1. Coherent excited states in superconductors due to a microwave field
A.V. Semenov, I.A. Devyatov,
P.J. de Visser, T.M. Klapwijk
Coherent excited states in superconductors
due to a microwave field
Seminar in Laboratory of Artificial Quantum Systems
December 8, 2016

2. Outline - One old hole in the theory of interaction between
superconductor and MW field
- Dressed states of an electron in MW field
- DOS and other spectral properties
of a dirty superconductor in MW field
- Comparison with the experiment

3. Theory of superconductor in MW field
Microscopic theory of superconductivity – BCS, 1957

4. Theory of superconductor in MW field
Microscopic theory of superconductivity – BCS, 1957
Effect of dc supercurrent on the ground state
of superconductor – Anderson, 1958

5. Theory of superconductor in MW field
Microscopic theory of superconductivity – BCS, 1957
Effect of dc supercurrent on the ground state
of superconductor – Anderson, 1958
High-frequency conductivity of superconductor
– Mattis and Bardeen, 1958

6. Theory of superconductor in MW field
Microscopic theory of superconductivity – BCS, 1957
Effect of dc supercurrent on the ground state
of superconductor – Anderson, 1958
High-frequency conductivity of superconductor
– Mattis and Bardeen, 1958
Effect of MW field on quasiparticle distribution
in superconductor – Eliashberg, 1968, 1971

7. Theory of superconductor in MW field
Microscopic theory of superconductivity – BCS, 1957
Effect of dc supercurrent on the ground state
of superconductor – Anderson, 1958
High-frequency conductivity of superconductor
– Mattis and Bardeen, 1958
Effect of MW field on quasiparticle distribution
in superconductor – Eliashberg, 1968, 1971
Effect of MW field on the ground state of
superconductor – has not been elaborated!

8. Direct depairing by dc current
Γ≡2e2DA2 ≡2Dps2

9. Direct depairing by low-frequency current
Γ(t)≡2e2DA2(t) =2e2DE2(t+T/4)/ω2
Gurevich, A. (2014). Physical review letters, 113(8),

10. Direct depairing by low-frequency current
Γ(t)≡2e2DA2(t) =2e2DE2(t+T/4)/ω2
Gurevich, A. (2014). Physical review letters, 113(8),
BUT!
ћω<<Γ
What is in the opposite case?

11. Single electron in a periodic field

12. Single electron in a periodic field
ħω vs. (eA)2/2m
ħω <<. (eA)2/2m - classical e
ħω >>. (eA)2/2m - quantum
Diffuse limit ωτ << 1:
m -> ħ /D

13. Dressed state in periodic field The simplest case

14. Dressed state in periodic field The simplest case
Vcosωt

15. Dressed state in periodic field The simplest case
Vcosωt

16. Dressed state in periodic field The simplest nontrivial case

17. Dressed state in periodic field The simplest nontrivial caseħω εp
Vcosωt

18. Dressed state in periodic field The simplest nontrivial caseħω εp
Vcosωt

19. Dressed state in periodic field The simplest nontrivial caseħω εp
Vcosωt

20. Energy + A(t) Energy Quasi-energy Back to E Quasi-energy
ΔE~q2A2
Quasi-energy
Back to E
representation
Quasi-energy ω ω ω ω
Energy
Energy

21. Model Keldysh-Usadel formulation (Larkin, Ovchinnikov, 1977) E
Dirty superconductor
No spatial gradients
Keldysh-Usadel formulation (Larkin, Ovchinnikov, 1977)
Retarded Usadel equation
rf field term
Normalization condition

22. Model Monochromatic field, ω G and F are expanded
in even harmonics of ω
Retarded Usadel equation in E-ω representation
Normalization condition
α≡e2DE2/ω2
En≡E+nω/2

23. Closed equations for time-averaged
Green functions
Retarded Usadel equation
α<<ω
Normalization condition
rf field term
f± ≡ f(E ± ω)
For comparison,
α≡e2DE2/ω2
R Usadel equation in dc case
Essentially the same as
in MW absorption theory
ω<<α
Our R Usadel is
nonlocal in energy
Qualitatively different solution

24. Solution: Density of states
Time averaged DOS
N(E)=ReG0(E)

25. Solution: Density of states
Time averaged DOS
N(E)=ReG0(E) ω
“photon points”

26. Solution: Density of states
Time averaged DOS
N(E)=ReG0(E) ω
“photon points”

27. Solution: conductivity
Linear conductivity
ħω<<Δ
α<<ħω<<Δ

28. Comparison with the experiment

29. Effect on quasiparticle number
Nqpth depends on DOS
Should increase with α and ω

30. Effect on quasiparticle number
Nqpth depends on DOS
Should increase with α and ω
Rapid increase expected above some threshold α and ω

31. Conclusion Microscopic description of depairing by rf supercurrent
in quantum regime ω>>α is investigated
Anomalous strong action of rf power to resonant frequency
of Al micro-resonator is explained

32. Thank you for your attention!