1. Moscow State Pedagogical University
MSPU
Nonequilibrium Superconductivity and Ultrasensitive Detectors and Mixers
Gregory Goltsman
Moscow State Pedagogical University
Moscow, Russia

2. Lecture 1. Nonequilibrium Superconductivity and Ultrasensitive Detectors and Mixers
Quasi-particle disequilibrium in BCS superconductors
- Energy-mode vs. charge-mode disequilibrium
- "Electrons" and "holes" in superconductors
- Enhancement and suppression of superconductivity by microwaves
- Normal metal - superconductor interface and Andreev reflection
- Electric field penetration into superconductor
- Time-dependent charge-mode disequilibrium: phase-slip centers
Superconducting single-photon detectors based on nonequilibrium superconductivity (TES, STJ, SSPD)
- Operation principles of the detectors
- Comparison of the detector characteristics: response time, quantum efficiency, operating wavelength range, dark counts rate, energy resolution
Applications of single-photon detectors
- CMOS IC testing
- Quantum communication and quantum cryptography

3. Ground state in normal metal and in superconductor
Ground state in normal metal at T=0K, all states with k<kF are occupied, all states with k>kF are free. The excited state with arbitrary small energy can be created by moving of an electron from point o inside the sphere to point x outside it.
Fermi surface with energy eF a b D
(a) Ground-state of normal metal. Probability that single-electron state with energy e is occupied, T=0K
(b) Ground state of superconductor.
It differs from metal ground state in the small (~ D) region on the Fermi surface, T=0K

4. Fundamentals of BCS Theory

5. Quasi-particle excitation energy in normal metal and in superconductor.
In normal state:
for k>kF (electron)
for k<kF (hole)
In superconducting state:
where D is energy gap.
Spectrum of elementary excitations in superconductor. The slope of the dashed line is ћvc, where vc is critical velocity.

6. Energy-mode vs. charge-mode disequilibrium
Even ("energy") mode
T* >T
Odd ("charge") mode
"Branch imbalance"
Q* >0

7. Enhancement and suppression of superconductivity by microwaves
Al bridges 1 mm wide and 100 mm long
Probabilities of quasiparticles relaxation due to electron-phonon interaction (EPI) and electron-electron interaction (EEI).
l is electron mean free path
E.M. Gershenzon, G.N. Gol'tsman, V.D. Potapov, A.V. Sergeev, Physica B 169(1991)

8. Branch imbalance of the quasi-particle spectrum
Non-equilibrium distribution of superconducting electrons vk2 and quasi-particle spectrum Ek in superconductor in non-equilibrium state. The dashed line shows equilibrium distribution vk2, when ms=eF. Gap D retained its value, chemical potential mn became greater than eF.

9. Andreev reflection Superconductor Normal metal
The charge of the quasiparticle (electron) is gradually changing as the quasiparticle moves from normal metal to superconductor

10. Phase-slip centers
Schematic diagram of a model of the phase-slip center. The oscillation of the gap magnitude occurs in a core length ~2x, whereas the nonequilibrium quasi-particles producing charge imbalance diffuse a distance ~L in either direction before mn relaxes to mp.
The oscillatory supercurrent in the core region, which average value ~Ic/2.
Schematic I-V curve of a bridge containing only a single phase-slip center. A is the cross-sectional area of the filament and rn is its normal resistivity.
[Tinkham M., Revs. Mod. Phys. 46, 587 (1974).)]

11. Phase-slip centers
Spatial variation of the superconducting and normal electron potentials, Vs and Vn, measured by tunnel probes near a phase-slip center in a tin film strip. (After Dolan and Jackel.)

