Non-equilibrium superconductivity in
microwave resonators
CooperPairs
2Δ
hν
Pieter de Visser
Quasipar/cles
SRON: Stephen Yates, Jochem Baselmans, Pascale Diener, Andrey Baryshev
Delft: Teun Klapwijk, Nuria Llombart, Andrea Neto
Cambridge: Tejas Guruswamy, David Goldie, Stafford Withington
Moscow: Sasha Semenov, Igor Devyatov
Superconductivity and Photons
From light to signal
CooperPairs
2Δ
hν
S21 [dB]
Quasipar/cles
δf
F [Ghz]
F0
Incoming photons break Cooper pairs
=>quasipar/cles
=>Higherresistanceandinductance
=>Resonanceshi@sandgetsshallower
Microwavereadout,energiesfarbelowthegap
P. Day, et al., Nature 425, 817 (2003)
From light to signal
CooperPairs
2Δ
hν
Quasipar/cles
Microwave:Qi,A
Pairbreaking
Microwave:fres,θ
Nonequilibrium
Absorp/on:
-  Cooperpairbreakingbyphotons
-  Microwaveabsorp/onbyquasipar/cles
Fieldeffect:
-  Densityofstatesbroadensduetofield=>nonlinearity
Removing nonequilibrium QP’s with trap/sink tricks does
notworkfordetectors,wewanttocollectthem!
Nonequilibrium due to absorption
Injec/onrateofquasipar/clesatenergyE
-  Microwave
-  Cooper-Pairbreaking
Excessquasipar/cles
Microwave power dependent
Phys. Rev. Lett. 106, 167004 (2011)
Appl. Phys. Lett. 100, 162601 (2012)
Influenceofmicrowavedissipa/onon
pair-breakingresponse(1.5THz)
Detector sensitivity limited by excess QPs due to microwave readout
We need the microwave power, because we want to be limited by qp-fluctuations
Nature Communications 5, 3130 (2014)
Influenceofmicrowavedissipa/onon
pair-breakingresponse(1.5THz)
Not limited by stray-light
Detector sensitivity limited by excess QPs due to microwave readout
Nature Communications 5, 3130 (2014)
Non-linearresonatorresponsecurves
LowTquasipar/clecrea/on,butat
higherTQienhancement
Non-equilibriumf(E)
Ivlev, Lisitsyn, Eliashberg, JLPT 10, 449 (1973) - Microwave absorption, gap enhancement
close to Tc
Chang and Scalapino, PRB 15, 2651 (1977) - kinetic equations
Goldie and Withington, SuST 26, 015004 (2013) – low temperature, resonators
Non-equilibriumf(E)
Ivlev, Lisitsyn, Eliashberg, JLPT 10, 449 (1973) - Microwave absorption, gap enhancement
close to Tc
Chang and Scalapino, PRB 15, 2651 (1977) - kinetic equations
Goldie and Withington, SuST 26, 015004 (2013) – low temperature, resonators
Non-equilibriumf(E)–steadystate
Goldie and Withington, SuST 26, 015004 (2013)
Phys. Rev. Lett. 112, 047004 (2014)
Examplef(E)->σ1,Qi
Phys. Rev. Lett. 112, 047004 (2014)
Nonequilibrium due to absorption
Injec/onrateofquasipar/clesatenergyE
-  Microwave
-  Cooper-Pairbreaking
‘Efficiency’ in converting photon
energy to QPs close to the gap
Phonon trapping factor
Guruswamy, Goldie, Withington, SuST 27, 055012 (2014)
Arises because observable is mainly sensitive to quasiparticles close to gap
Broadband antenna + lens
Tantalum KID, energy gap at 324 GHz
Absorber detector will not work, due to Zs(ω), constant power needed
Neto, IEEE Trans. Antennas and Prop. 58, 2238 (2010)
Neto et al. IEEE Trans. THz Sci. Tech. 4, 26 (2013)
FTS response of Tantalum resonator
Absorption measurement,
Detector phase response (a.u.)
