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Physics of Microwave Kinetic Inductance Detectors

(MKIDs)

- PhD Candidate Jiansong Gao
- Advisor Jonas Zmuidzinas
- Dec 9, 2005

Outline

- Introduction to MKIDs
- Device Physics
- Overview
- Kinetic Inductance
- Excess Phase Noise
- Future Research Plan

- Theory Experiment
- What has been solved or understood whats not

MKIDs Pair-breaking Superconducting Detectors

- Analogous to semiconductor detectors

Principle of Operation

- We use transmission line resonator to readout

change in Zs

- Superconductor LmLki(nqp(hn))

anim.avi

CPW coplanar waveguide

Advantages

- Simple fabrication
- Powerful multiplexing capability

Applications

- MKIDs for mm, submm

- Optical/UV/X-ray detector array

- Dark matter detection (phonon detector)

MKIDs Physics Overview

- Responsivity

- Noise

- - QP generation-recombination noise
- HEMT amplifier noise

Excess Phase Noise !

Calculation of Kinetic Inductance

- Superconducting transmission line

I Surface Impedance Zs and Penetration Depth leff

- Mattis-Bardeen theory

R Popel

- Local Limit
- lltltx0, lltltlL ? q1gtgt1

- Extreme Anomalous Limit
- lLltltx0, lLltltl ? q12 ltlt1

- K(q), s1, s2 generally involve very complicated

integrals and has to be solved numerically. Under

the condition TltltTc and hwltltkbTc, it has

analytical expression

- Tltlt hw

Numerical results I

- Zs(T)

- Effective penetration depth

Numerical results II

- Fit the f0, Q data for a

Parameters Tc, lL, v0, l, D0/kTc taken from last

page.

II Kinetic Inductance Fraction (a)

- Shwarz-Christoffel Mapping (Conformal Mapping)

z-plane

- Lm, C

w-plane

- geometric factor g

- Kinetic Inductance Fraction (a) by Matlab

e.g. Al CPW resonator, s3mm, g2mm, t200nm,

er12

Lm 0.3185m0, C 18.95 e0, g 4.3e005,

leff51.4nm, Lki0.0221m0

Experimental Determination of a

- Direct determination of a from f0

- e.g., if fsc0 or fm0 has an relative error of 1,

the relative error in a will be 98 for a 2,

- Determination of a from df0(T)

Doesnt require theoretical model on leff

- Alpha test device

- 5 different geometry
- one geometry has large a which can be determined

directly from f0 - other 4 geometries indirectly from df0(T) data

200nm Thick Al Film Result

Calculation agrees well with the experimental

results.

af directly from resonance frequency ar from

the temperature curve and the ratio of a atheo

theoretical calculation from conformal mapping

and M-B theory

20nm Thin Al Film Result

T(K)

T(K)

leff goes up dramatically for thin film

Unsolved, Future Work

- Theoretical calculation of kinetic inductance for

thin film

- solve M-B non-local equation in 2D

- Measurement of different thickness and other metal

- tested 20nm, 40nm, 200nm, 320nm
- other metal Nb, Re

Noise

- On resonance excess phase noise

Observations of Excess Phase Noise I

- In the phase direction

- IQ mixer

- synthesizer phase noise

- amplifier phase noise

- QP generation-recombination noise

The noise source has to be inside the resonator!

Observations of Excess Phase Noise II

- Power Dependant

slope -0.5

Frequency noise

Internal power

Frequency noise scales with internal power

(field) by power law

Observations of Excess Phase Noise III

- Metal and Substrate Dependant

- In general,
- lower noise on sapphire than on Si

Noise is related with substrate.

- However,
- Nb on Si as good as Al on sapphire

Nb

Observations of Excess Phase Noise IV

- Geometry Dependant

Noise and dissipation decrease as goes to the

wider geometry.

Preliminary Two Level System Model

- Two Level Systems

- Resonant Fluorescence

A Qualitative Picture of Phase Noise from TLS

Q

I

Quantum Mechanical Treatment of Resonant

Fluorescence

- Hamiltonian (Schrodinger picture)

-TLS Quantum Mechanics, -E Field Classical -b,

b Phonon bath

- Master Equation (Interaction picture)

-g decay rate of upper level, Wgtgtg -Dw atomic

detuning

- Bloch Equation (Interaction picture)

Resonant Fluorescence

- Two-time Correlation Function and Quantum

Regression Theory

- Fluorescent Light

Y dipole radiation pattern

- Spectrum of Fluorescent Light

Strong driving Wgtgtg Mallow triplet

Squeezed Spectrum Noise Blob

- Squeezed spectrum

covariance matrix

Two channel spectrum analyzer

power spectrum matrix

v1

v2

SII

SQQ

Why phase direction?

- Direction of the noise blob

2q

- Noise blob rotated by Argab

- Side peak LP filtered out by resonator

resonator bandwidth 10KHz to 100KHz ltlt Rabi

frequency

Prediction of the model

- Power dependence

wTLS

wdriving

Assume wTLS has a uniform distribution, results

from single TLS need to be integrate over d

a

r

Unsolved, Future WorkI Experiment

- Complete information of excess phase noise

- Where is the TLS noise source? In volume or near

surface?

- surface of metal
- surface of gap
- metal-substrate interface
- thin layer into the substrate
- bulk substrate

noise v.s. geometry

Unsolved, Future WorkII Theory

- Complete the Model
- temperature dependence
- explain df0
- full QM model
- nonlinear effect bistability, hysteresis
- many TLSs
- various parameters in the model
- g, wTLS, g, W

Future WorkResearch Goal

- Put up a complete picture of the device physics
- Establish general formulations to calculate and

predict responsivity and noise - Propose an optimal design of the most sensitive

device

Summary of Questions Need to be Answered

Thank you !

Observations of Excess Phase Noise V

- Other experimental facts

- Apply a DC field

- Drive at nearby frequency

- Drive at next resonance

Readout Power Saturation

- Can we increase the readout power to suppress the

noise?

The resonator become nonlinear at high readout

power.

Modeling the Nonlinear Resonator

T312

Assume f0 (Pint), Q (Pint) monotonously decrease

with power.

f

Pint

low power - normal

high power - distorted

very high power - discontinuous

Observations of Readout Power Saturation

- All resonator of same geometry saturate at the

same internal field

- Superconductor dependence
- Nb resonators can be readout at 30dB more

microwave power than Al resonators - Substrate dependence
- Al on Sapphire resonators can be readout at 5dB

more microwave power than Al on Si resonators - Geometry dependence
- Resonators with small geometry (larger alpha) are

easier to saturate than large geometry (small

alpha)

Unsolved, Future Work

- What is the mechanism of this saturation?
- Magnetic field, critical current
- explains superconductor, geometry dependence
- substrate heating
- explains substrate dependence
- Theoretical calculation of saturation power