12. Phase-slip centers
Current-voltage characteristics of tin "whiskers" showing regular step structures due to successive establishment of phase-slip centers. (Here DT=Tc-T). (After Meyer)
Meyer J., v. Minnigerode G. Phys. Lett., 1972, 38A, 529

13. Lecture 1. Nonequilibrium Superconductivity and Ultrasensitive Detectors and Mixers
Quasi-particle disequilibrium in BCS superconductors
- Energy-mode vs. charge-mode disequilibrium
- "Electrons" and "holes" in superconductors
- Enhancement and suppression of superconductivity by microwaves
- Normal metal - superconductor interface and Andreev reflection
- Electric field penetration into superconductor
- Time-dependent charge-mode disequilibrium: phase-slip centers
Superconducting single-photon detectors based on nonequilibrium superconductivity (TES, STJ, SSPD)
- Operation principles of the detectors
- Comparison of the detector characteristics: response time, quantum efficiency, operating wavelength range, dark counts rate, energy resolution
Applications of single-photon detectors
- CMOS IC testing
- Quantum communication and quantum cryptography

14. Semiconducting vs. superconducting single-photon detectors for 1. 3-1
Semiconducting vs. superconducting single-photon detectors for mm wavelength
Semiconductors
One optical photon creates only one
electron-hole pair
(typical bandgap 1-2 eV).
Room temperature and cryogenic operation.
Large dark counts.
Complicated biasing schemes.
Superconductors
One optical photon creates ~100–1000 excited electrons
(superconducting gap
~ 2 meV for NbN).
Relaxation times are picosecond.
Extremely low dark counts.
No gating required, simple biasing source.
Low temperature environment reduces background noise and thermal fluctuations responsible for dark counts.

15. Transition-edge detector
(a) Microphotograph of a transition-edge, hot-electron quantum detector and (b) the corresponding equivalent circuit. The device was a 20x20 μm2 square of 40 nm thick tungsten film having Tc=80 mK with a transition width of 1mK. The device was operated at a bath temperature of 40 mK in a voltage-bias regime that maintained the sensor within the transition region via negative electrothermal feedback.
(Miller et al IEEE Trans. Appl. Supercond ©1999 IEEE).

16. Hot-electron microcalorimeter based on superconducting tunnel junction
Photon absorption gives rise to Te in a metal absorber and is measured using the I–V characteristics of a normal-insulator-superconductor tunnel junction, in which a part of the absorber forms the normal electrode. The current through the junction was measured with a low-noise dc SQUID. The absorber had an area of 100x100 μm2 and was deposited on a silicon nitride membrane. The microcalorimeter was operated at 80 mK with a time constant of 15 μs and demonstrated an energy resolution of 22 eV for 6 keV photons.
(Nahum M. and Martinis J. M Appl. Phys. Lett )

17. STJ microbolometer with Andreev reflection of quasiparticles
A hot-electron microbolometer using Andreev reflections of quasiparticles from superconducting contacts and the corresponding I–V characteristics.
The device relyes on Andreev reflections of low-energy, thermal quasiparticles at the edges of the stripe and on the weak electron–phonon coupling at low temperatures. Both effects confined the energy delivered by the photons, providing a large rise of Te. This was subsequently read out by the superconductor-insulator-normal metal junction, for which the metal strip formed the normal electrode.
(Nahum M. and Martinis J. M Appl. Phys. Lett )

18. Single-photon detectors: desired properties
High quantum efficiency (QE reaching 100%)
Broadband operation (200 nm to >2000 nm)
Low dark count rates
no false/unwanted counts
no afterpulsing
Very high speed
fast, picosecond signal rise and recovery
no “dead” time between counts
Energy resolving - photon number resolving

19. Superconducting Single-Photon Detector (SSPD) Mechanism of Photon Detection

20. Energy Relaxation Process
Schematic description of relaxation process in an optically excited superconducting thin film.

