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

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MKIDs Pair-breaking Superconducting Detectors

• Analogous to semiconductor detectors

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Principle of Operation

• We use transmission line resonator to readout
  change in Zs

• Superconductor LmLki(nqp(hn))

anim.avi
CPW coplanar waveguide
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Advantages

• Simple fabrication
• Powerful multiplexing capability

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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 !
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Calculation of Kinetic Inductance

• Superconducting transmission line

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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

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Numerical results I

• Zs(T)

• Effective penetration depth

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Numerical results II

• Fit the f0, Q data for a

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

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

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Noise

• On resonance excess phase noise

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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!
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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
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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
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Observations of Excess Phase Noise IV

• Geometry Dependant

Noise and dissipation decrease as goes to the
wider geometry.
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Preliminary Two Level System Model

• Two Level Systems

• Resonant Fluorescence

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A Qualitative Picture of Phase Noise from TLS
Q
I
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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)

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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
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Squeezed Spectrum Noise Blob

• Squeezed spectrum

covariance matrix
Two channel spectrum analyzer
power spectrum matrix
v1
v2
SII
SQQ
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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
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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
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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
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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

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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

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Summary of Questions Need to be Answered
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Thank you !
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Observations of Excess Phase Noise V

• Other experimental facts

• Apply a DC field

• Drive at nearby frequency

• Drive at next resonance

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Readout Power Saturation

• Can we increase the readout power to suppress the
  noise?

The resonator become nonlinear at high readout
power.
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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
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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)

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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