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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


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


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


LN Vessel(12 L)

LHe Vessel(27 L)

Outer VacuumJacket

77K Shield4K Cold Finger

𝑃R < 2×10T_Torr

MOT

CPW


LN Vessel(12 L)

LHe Vessel(27 L)

Outer VacuumJacket


MOT

CPW


LN Vessel(12 L)

LHe Vessel(27 L)

Outer VacuumJacket


MOT

CPW


LN Vessel(12 L)

LHe Vessel(27 L)

Outer VacuumJacket


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


𝜆𝐻 = 𝐻=𝑒Tl/mAnomalousskin effect

In SC𝑙-./ ≈ 𝜆

Two-Fluid Model

𝜎4- Resistive Channel

𝜎:- Reactive Channel


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


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


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