Josephson Parametric Amplifiers: Theory and Application Andrew Eddins � D. Wright R. Lolowang A. Dove D.M. Toyli I. Siddiqi Quantum Nanoelectronics Laboratory, Department of Physics, University of California, Berkeley Workshop on Microwave Cavity Design for Axion Detection Livermore Valley Open Campus August 25-27, 2015
Outline • 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
Josephson Parametric Amplifiers Josephson parametric amplifiers (JPA) are an enabling technology for superconducting qubit measurement Quantum Jumps Weak measurements Squeezed microwaves R. Vijay et al. , PRL (2011) M. Hatridge, et al. , Science (2013); K.W. Murch et al. , Nature (2013); S. Weber et al. , Nature (2014); High-Fidelity Readout Quantum Feedback 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) R. Vijay et al. , Nature (2012) E. Jeffrey et al. , PRL (2014) Seminal work on parametric amplifiers: B. Yurke Many related approaches: Yale, JILA, Saclay, UCSB, and others…
Amplification and SNR Q ~( h ω /2) 1/2 I qubit 1 (or axions) to room-temp in cavity electronics HEMT amplifier (commercial)
Amplification and SNR Q dissipative! ~( h ω /2) 1/2 I qubit 1 (or axions) to room-temp in cavity electronics ~10 noise photons
Amplification and SNR Q Q dissipative! ~(10 h ω *G tot ) 1/2 ~( h ω /2) 1/2 I I qubit G tot 1/2 1 (or axions) to room-temp in cavity electronics ~10 noise photons SNR down ~13 dB!
Amplification and SNR Q Q dissipative! ~(10 h ω *G tot ) 1/2 ~( h ω /2) 1/2 I I qubit G tot 1/2 1 (or axions) to room-temp in cavity electronics ~10 noise photons SNR down ~13 dB! qubit (or axions) in cavity JPA
Amplification and SNR Q Q dissipative! ~(10 h ω *G tot ) 1/2 ~( h ω /2) 1/2 I I qubit G tot 1/2 1 (or axions) to room-temp in cavity electronics ~10 noise photons SNR down ~13 dB! super- Q ~(100 h ω ) 1/2 conducting! I qubit ~100 1/2 (or axions) in cavity vacuum
Amplification and SNR Q Q dissipative! ~(10 h ω *G tot ) 1/2 ~( h ω /2) 1/2 I I qubit G tot 1/2 1 (or axions) to room-temp in cavity electronics ~10 noise photons SNR down ~13 dB! super- Q ~(100 h ω ) 1/2 conducting! I qubit ~100 1/2 (or axions) in cavity vacuum ~10 noise photons
Amplification and SNR Q Q dissipative! ~(10 h ω *G tot ) 1/2 ~( h ω /2) 1/2 I I qubit G tot 1/2 1 (or axions) to room-temp in cavity electronics ~10 noise photons SNR down ~13 dB! super- Q Q ~(1.1 h ω ~(100 h ω ) 1/2 conducting! * G’ tot ) 1/2 I I qubit G’ tot1/2 ~100 1/2 (or axions) in cavity vacuum ~10 noise SNR down only ~3 dB photons (phase preserving)
Amplification and SNR Q Q dissipative! ~(10 h ω *G tot ) 1/2 ~( h ω /2) 1/2 I I qubit G tot 1/2 1 (or axions) to room-temp in cavity electronics ~10 noise photons SNR down ~13 dB! super- Q Q ~(1.1 h ω ~(100 h ω ) 1/2 conducting! * G’ tot ) 1/2 I I qubit G’ tot1/2 ~100 1/2 (or axions) in cavity vacuum ~10 noise SNR down only ~3 dB photons (phase preserving) • JPA improves SNR ~10dB Averaging time reduced ~100x !
