Josephson Parametric Amplifiers: Theory and Application Andrew - - PowerPoint PPT Presentation

Josephson Parametric Amplifiers:
 Theory and Application

Andrew Eddins

• D. Wright
• R. Lolowang
• A. Dove

D.M. Toyli

• I. Siddiqi

Workshop on Microwave Cavity Design for Axion Detection Livermore Valley Open Campus August 25-27, 2015 Quantum Nanoelectronics Laboratory, Department of Physics, University of California, Berkeley

• Introduction
• JPAs in cQED
• Amplification and SNR
• Parametric Amplification

• Standard 4-8 GHz JPAs
• Basic design
• Characterization and performance
• Lower frequency JPAs
• Cryo-housing
• Dynamic range
• ~1-2 GHz device (L-band)
• ~500-700 MHz device

Outline

Quantum Jumps

Josephson parametric amplifiers (JPA) are an enabling technology for superconducting qubit measurement

Seminal work on parametric amplifiers: B. Yurke Many related approaches: Yale, JILA, Saclay, UCSB, and others…

Squeezed microwaves

• F. Mallet et al., PRL (2011);
• C. Eichler et al., PRL (2011);

E.P. Menzel et al., PRL (2012); K.W. Murch et al., Nature (2013)

High-Fidelity Readout

• R. Vijay et al., PRL (2011)
• E. Jeffrey et al., PRL (2014)

Quantum Feedback

• R. Vijay et al., Nature

(2012)

Josephson Parametric Amplifiers

Weak measurements

• M. Hatridge, et al., Science (2013);

K.W. Murch et al., Nature (2013);

• S. Weber et al., Nature (2014);

qubit (or axions) in cavity to room-temp electronics I Q ~(hω/2)1/2

1

HEMT amplifier (commercial)

Amplification and SNR

~10 noise photons qubit (or axions) in cavity dissipative! to room-temp electronics I Q ~(hω/2)1/2

1

Amplification and SNR

~10 noise photons qubit (or axions) in cavity dissipative! to room-temp electronics I Q ~(hω/2)1/2

1 Gtot1/2

Q I ~(10hω*Gtot)1/2

Amplification and SNR

SNR down ~13 dB!

~10 noise photons qubit (or axions) in cavity dissipative! to room-temp electronics I Q ~(hω/2)1/2

1 Gtot1/2

Q I ~(10hω*Gtot)1/2 qubit (or axions) in cavity JPA

Amplification and SNR

SNR down ~13 dB!

~10 noise photons qubit (or axions) in cavity dissipative! to room-temp electronics I Q ~(hω/2)1/2

1

super- conducting! vacuum I Q ~(100hω)1/2

~1001/2 Gtot1/2

Q I ~(10hω*Gtot)1/2 qubit (or axions) in cavity

Amplification and SNR

SNR down ~13 dB!

~10 noise photons qubit (or axions) in cavity dissipative! to room-temp electronics I Q ~(hω/2)1/2

1

super- conducting! vacuum I Q ~(100hω)1/2

~1001/2

~10 noise photons

Gtot1/2

Q I ~(10hω*Gtot)1/2 qubit (or axions) in cavity

Amplification and SNR

SNR down ~13 dB!

~10 noise photons qubit (or axions) in cavity dissipative! to room-temp electronics I Q ~(hω/2)1/2

1

super- conducting! vacuum I Q ~(100hω)1/2

~1001/2

~10 noise photons

G’tot1/2

Q I ~(1.1hω * G’tot)1/2

Gtot1/2

Q I ~(10hω*Gtot)1/2 qubit (or axions) in cavity

Amplification and SNR

SNR down ~13 dB! SNR down only ~3 dB


(phase preserving)

~10 noise photons qubit (or axions) in cavity dissipative! to room-temp electronics I Q ~(hω/2)1/2

1

super- conducting! vacuum I Q ~(100hω)1/2

~1001/2

~10 noise photons

G’tot1/2

Q I ~(1.1hω * G’tot)1/2

Gtot1/2

Q I ~(10hω*Gtot)1/2

• JPA improves SNR ~10dB

Averaging time reduced ~100x ! qubit (or axions) in cavity

Amplification and SNR

SNR down ~13 dB! SNR down only ~3 dB


(phase preserving)

Parametric Amplification

• Resonance frequency ω0 modulated at ~2ω0
• Work done on in-phase field quadrature


(phase-sensitive amplification)


• Detune pump ➡ work done on both quadratures 


(phase-preserving amplification)

Parametric Amplification

• Resonance frequency ω0 modulated at ~2ω0
• Work done on in-phase field quadrature


(phase-sensitive amplification)


• Detune pump ➡ work done on both quadratures 


(phase-preserving amplification)

Parametric Amplification

• Resonance frequency ω0 modulated at ~2ω0
• Work done on in-phase field quadrature


