Transcript Outline - Lafe Spietz

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*?
Temperature of matched load which
doubles noise at output
*for T>>hf/k
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
semiconductor
amplifier
superconductor
amplifier
Quantum Noise of a Resistor
7 GHz  170 mK
n = ½Coth(hf/2kT)
Quantum Limits to Amplifiers I
f(t) = A Cos(wt + f)
f(t) = X Cos(wt) + Y Sin(wt)
Phase quadratures are
conjugate variables, subject to
an uncertainty principle
DX·DY ≥ ½
Quantum Limits to Amplifiers II
Amplified coherent state
Quantum limit
Coherent state
Noise above quantum limit
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/∂F gives gain
From 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 Construction
and Interchangeable Parts
Assembly Line Construction
and Interchangeable Parts
Impedance Measurement
and 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
3f0 =5.04 GHz
f0 =1.68 GHz
Impedance Measurement
>95% power coupling to 0.18 W
source
Impedance Model
• With physically small squids, we treat them as lumped
elements with minimal stray reactances
*
Measured Real[Zin]
Voltage [mV]
Voltage [mV]
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 Amplification
Vary some parameter of an oscillator
to pump energy into or out of the system
Josephson Parametric Amplifiers
signal
pump
• 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
Josephson Parametric Amplifiers
Driven by needs of QC community
Rapidly growing field!
• 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.
Amplification: The Dream
Amplifier Technologies
HEMT
SQUID
Parametric
System
noise
Power
dissipation
Bandwidth
~10 K
~1 K
~ 0.1 K
~10 mW
~ 1 mW
< 1 pW
>14 GHz
400 MHz
100 kHz
Availability
Commercial Beginning
distribution
Largely
in-house
SNR Improvement: Before
20 hours No SQUID
SNR Improvement: After
5 hours
SQUID amp
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
•
•
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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 Amplification
Vary 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
•
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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
•
•
•
•
•
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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