1
resonator is detector in FTS
0.8
0.6
0.4
4Δ
0.2
0
2Δ
200
400
600
800
Frequency (GHz)
1000
• 
FTS dependence (calibrated)
• 
Antenna efficiency
• 
Absorption superconductor
• 
Response superconductor
CPW absorption x antenna efficiency
Detector phase response (a.u.)
1
0.8
0.6
Energy
0.4 gap Ta: 324 GHz
0.2
0
200
400
600
800
Frequency (GHz)
1000
Steady state f(E)
Non-equilibrium
quasiparticle distribution
Constant power, only effect is
F-dependence through f(E)
Steady state f(E)
QP creation efficiency
Non-equilibrium
quasiparticle distribution
1
0.8
0.6
0.4
0.2
Constant power, only effect is
F-dependence through f(E)
0
200
400
600
800
Frequency (GHz)
1000
We measured ‘pair-breaking efficiency’ due to f(E,F)
Appl. Phys. Lett. 106, 252602 (2015)
• 
• 
Monochromatic pair-breaking illumination (high energy)
Microwave power dependence consistent with our
observations
Phys. Rev. B 93, 024514 (2016)
R. P. Budoyo, PhD Thesis (2015)
Absorp/ondoesnotexplaineverything
One level deeper
Absorp/onisonlypartofthenon-equilibriumstoryofasuperconductorin
anACfield.
Vectorpoten/alA,pullsapartthepairinmomentumspace
-  Inequilibriumthetwoelectronshaveoppositemomenta:k1+k2=0.
-  InaDC-fieldthisbecomesk1+k2=q=>densityofstatesbroadening=>
nonlinearL
DC
Anthore et al. PRL 90, 127001 (2003)
Eom et al. Nature Phys. 8, 623-627 (2012)
Densityofstatesbroadens,butgapremains‘hard’.
Inductance shows an I2 non-linearity => used to model (RF!) travelling
waveparametricamplifier
DC
Anthore et al. PRL 90, 127001 (2003)
Eom et al. Nature Phys. 8, 623-627 (2012)
Densityofstatesbroadens,butgapremains‘hard’.
Inductance shows an I2 non-linearity => used to model (RF!) travelling
waveparametricamplifier
One level deeper
Absorp/onisonlypartoftheinfluenceofthefieldonthesuperconductor,
throughf(E).
Vectorpoten/alAcos(ωt),pullsapartthepairinmomentumspace
-  Inequilibriumthetwoelectronshaveoppositemomenta:k1+k2=0.
-  InaDC-fieldthisbecomesk1+k2=q=>densityofstatesbroadening=>
nonlinearL
-  Forfinitefrequency:k1+k2=q0cos(ωt),nowitdependsonthefrequency
andfieldstrength
NOTE:themomentumeffectisalsoknownasdepairingor‘pair-breaking’,
butitisNOTthesameaspair-breakingduetoaphoton/phononwithE>2Δ
Microwave: ‘Coherent excited states’
Semenov, Devyatov, de Visser, Klapwijk, arXiv:1603.02726
Superconducting state (density
of states) changes drastically
2 differences compared to DC:
Steps at multiples of hf
Exponential subgap tail
triggers absorption?
Much richer structure than DC
Effect on complex conductivity
Nonlinear frequency-shift for Al resonator that is
not due to f(E) effect, is quantitatively explained!
But needs other type of experiments to fully
explore the density of states.
Semenov, Devyatov, de Visser, Klapwijk, arXiv:1603.02726
Summary
Phys. Rev. Lett. 112, 047004 (2014)
Nature Comm. 5, 3130 (2014)
Appl. Phys. Lett. 106, 252602 (2015)
arXiv:1603.02726
Current direction: move to much smaller detection volumes => nonlinear, single quasiparticle