21. SSPD response mechanism
Concentration of nonequilibrium quasipaticles across the width of the film at different moments after the photon has been absorbed. Time delays are 0.8, 2.0 and 5.0 measured in units of the thermalization time. Distance from the absorption site is shown in units of the thermalization length. Inset illustrates redistribution of supercurrent in the superconducting film with the normal spot - the basis of quantum detection. It shows the cross-section of the film drawn through the point where photon has been absorbed.
Semenov A., Gol'tsman G., Korneev A., Physica C 351 (2001)

22. SSPD response mechanism
Schematic of the resistive state formed in the film after the current density in sidewalks has exceeded the critical value. The dark circle represents the normal spot; grey zones correspond to the area of superconductor with penetrating electric field. Profiles of the electric field (E) and the energy gap (D) are shown along lines crossing the normal spot (a) and the sidewalk (b).
Phase Slip Center
Semenov A., Gol'tsman G., Korneev A., Physica C 351 (2001)

23. Scanning Electron microscope image.
Fabrication:
DC reactive magnetron sputtering of 4-nm-thick NbN film
Patterning of meander-shaped structure by direct e-beam lithography.
Formation of Au contacts with optical lithography.
Gol'tsman G. et al, Appl. Phys. Lett. 79 (2001) 705
Korneev A. et al, Appl. Phys. Lett. 84 (2004) 5338

24. SSPD placed inside a cryostat
10 mm
Contacts made to gold pads on detector. Actual NbN detector is at center of 3mm x 3mm chip in photo. Close-up of the detector is electron micrograph (SEM image), showing meander structure.
5 mm
meander
Au contacts

25. Direct electron beam lithography and reactive ion etching process
Resistance vs Temperature Curves for Sputtered NbN Film 3.5 nm Thick and for SSPD Device
Direct electron beam lithography and reactive ion etching process

26. IV-curves of the 3.5-nm thick film devices at 4.5 K

27. Time-resolved SSPD photoresponse signal
The measured FWHM of the response signal is about 150 ps and includes both the risetime and falltime jitter

28. Jitter of a NbN SSPD at 1.55 mm and 778 nm wavelengths is below 18 ps
1.0
0.8
778 nm
0.6
FWHM
0.4
~18 ps
0.2
0.0
1.0
0.8
1550 nm
0.6
FWHM
0.4
~18 ps
0.2
0.0
Oscilloscope: 50-GHz bandwidth Tektronix TDS-8000B
Laser source: Pritel OptiClock 1 GHz rate, 1.6 ps pulses, 70 fs jitter,
Signal amplifiers: Miteq JS , GHz bandwidth
Korneev et al., APL, 84, 5339 (2004)c

29. Counting speed of 3. 5-nm-thick SSPDs is above 2 GHz for 1
Counting speed of 3.5-nm-thick SSPDs is above 2 GHz for 1.55-mm photons
T = 4.2 K
Detector photoresponse speed is limited by the acquisition
electronics:
t = 134 ps.
1-GHz-rate photoresponse train (real-time oscilloscope picture).
Korneev et al., APL, 84, 5339 (2004)

30. Experimental data for QE (open symbols) and the dark count rate (closed symbols) vs. the bias current measured for 1.55-μm photons

31. Experimental quantum efficiency and dark counts rate vs
Experimental quantum efficiency and dark counts rate vs. normalized bias current at 2 K

32. Spectral dependencies of the quantum efficiency measured for a NbN SSPD at 3 K temperature and different bias currents
Ic =29.7mA at 3 K

33. The NEP and the dark counts (inset) measured at 1. 26, 1. 55 and 5
The NEP and the dark counts (inset) measured at 1.26, 1.55 and 5.6 mm wavelengths at 2 K.

34. Comparison of traditional single-photon detectors and superconducting single-photon detectors at ~1.3 mm wavelength

35. Lecture 1. Nonequilibrium Superconductivity and Ultrasensitive Detectors and Mixers
Quasi-particle disequilibrium in BCS superconductors
- Energy-mode vs. charge-mode disequilibrium
- "Electrons" and "holes" in superconductors
- Enhancement and suppression of superconductivity by microwaves
- Normal metal - superconductor interface and Andreev reflection
- Electric field penetration into superconductor
- Time-dependent charge-mode disequilibrium: phase-slip centers
Superconducting single-photon detectors based on nonequilibrium superconductivity (TES, STJ, SSPD)
- Operation principles of the detectors
- Comparison of the detector characteristics: response time, quantum efficiency, operating wavelength range, dark counts rate, energy resolution
Applications of single-photon detectors
- CMOS IC testing
- Quantum communication and quantum cryptography

