 backfillUHV+UV
Madison SQUID Noise Measurements
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Noise Measurementsrun-to-run variation
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Magnetism of Adsorbed O2
For O2 adsorbed on sapphire,spin polarization similar to free O2 molecule(C.C. Yu, R. Wu)
• Magnetization localized in planeperpendicular to molecular axis
• Calculated ferromagnetic exchange energy J = 1.6 K
(assumes 0.48 nm separation; DFTresult for O2 on c-Al2O3)
• Curie temperature Tc = 4.3 K
(C.C. Yu, R. Wu)
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Lawrence Livermore National Laboratory LLNL-PRES-81207131
O2 Exchange Coupling on Al-Terminated α-Al2O3
J = Euu,uu – Euu,dd = -
Exchange Coupling (a negative value shows ferromagnetism)
J = -4.0 meV (48 K)
J = -10 meV (113 K)
J = -0.55 meV (6.4 K)
J = -2.7 meV (32 K)
J = -0.46 meV (5.3 K)
§ Ferromagneticexchange couplings depend on the relative orientation of O2 molecules
§ Ferromagnetic clusters of varying size and coupling may exist due to random O2orientations frozen in at low temperatures
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Correlatednoiseinspinmodels(Ioffe,Faoro)
Mainingredientsofthemodel:• Ferromagneticgroundstate• Frustration(simpleferromagnets formdomains)• Broadrangeofinteractionstrength• Randomanisotropy
Examplemoststudied(natural?):RRKY+randomanisotropy
2
4
) cos
cos( ) ( ) ( )( )
(
sinij i j an i i ac
ij ij ijij
ij
H J S J hkr kr kr
J
S n
k
S t
r
ω
−
= + +
=
∑ ∑r rrr
Qualitativepicture:highenergyobjects,duetostronglyinteractingspinclusterswherespinspointsawayfromtheeasyplanedirection,liveforaverylongtimeandproducelargenoise.
NoiseinsusceptibilityNoiseinmagnetization Noisecorrelations
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Device Geometry, Layer Stack
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Simplified toroidal model of SQUID
(reciprocity)
µ
Dependence of Noise on Device Geometry
Expect SΦ ~ σ (R/r), apart from log corrections
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Dependence of Noise on Device Geometry
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• For devices co-fabbed on asingle wafer, clear linear scaling of noise power with aspect ratio
• SiNx-encapsulated devices have lower noise
• No clear dependence of α on geometry or materials
Dependence of Noise on Device Geometry, Materials
SiOx
SiNx
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ΔE = 230 mK ΔE = 580 mK
ΔE = 0 ΔE = 460 mK
Magnetic Activity of Adsorbed O2
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Conclusions and Future Directions
• Adsorbed molecular O2 the dominant contributor to low-frequency 1/f flux noise
• Need to care about the vacuum integrity of SC qubits!
• Open questions: effect of surface treatments on high-frequencypart of 1/f flux noise spectrum
• Coming soon: integration with qubit circuits
arXiv:1604.00877