Practical Microwave Amplifiers with Superconductors
Lafe Spietz
Leonardo Ranzani
Minhyea Lee
Kent Irwin
Norm Bergren
José Aumentado
Outline
• Motivation
• The NIST DC-SQUID microwave amp
• Parametric amplifiers
Motivation
• Some qubit readouts are limited by amplifier
• Improve the amplifer, improve the readout• Present state of the are amplifiers are
transistor amplifiers which must be separated from the experiment
• SQUIDs provide lower noise and can be closer to experiment than transistor amplfiers
What is Noise Temperature*?
*for T>>hf/k
Temperature of matched load which doubles noise at output
Better Amplifiers Provide Orders of Magnitude Speedup:
• Dicke Radiometer Formula:
• Thus
• 40x lower TN gives 1600x speedup in measurement times!
Comes from Poisson statistics!
Microwave Quantum Circuits
semiconductoramplifier
superconductoramplifier
Quantum Noise of a Resistor
n = ½Coth(hf/2kT)
7 GHz 170 mK
Quantum Limits to Amplifiers If(t) = A Cos(t + )
f(t) = X Cos(t) + Y Sin(t)
Phase quadratures are conjugate variables, subject to
an uncertainty principle
X·Y ≥ ½
Noise above quantum limit
Quantum limitCoherent state
Amplified coherent state
Quantum Limits to Amplifiers II
Present Commercial State of the Art Semiconducting Amplifier:
HEMT Amps from Weinreb Group• 0.1-14 GHz
• 35 dB gain
• TN = 1.5-3 K (5- 40 photons added)
• $5000 each
• Typical system noise
~10-20 K
DC Squids: Flux to Voltage Amplifier
∂V/∂gives gainFrom power coupled to flux
Statement of the Problem:DC Squids in the Microwave
(Nomenclature Disaster)
Stray capacitances shunt incoming microwave signal making it difficult to couple power in:
Our Approach• Shrink the physical size of the SQUID until
it can be treated as a lumped element component
• Model and experimentally characterize input and output impedance
• Design input and output impedance transformers
• Design box/board infrastructure to make a usable “product” which can be easily disseminated
NIST SQUID design• Kent Iriwin’s octopole gradiometer squid design
Assembly Line Constructionand Interchangeable Parts
Assembly Line Constructionand Interchangeable Parts
Impedance Measurementand Matching
• Measure S parameters at harmonics of a quarter wave resonator to learn about input impedance
V(x)
V(x)
Chip Layout of Quarter Wave
8 mm
Multiple Harmonics
f0 =1.68 GHz3f0 =5.04 GHz
Impedance Measurement
>95% power coupling to 0.18 source
Impedance Model• With physically small squids, we treat them as lumped
elements with minimal stray reactances
*
Measured Real[Zin]
Voltage [V]
Voltage [V]
Transfer Function
Gain and Noise Measurement
(or shot noise source)
Typical Gain Curves
Broadband Gain
1 GHz
Noise Temperature
Noise Temperature
Gain Map (5.4 GHz)
Gain Scan Zoom
Extreme Zoom Steep Ridge
Drift Test:Gain Dependence on Flux
Overnight Gain Drift
Dynamic Range
Parametric AmplificationVary some parameter of an oscillator
to pump energy into or out of the system
Josephson Parametric Amplifiers
• Use the nonlinearity of JJ circuits to modify some resonant frequency in a microwave circuit
• No quantum limit• Usually reflection amplifiers• Can create “squeezed states” of microwave
radiation
signal pump
Josephson Parametric Amplifiers
• Lehnert et al. at JILA (beat quantum limit in a practical experiment!)
• Nakamura et al. at NEC
• Aumentado et al. at NIST
• Devoret et al. at Yale
• Siddiqi et al. at Berkeley
• Etc.
Rapidly growing field!
Driven by needs of QC community
Amplification: The Dream
Amplifier Technologies
HEMT SQUID Parametric
System noise
~10 K ~1 K ~ 0.1 K
Power dissipation
~10 mW ~ 1 W < 1 pW
Bandwidth >14 GHz 400 MHz 100 kHz
Availability Commercial Beginning distribution
Largely in-house
SNR Improvement: Before
20 hours No SQUID
SNR Improvement: After
5 hoursSQUID amp
END
Imaginary Component of Input Impedance
DC IV Characteristics
Output Matching
170 pH 700 pH
4 pF 0.9 pF
Summary• Measured input impedance at a range of
microwave frequencies
• Demonstrated minimal stray reactance
• Demonstrated useful gains and bandwidths in 4-8 GHz frequency range
• Constructed system for easy production and deployment of SQUID amplifiers
• Demonstrated extreme stability of SQUIDs over hours of measurement time
Future Work
• Improve ultra-broadband design
• Build amplifiers at several more frequencies
• Understand and improve noise
• Measure shot noise with amplifiers
• Distribute amplifiers to collaborators
Output Matching
Output Matching
Broadband Design
Target: High frequency, maximum bandwidth
Multipole lumped-element transformers at input and output
Broadband Test: First Attempt
• Microwave design needs work!!
• Gain bandwidth product is encouraging
Parametric AmplificationVary some parameter of an oscillator
to pump energy into or out of the system
Bias Modulates Frequency
DC SQUID/Parametric amp hybrid
Parametric mode acts as preamp:
Phase Dependent Added Gain
Differential Resistance
High Frequency: First Attempt
• Shorter resonator
• Matched input
• Lower Q
Transfer Function and Gain
Gain Map: Resonances
I-V Curves
SNR Improvement
10x Faster Measurement at 7 GHz
7 GHz Gain
100 MHz
Outline
• Motivation
• Our Approach
• Amplifier Characterization
• Milestones and future work
Other Superconducting Efforts:A renaissance is in progress!
• Yurke JPA work (1980’s)
• Clarke group DC SQUID amps
• Japanese DC SQUID amps and parametric amps(NEC)
• Lehnert Group(NIST/JILA/CU)
• Yale Quantronics Group J-Bridge amp
• All-invited session at March Meeting and ASC on amplifiers!
Motivation
• Radio Astronomy
• Quantum computing
• Noise studies
• Microwave quantum optics
• RF-SET readout
• Fundamental measurement science
Superconducting Microwave Amplifiers at NIST
Lafe Spietz
José Aumentado
Resonator Length
Typical High-f Input Resonator