prelim talk pp 12-3-15 pdf
DESCRIPTION
Preliminary examination slidesTRANSCRIPT
CouplingRydbergAtomstoSuperconductingQubits ViaASuperconductingCoplanar
WaveguideResonator
MatthewBeckPreliminaryExamination
December9,2015
Outline
1. Motivation
2. Rydberg Atom – Superconductor Interface Design and Characterization
3. Proposed Initial Experiments
4. Cryostat Design and Characterization
5. Future Work
6. Conclusions
Rydberg Atoms / Superconductors For Quantum Computing
Ze-Liang Xiang, et al., Rev. Mod. Phys. 85, 623
Bridge computational speed of SC with long livedstates of atomic systems
Market For A Hybrid Quantum Interface
Market For A Hybrid Quantum Interface
Critical Element
Current Efforts - Tubingen
Fortagh GroupTubingen • Rb MOT in 6 K stage
• Magnetic Transport tomilliKelvin stage
• Hyperfine transitioncoupling, f = 6.835 GHz
• Superconducting Element?
Current Efforts – JQI, Maryland
Wellstood Group, JQI
• Rb atoms trapped inevanescent wave ofoptical nanofiber
• SC – lumped elementResonator
Atom – SC Coupling
• Utilize magnetic moment of hyperfine splitting in Rb ground state- Rely on ensemble coupling of many
atoms to compensate small mag. moment
• Road to bridging atom trapping with mKenvironment still unclear
• Utilize large electric dipole moment of Cs Rydberg atom- Strong coupling with 1 atom
• Initial experiments to demonstrate strong couplingto be conducted at 4 K
Our Approach
Current Approaches
Rydberg Atom-SC CPW Interface - In Theory
Cs Ground Hyperfine Ensemble Coupling[ Vienna, Tübingen, NIST ]
Rydberg Level Electric Dipole Transition
n𝑙 = 0
𝑙 = 15-10 GHz
5-10 GHz
CPW Electric Field Loss Rate @ 4K
Strong Atom - CPW Coupling At LHe Temperatures
Rydberg Atom-SC CPW Interface - In Practice
Resonant Dispersive
Rydberg Atom-SC Interface - In Practice
Strong Atom - CPW Coupling At LHe Temperatures
•Quality factor, Q, is dominated by non-equilibrium thermal quasiparticle loss
- Max Q = CPW Theory + Mattis – Bardeen•Coupling strength,
- Maximize Electric Field Spatial Extent
MB + CPW Theory
𝑅'𝐿) + C𝐿+
𝐿)𝐿+𝑅' C
MB Surface Z CPW Geometry 4K CPW Resonator
MB + CPW Theory – Anomalous Skin Effect
𝑅'𝐿) + C𝐿+
𝐿)𝐿+𝑅'
MB Surface Z CPW Geometry 4K CPW Resonator
C
𝜆Anomalous Skin
Effect In SC𝑙-./ ≈ 𝜆
MB + CPW Theory – CPW Geometry
𝑅'𝐿) + C𝐿+
𝐿)𝐿+𝑅' C
MB Surfce Z CPW Geometry 4K CPW ResonatorMB Surface Z
MB + CPW Theory – Quality Factor = dependent on geometry
𝑅'𝐿) + C𝐿+
𝐿)𝐿+𝑅' C
MB Surfae Z CPW Geometry 4K CPW ResonatorMB Surface Z
Mattis–Bardeen Conductivity: Anomalous Skin Effect in SC
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110−20
10−15
10−10
10−5
100
T /Tc
σ1(T
) / σ
n
𝑑𝐸
𝜎 4(𝑇)/𝜎 9
Mattis–Bardeen Conductivity: Anomalous Skin Effect in SC
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2
0
0.2
0.4
0.6
0.8
1
1.2
T/Tc
σ2(T)/σ2(0)
𝜎 :(𝑇)/𝜎 :(0)
CPW Theory – Inductance Vs. Geometry
4𝐿+𝜇=>
𝑠(𝑢𝑚)
CPW Theory – Kinetic Inductance
𝑗
~ Thick. Correction
~ Geom. Correction
Numerical Closed Form
Clem, JR J. Appl. Phys. 113, 013910 (2013)
CPW Theory – Kinetic Inductance: Numerical Results
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250.5
1
1.5
2
2.5
3
3.5
4x 10−8
Gap Width, S (um)
Lk (H
enry
/Met
er)
w = 5, Numericalw = 5, ClemW = 10, NumericalW = 10, ClemW = 15, NumericalW = 15, ClemW = 20, NumericalW = 20, Clem
Quality Factor Vs. CPW Geometry
Mattis – Bardeen Limited CPW: Measurement
Sputtered NbSapphire Subst.