Parametric Amplification • Resonance frequency ω 0 modulated at ~2 ω 0 � • Work done on in-phase field quadrature (phase-sensitive amplification) • Detune pump ➡ work done on both quadratures (phase-preserving amplification)
Parametric Amplification • Resonance frequency ω 0 modulated at ~2 ω 0 � • Work done on in-phase field quadrature (phase-sensitive amplification) • Detune pump ➡ work done on both quadratures (phase-preserving amplification)
Parametric Amplification • Resonance frequency ω 0 modulated at ~2 ω 0 � • Work done on in-phase field quadrature (phase-sensitive amplification) • Detune pump ➡ work done on both quadratures (phase-preserving amplification) • Josephson junction = nonlinear inductor L J ( I ) = ( φ 0 / Ι 0 ) (1 + I 2 / I 02 + …) ω r ≈ ω 0 + Δ ω ( I pump )cos(2 ω pump t ) “Current-pump” at ~ ω 0
Parametric Amplification • Resonance frequency ω 0 modulated at ~2 ω 0 � • Work done on in-phase field quadrature (phase-sensitive amplification) • Detune pump ➡ work done on both quadratures (phase-preserving amplification) • Josephson junction = nonlinear inductor L J ( I ) = ( φ 0 / Ι 0 ) (1 + I 2 / I 02 + …) ω r ≈ ω 0 + Δ ω ( I pump )cos(2 ω pump t ) “Current-pump” at ~ ω 0 Q phase- ω pump = ω signal + Δ preserving I Q phase- ω pump = ω signal sensitive I
Standard JPA Design Ζ 0 I 0 C Resonant Bandwidth Frequency ( Q ) 40 µm
Standard JPA Design Ζ 0 I 0 C I 0 C Resonant Bandwidth Frequency ( Q ) 40 µm
Standard JPA Design Ζ 0 I 0 C I 0 C Q = Z 0 ω C L jn = φ 0 / I 0 Resonant Bandwidth Frequency ( Q ) 40 µm
Standard JPA Design Ζ 0 I 0 C I 0 C Q = Z 0 ω C L jn = φ 0 / I 0 Resonant Bandwidth Frequency ( Q ) dielectric • Aluminum device BW ~ 20 MHz @ G ~ 20dB tunes over 4-8 GHz ����� • C ~ 3.2 pF Parallel plates with 16nm AlO x dielectric ������������ • L J ~ 140 pH 40 µm
Standard JPA Design Ζ 0 I 0 C I 0 C Q = Z 0 ω C L jn = φ 0 / I 0 Resonant Bandwidth Frequency ( Q ) dielectric • Aluminum device BW ~ 20 MHz @ G ~ 20dB tunes over 4-8 GHz ����� • C ~ 3.2 pF Parallel plates with 16nm AlO x dielectric ������������ • L J ~ 140 pH 40 µm
Standard JPA Design Ζ 0 I 0 C I 0 C Q = Z 0 ω C L jn = φ 0 / I 0 Resonant Bandwidth Frequency ( Q ) dielectric • Aluminum device BW ~ 20 MHz @ G ~ 20dB tunes over 4-8 GHz ����� • C ~ 3.2 pF Parallel plates with 16nm AlO x dielectric ������������ • L J ~ 140 pH 40 µm
Device Characterization Typical performance (C-band) • G x BW ~ 200 MHz dielectric • P 1dB ~ -130 dBm hybrid Ζ 0 Δ ����� � Σ ������������ 40 µm Frequency (GHz) 7.5 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4 4.0 -10 -5 0 5 10 Coil current (mA) (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” • 1”x1”x0.8” (1-port box) • Cu thermalization strap • Superconducting coil (flux-bias) Designers: D. Wright R. Lolowang
Dynamic Range and Nonlinearity I 0 C I 0 C Resonant Bandwidth Frequency ( Q )
Dynamic Range and Nonlinearity I 0 C I 0 C P max ~ I 02 Dynamic Resonant Bandwidth Range Frequency ( Q )
Dynamic Range and Nonlinearity I 0 C I 0 C P max ~ I 02 Dynamic Resonant Bandwidth Range Frequency ( Q ) at Room Temperature Drive Power (dBm)
Dynamic Range and Nonlinearity I 0 C I 0 C P max ~ I 02 Dynamic Resonant Bandwidth Range Frequency ( Q ) (I/I 0 ) 2 at at Room Temperature Drive Power (dBm) critical value
Dynamic Range and Nonlinearity N I 0 I 0 C P max ~ I 02 N C N I 0 Dynamic Resonant Bandwidth Range Frequency ( Q ) (I/I 0 ) 2 at • Josephson inductance unchanged at Room Temperature Drive Power (dBm) critical • Critical current scaled by N value
Dynamic Range and Nonlinearity N I 0 I 0 I 0 C C N N C N I 0 Dynamic Resonant Bandwidth Range Frequency ( Q ) (I/I 0 ) 2 at • Josephson inductance unchanged at Room Temperature Drive Power (dBm) critical • Critical current scaled by N value
Dynamic Range and Nonlinearity N I 0 I 0 I 0 C C N N C N I 0 Dynamic Resonant Bandwidth Range Frequency ( Q ) N = 1 N = 2 N = 5 (I/I 0 ) 2 at at Room Temperature Drive Power (dBm) critical value
Dynamic Range and Nonlinearity N I 0 I 0 I 0 C C N N C N I 0 Dynamic Resonant Bandwidth Range Frequency ( Q ) N = 1 N = 2 N = 5 (I/I 0 ) 2 at at Room Temperature Drive Power (dBm) critical value
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 Compression at 6 GHz: Normalized to N =1 device performance
L-Band JPA Parallel plate AlO x capacitor � � • 5-SQUID design � • SSBW ~ 4-6 MHz • 10-13dB SNR improvement Aluminum SQUIDs observed I c,SQUID ~ 5 µA • Delivered to ADMX at Washington U.
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