36. Application: CMOS Device Debug
Normally operating nMOS transistor emits near IR photons ( um) when current passes through the channel
Time-correlated photon emission detection measures transistor switching time
Vdd (1)
Vdd (1)
Vdd (1)
Vss (0)
Vss (0)
Vss (0)
Kash, J. A. and J. C.-H. Tsang (1999). Noninvasive optical method for measuring internal switching and other dynamic parameters of CMOS circuits. USA, International Business Machines Corporation. US Patent # 5,940,545

37. TRPE system setup
TRPE: Time-Resolved Photon Emission

38. OptiCA® System with NbN SSPD commercialized by NPTest, Inc.
For more information:

39. Single-photon emission from CMOS transistors
0.35-mm linewidth, 3.3-V bias CMOS circuit running at 100 MHz
Mepsicron II
detector
0.13-mm linewidth, 1.3-V bias CMOS circuit running at 100 MHz
NbN SSPD
detector

40. Single-photon emission from both nMOS and pMOS transistors
0.13-mm linewidth, 1.3-V bias CMOS circuit running at 100 MHz
Zhang et al., El. Lett, 39, 1086 (2003)

41. Quantum Cryptography (QC) based on
single-photon communication assures unconditional security
Bob
(Receiver)
Alice
(Sender)
[from Simon Benjamin, Science 290, 2273 (2000)]
Unconditionally secret, quantum key distribution is possible in actual physical environments due to Heisenberg Indeterminacy Principle:
It is impossible to measure the state of a quantum bit without altering it.
Alice (Sender) - single-photon source.
Bob (Receiver) - single-photon detector.

42. Free-space, satellite-based quantum key distribution will provide us with high-speed and unconditional security communications
(from

43. Conclusion
- It is convenient to characterize the departure from thermal equilibrium by introducing two parameters T* and Q*, representing the nonequilibrium temperature and quasi-particle charge density, respectively. These approaches are called energy-mode and charge-mode disequilibrium.
- Nonequilibrium effects such as enhancement of superconductivity by microwaves, Andreev reflection, phase-slip centers are widely used in practical ultrasensitive detectors.
- Superconducting single-photon detectors outperform traditional avalanche photodiodes and photon multiplier tubes. Superconducting detectors are already used in science and industrial applications.

45. Andreev reflection
Schematic diagram of energy vs. momentum on the two sides of an NS interface. The diagram includes degenerate states both inside and outside the Fermi surface and on both forward and reverse sides of the Fermi sphere. The open circles denote holes; the closed circles, electrons; and the arrows point in the direction of the group velocity, ∂Ek/∂k. This describes an incident electron at (0), along with the resulting transmitted (2, 4) and reflected (5, 6) particles. A refers to the Andreev-reflected hole.

46. Enhancement and suppression of superconductivity by microwaves
Al bridges 1 mm wide and 100 mm long
Probabilities of quasiparticles relaxation due to electron-phonon interaction (EPI) and electron-electron interaction (EEI).
l is electron mean free path
E.M. Gershenzon, G.N. Gol'tsman, V.D. Potapov, A.V. Sergeev, Physica B 169(1991)

47. Equilibrium state of superconductor at temperature T
Equilibrium at T

48. Quasi-particle disequilibrium
Energy-mode disequilibrium
Charge-mode disequilibrium

49. Enhancement by extraction of quasi-particles
Schematic diagram of tunnel process showing net extraction of quasi-particles from the superconductor having the smaller gap and hence a greater density of quasi-particles.

50. Phase-slip centers a b
Graphical representation of complex current-carrying Ginzburg-Landau wavefunction in one-dimensional superconductors. (a) Uniform solution. (b) Nonuniform solution just before phase-slip event.