100 nm thickTc ~ 8.5 KRIE Etch
Cc ~ 5 fF
Mattis – Bardeen Limited CPW: Measurement
4.67 4.672 4.674 4.676 4.678 4.68x 109
−15
−10
−5
Frequency (Hz)
S 21 d
B
Data Fit
0 0.5 1 1.5−0.4
−0.2
0
0.2
0.4
0.6
Re[S21]
Im[S21]
DataFit
Mattis – Bardeen Limited CPW: Quality Factor Data
0 5 10 15 20 25 30 350
2000
4000
6000
8000
10000
12000
14000
16000
CPW Gap Width (um)
Inte
rnal
Q
W = 5 um, DataW = 5 um ThyW = 10 um, DataW = 10 um, ThyW = 20 um, DataW = 20 um, ThyW = 30 um, DataW = 30 um, ThyW = 50 um DataW = 50 um Thy
Mattis – Bardeen Limited CPW: Quality Factor Data
0 5 10 15 20 25 30 350
2000
4000
6000
8000
10000
12000
14000
16000
CPW Gap Width (um)
Inte
rnal
Q
W = 5 um, DataW = 5 um ThyW = 10 um, DataW = 10 um, ThyW = 20 um, DataW = 20 um, ThyW = 30 um, DataW = 30 um, ThyW = 50 um DataW = 50 um Thy
Can maximize Q with wider center traces and wider CPW gaps
CPW Electric Field
x (µm)
z(µ
m)
(a) (b)
−40 −20 0 20 400
20
40
60
80
|E0|(V
/m)
0
0.02
0.04
0.06
0.08
0.1
0 10 20 30 40 500
0.02
0.04
0.06
0.08
0.1
z (µm)
0
1
2
3
4
5
g/2π(M
Hz)
x=0x= (s+w)/2
-100 -50 0 50 100
CPW Electric Field
x (µm)
z(µ
m)
(a) (b)
−40 −20 0 20 400
20
40
60
80
|E0|(V
/m)
0
0.02
0.04
0.06
0.08
0.1
0 10 20 30 40 500
0.02
0.04
0.06
0.08
0.1
z (µm)
0
1
2
3
4
5
g/2π(M
Hz)
x=0x= (s+w)/2
For achievable atom-CPW distances,coupling is low
Must extend electric field off chip to achieve strong coupling
-100 -50 0 50 100
CPW Electric Field Extension – Chip Design
17.5 mm
Niobium Sapphire
𝛌/𝟒
CPW Electric Field Extension – Chip Design
17.5 mm
CPW Electric Field Extension – Layer Stack-Up
17.5 mm
Nb
Ti/Pd
Cu
Sub - 500 um
- 200 nm
- 3/30 nm
- 50 um
CPW Electric Field Extension - Realization
125 um75 um
150 um
100 um
200 um
Re[S21]0.4 0.6 0.8 1 1.2
Im[S21]
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
CPW Electric Field Extension - Realization
𝑄F.FG = 3×10J ≈ 𝑄-KNo added loss from Cu structures
DataFit
Rabi Oscillations
90
70
50
30
10
𝑄F
𝑔/2𝜋 (MHz)
𝑛PQRF
Proposed Coupling Measurement - Log Magnitude
𝐸 = 6×10T:V/m𝑔 = 3.2𝑀𝐻𝑧 ×2𝜋
Proposed Coupling Measurement - Phasor
Proposed Coupling Measurement – IQ Plane
𝑫 = 𝜶[ − 𝜶T
Measurement – SNR
Measurement – SNR
Increasing cavity photon number will increaseSeparation and SNR
Experimental Apparatus – Custom 4K Cryostat, Design
• UHV Compatible- Conflat seals - Low outgassing Materials
• Long Cryogen Hold Times- Low Thermal Conductivity to 300 K- Minimization of stray light from optical access
ports
• Low Vibration- Rigid frame for mounting to an optical table
Experimental Apparatus – Custom 4K Cryostat, Design
LN Vessel(12 L)
LHe Vessel(27 L)
Outer VacuumJacket