(phase-sensitive amplification)


• Detune pump ➡ work done on both quadratures 


(phase-preserving amplification)

• Josephson junction = nonlinear inductor

LJ (I) = (φ0 / Ι0) (1 + I2/I02 + …) ωr ≈ ω0+ Δω(Ipump)cos(2ωpumpt) “Current-pump” at ~ω0

Q I

Parametric Amplification

• Resonance frequency ω0 modulated at ~2ω0
• Work done on in-phase field quadrature


(phase-sensitive amplification)


• Detune pump ➡ work done on both quadratures 


(phase-preserving amplification)

• Josephson junction = nonlinear inductor

LJ (I) = (φ0 / Ι0) (1 + I2/I02 + …) ωr ≈ ω0+ Δω(Ipump)cos(2ωpumpt) “Current-pump” at ~ω0 Q I ωpump = ωsignal + Δ ωpump = ωsignal phase- preserving phase- sensitive

Standard JPA Design

Resonant Frequency Bandwidth (Q)

I0 C

Ζ0

40 µm

Standard JPA Design

Resonant Frequency Bandwidth (Q)

I0 C

C I0

Ζ0

40 µm

Standard JPA Design

Resonant Frequency Bandwidth (Q)

I0 C

C I0

Ljn =φ0/I0 Q = Z0ωC

Ζ0

40 µm

dielectric

• Standard JPA Design

Resonant Frequency Bandwidth (Q)

I0 C

C I0

Ljn =φ0/I0

• Aluminum device


BW ~ 20 MHz @ G ~ 20dB
 tunes over 4-8 GHz


• C ~ 3.2 pF


Parallel plates with 16nm AlOx dielectric


• LJ ~ 140 pH

Q = Z0ωC

Ζ0

40 µm

dielectric

• Standard JPA Design

Resonant Frequency Bandwidth (Q)

I0 C

C I0

Ljn =φ0/I0

• Aluminum device


BW ~ 20 MHz @ G ~ 20dB
 tunes over 4-8 GHz


• C ~ 3.2 pF


Parallel plates with 16nm AlOx dielectric


• LJ ~ 140 pH

Q = Z0ωC

Ζ0

40 µm

dielectric

• Standard JPA Design

Resonant Frequency Bandwidth (Q)

I0 C

C I0

Ljn =φ0/I0

• Aluminum device


BW ~ 20 MHz @ G ~ 20dB
 tunes over 4-8 GHz


• C ~ 3.2 pF


Parallel plates with 16nm AlOx dielectric


• LJ ~ 140 pH

Q = Z0ωC

Ζ0

40 µm

dielectric

• 40 µm

Device Characterization

Typical performance (C-band)

• G x BW ~ 200 MHz
• P1dB ~ -130 dBm

hybrid Δ

• Σ

Ζ0

7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0

Coil current (mA) Frequency (GHz) 4 7.5

• 5
• 10

5 10

(offset due to no cryoperm shield)

Designing for Lower Frequencies

• I. Device must be single-ended (vs. differential)

• 180° hybrid too big at low frequencies!
• II. Device needs sufficient dynamic range
• Low frequency/bandwidth JPAs saturate at lower powers
• Saturation from incident quantum/thermal noise can degrade performance
• III. Need large capacitance in compact design
• Excess geometric inductance can cause device instabilities

Single-Ended JPA Housing

• Aluminum magnetic shield
• Near light-tight enclosure
• 1”x1”x0.8” (1-port box)
• Cu thermalization strap
• Superconducting coil (flux-bias)

1”

Designers:


• D. Wright
• R. Lolowang

Dynamic Range and Nonlinearity

Resonant Frequency Bandwidth (Q) C I0

I0 C

Dynamic Range and Nonlinearity

Resonant Frequency Bandwidth (Q) C I0

I0 C

Dynamic Range Pmax ~ I02

Drive Power (dBm) at Room Temperature

Dynamic Range and Nonlinearity

Resonant Frequency Bandwidth (Q) C I0

I0 C

Dynamic Range Pmax ~ I02

Drive Power (dBm) at Room Temperature

Dynamic Range and Nonlinearity

Resonant Frequency Bandwidth (Q) C I0

I0 C

Dynamic Range Pmax ~ I02

(I/I0)2 at
 critical value

Drive Power (dBm) at Room Temperature

Dynamic Range and Nonlinearity

Resonant Frequency Bandwidth (Q) C I0 Dynamic Range Pmax ~ I02

(I/I0)2 at
 critical value I0 C I0 N N N

• Josephson inductance unchanged
• Critical current scaled by N

Drive Power (dBm) at Room Temperature

Dynamic Range and Nonlinearity

Resonant Frequency Bandwidth (Q) C I0 Dynamic Range

(I/I0)2 at
 critical value I0 C I0 N N N

C I0 N

• Josephson inductance unchanged
• Critical current scaled by N

Drive Power (dBm) at Room Temperature

N = 2 N = 5

Dynamic Range and Nonlinearity

Resonant Frequency Bandwidth (Q) C I0 Dynamic Range

N = 1

(I/I0)2 at
 critical value I0 C I0 N N N

C I0 N

Drive Power (dBm) at Room Temperature

N = 2 N = 5

Dynamic Range and Nonlinearity

Resonant Frequency Bandwidth (Q) C I0 Dynamic Range

N = 1

(I/I0)2 at
 critical value I0 C I0 N N N

C I0 N

Compression at 6 GHz:

Normalized to N=1 device performance

Dynamic Range and Nonlinearity

Compression at 6 GHz:

Normalized to N=1 device performance

Dynamic Range and Nonlinearity

Compression at 6 GHz:

Normalized to N=1 device performance

Dynamic Range and Nonlinearity

L-Band JPA

• Parallel plate AlOx capacitor

Aluminum SQUIDs
 Ic,SQUID ~ 5 µA

• 5-SQUID design
• SSBW ~ 4-6 MHz

• 10-13dB SNR improvement

• bserved

• Delivered to ADMX at


Washington U.

~500-700 MHz JPA

500 550 600 650 700 5 10 15 20

• Freq. (MHz)

Gain (dB)

nominal circulator band

• 6-SQUID design
• SSBW ~ 1.5-2.5 MHz

• P1dB ~ -140 dBm


— improve with more SQUIDs?


• >13dB SNR improvement observed
• Tunability limited by circulator

Summary and Outlook

• JPAs dramatically improve measurement efficiency of very


small microwave signals


• L-band JPA has been developed, tested, and


delivered to ADMX

• 500-700 MHz JPA has been developed and tested.
• Single-ended C-band (4-6 GHz) JPA in development

Thank you!

EXTRA SLIDES

Output field imaging setup

Not shown: DC line with Cu-powder filters for JPA coil.

Device Design III: Bandwidth and Stability

• Any real circuit has some linear inductance, by design or geometric necessity:
• Total ΔV spread over SQUID, Lg.


Nonlinearity reduced ➡ greater DR

• Large Lg ➡ higher-order terms significant,


causes instability that limits gain

I0 C

Ζ0=50Ω

Lg

Q

10 100 20

• Josephson Participation

(LJ / Ltot) 100% 50% 10% 1%

➡ Rule of thumb: Q LJ/Ltot > ~5

• ➡ Minimum possible Q: ~5.


Limits maximum bandwidth!
 ➡ Geometric inductance must
 be minimized in layout to 
 achieve high BW

f (GHz) Drive (dBm)

Linear Inductance

chaos paramp regime

LJPA Operation

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd)

LJPA Operation

Drive Power Drive Frequency

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd)

LJPA Operation

Drive Power Drive Frequency Drive Power Reflected Phase

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd) 180

• 180

LJPA Operation

Drive Power Drive Frequency Drive Power Reflected Phase

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd) 180

• 180

LJPA Operation

Drive Power Drive Frequency Drive Power Reflected Phase

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd) 180

• 180

LJPA Operation

Paramp Drive Power Drive Frequency Drive Power Reflected Phase

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd) 180

• 180

LJPA Operation

Paramp Drive Power Drive Frequency Drive Power Reflected Phase

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd) 180

• 180

LJPA Operation

Bistable Paramp Drive Power Drive Frequency Drive Power Reflected Phase

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd) 180

• 180

LJPA Operation

Oscillator nonlinearity fixes pump amplitude

Bistable Paramp Drive Power Drive Frequency Drive Power Reflected Phase

ωr = ω0+ Δω(IRF)cos(2ωdt)

(ωd) 180

• 180

LJPA Dynamic Range

Gain reduced by 1 dB when signal ~ -130 dBm (1 dB compression point) Fixed pump amplitude Limits available power for amplification

(κ/2π = 4.9 MHz)

Measurement chain noise temperature (K) Signal power at paramp (dBm) Measurement cavity photon occupation

Measured Scaling of Critical Power with N

N = 1 N = 2 N = 5

Drive Power (dBm) at Room Temperature

Measured Scaling of Critical Power with N

N = 1 N = 2 N = 5

Drive Power (dBm) at Room Temperature

Measured Scaling of Critical Power with N

N = 1 N = 2 N = 5

Drive Power (dBm) at Room Temperature

• 2 SQUIDs -> 3-5 dB increase
• 5 SQUIDs -> 6-10 dB increase
• Significant increase!


Though sub-N2 scaling.

r r

Measured Scaling of Critical Power with N

N = 1 N = 2 N = 5

ç

Drive Power (dBm) at Room Temperature

Pcrit, N SQUIDs Pcrit, 1 SQUID (dB)