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