77K Shield4K Cold Finger
𝑃R < 2×10T_Torr
MOT
CPW
Experimental Apparatus – Custom 4K Cryostat, Design
LN Vessel(12 L)
LHe Vessel(27 L)
Outer VacuumJacket
77K Shield4K Cold Finger
MOT
CPW
Experimental Apparatus – Custom 4K Cryostat, Design
LN Vessel(12 L)
LHe Vessel(27 L)
Outer VacuumJacket
77K Shield4K Cold Finger
MOT
CPW
Experimental Apparatus – Custom 4K Cryostat, Design
LN Vessel(12 L)
LHe Vessel(27 L)
Outer VacuumJacket
77K Shield4K Cold Finger
MOT
CPW
Experimental Apparatus – Optical Access
Experimental Apparatus – Optical Access
Cryostat Design – Cold Lens
𝑇ab' = 100 K Reduced heat load on 4K stage by ~ 80 mW
Custom 4K Cryostat, Heat Load
Liquid Nitrogen
- Heat Load ~ 23 Watts
- Dominated by 300K radiation over large surface area
- 40 hour hold time for 11 L tank
Liquid Helium
- Heat Load ~ 270 mW
- 170 mW load originating from 300K optical access to cold finger
- 60 hour hold time for 27 L tank
Experimental Apparatus – Custom 4K Cryostat, Sample Mount
Cold Finger
SampleDC E Field Compensation
Pins
Custom 4K Cryostat, Vibration Characterization
852 nm
𝑃caQ'
𝑃Pad
Custom 4K Cryostat, Vibration Characterization
�̅� = 1.2𝜇𝑚
�̅� = ∫ 𝑃𝑆𝐷𝑑𝑓
@ 3 KHz BW
Future Plans – Cz gates in DR
Rotation
𝜋Pulse
𝜋Pulse
Cavity photon number dependent phase
Conclusions
• Resonator quality factors > 1e4
• CPW E Field – Cu EP’d structures
• Strong coupling achievable at 4K
• Custom UHV cryostat has P < 2e-9 T
• Sample vibration ~ 1 um
• Final preparations in progress for experimental realization
Mattis–Bardeen Conductivity: Anomalous Skin Effect in SC
𝜆𝐻 = 𝐻=𝑒Tl/mAnomalousskin effect
In SC𝑙-./ ≈ 𝜆
Two-Fluid Model
𝜎4- Resistive Channel
𝜎:- Reactive Channel
Mattis–Bardeen Conductivity: Anomalous Skin Effect in SC
𝑅' 𝐿)
MB + CPW Theory
𝑅'𝐿) + C𝐿+
𝐿)𝐿+𝑅'
Mattis Bardeen CPW Geometry 4K CPW Resonator
𝑠 𝑠 𝑠
C
CPW Theory - Basics
𝜖o
CPW Theory – Capacitance Vs. Geometry
𝐶`4𝜖o𝜖=
S (um)
CPW Theory – Kinetic Inductance: Numerical Results
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250.5
1
1.5
2
2.5
3
3.5
4x 10−8
CPW Gap Width, S (um)
Lk (H
enry
/met
er)
w = 5 umw = 10 umw = 15 umw = 20 um
Strong Coupling
Strong Coupling
Experimental Apparatus – Custom 4K Cryostat, Design
Proposed Measurement - Phase
Coupling Regimes
Γ = max 𝜅, 𝛾 = 𝜅 = 250KHz
𝑔Γ ~20
CPW-Rydberg
Δ = 𝜔Q − 𝜔|
Schuster, Ph.D Thesis, (2007)
Measurement – SNR
Can increase photon number in cavity to increase seperation
Mattis – Bardeen Limited CPW: Quality Factor Data
0 5 10 15 20 25 30 350
2000
4000
6000
8000
10000
12000
14000
16000
CPW Gap Width (um)
Inte
rnal
Q
W = 5 um, DataW = 10 um, DataW = 20 um, DataW = 30 um, DataW = 50 um Data