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Physics of Microwave Kinetic Inductance Detectors MKIDs

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Title: Physics of Microwave Kinetic Inductance Detectors MKIDs


1
Physics of Microwave Kinetic Inductance Detectors
(MKIDs)
  • PhD Candidate Jiansong Gao
  • Advisor Jonas Zmuidzinas
  • Dec 9, 2005

2
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

3
MKIDs Pair-breaking Superconducting Detectors
  • Analogous to semiconductor detectors

4
Principle of Operation
  • We use transmission line resonator to readout
    change in Zs
  • Superconductor LmLki(nqp(hn))

anim.avi
CPW coplanar waveguide
5
Advantages
  • Simple fabrication
  • Powerful multiplexing capability

6
Applications
  • MKIDs for mm, submm
  • Optical/UV/X-ray detector array
  • Dark matter detection (phonon detector)

7
MKIDs Physics Overview
  • Responsivity
  • Noise
  • - QP generation-recombination noise
  • HEMT amplifier noise

Excess Phase Noise !
8
Calculation of Kinetic Inductance
  • Superconducting transmission line

9
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

10
Numerical results I
  • Zs(T)
  • Effective penetration depth

11
Numerical results II
  • Fit the f0, Q data for a

Parameters Tc, lL, v0, l, D0/kTc taken from last
page.
12
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
13
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

14
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
15
20nm Thin Al Film Result
T(K)
T(K)
leff goes up dramatically for thin film
16
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

17
Noise
  • On resonance excess phase noise

18
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!
19
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
20
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
21
Observations of Excess Phase Noise IV
  • Geometry Dependant

Noise and dissipation decrease as goes to the
wider geometry.
22
Preliminary Two Level System Model
  • Two Level Systems
  • Resonant Fluorescence

23
A Qualitative Picture of Phase Noise from TLS
Q
I
24
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)

25
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
26
Squeezed Spectrum Noise Blob
  • Squeezed spectrum

covariance matrix
Two channel spectrum analyzer
power spectrum matrix
v1
v2
SII
SQQ
27
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
28
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
29
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
30
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

31
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

32
Summary of Questions Need to be Answered
33
Thank you !
34
Observations of Excess Phase Noise V
  • Other experimental facts
  • Apply a DC field
  • Drive at nearby frequency
  • Drive at next resonance

35
Readout Power Saturation
  • Can we increase the readout power to suppress the
    noise?

The resonator become nonlinear at high readout
power.
36
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
37
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)

38
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
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