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