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

Nonequilibrium Superconductivity and Ultrasensitive Detectors and Mixers

Gregory Goltsman

Moscow State Pedagogical UniversityMoscow, Russia

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

Fermi surface with energy F

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.

a b

(a) Ground-state of normal metal. Probability that single-electron state with energy is occupied, T=0K

(b) Ground state of superconductor.It differs from metal ground state in the small (~ ) region on the Fermi surface, T=0K

Ground state in normal metal and in superconductor

Fundamentals of BCS Theory

Quasi-particle excitation energy in normal metal and in superconductor.

In normal state:for k>kF (electron)

for k<kF (hole)

FFFkk kkkm

kkm

E 22

2222

2

kkkm

kkm

E FFFkk 22

2222

2

In superconducting state:

2/122 kkE where is energy gap.

Spectrum of elementary excitations in superconductor. The slope of the dashed line is ћvc, where vc is critical velocity.

Even ("energy") mode

T* >T

Odd ("charge") mode

"Branch imbalance"

Q* >0

Energy-mode vs. charge-mode disequilibrium

0.04 0.06 0.08 0.10

5

10

15

20

SuppressionEnhancement

max

min

, G

Hz

1/l, Å-1

Enhancement and suppression of superconductivity by microwaves

l is electron mean free path

)/( 111

eephephephep

pheee pp 1

Probabilities of quasiparticles relaxation due to electron-phonon interaction (EPI) and electron-electron interaction (EEI).

Al bridges 1 m wide and 100 m long

E.M. Gershenzon, G.N. Gol'tsman, V.D. Potapov, A.V. Sergeev, Physica B 169(1991) 629-630

Non-equilibrium distribution of superconducting electrons vk

2 and quasi-particle spectrum Ek in superconductor in non-equilibrium state. The dashed line shows equilibrium distribution vk

2, when s=F. Gap retained its value, chemical potential n became greater than F.

Branch imbalance of the quasi-particle spectrum

Andreev reflection

The charge of the quasiparticle (electron) is gradually changing as the quasiparticle moves from normal metal to superconductor

Normal metal Superconductor

Phase-slip centers

Schematic diagram of a model of the phase-slip center. The oscillation of the gap magnitude occurs in a core length ~2, whereas the nonequilibrium quasi-particles producing charge imbalance diffuse a distance ~ in either direction before n relaxes to p.

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 n is its normal resistivity.

[Tinkham M., Revs. Mod. Phys. 46, 587 (1974).)]

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.)

Phase-slip centers

Current-voltage characteristics of tin "whiskers" showing regular step structures due to successive establishment of phase-slip centers. (Here T=Tc-T). (After Meyer)

Meyer J., v. Minnigerode G. Phys. Lett., 1972, 38A, 529

Phase-slip centers







Semiconducting vs. superconducting single-photon detectors for 1.3-1.5 m wavelength

Semiconductors

a) One optical photon creates only one electron-hole pair

(typical bandgap 1-2 eV).

b) Room temperature and cryogenic operation.

c) Large dark counts.

d) Complicated biasing schemes.

Superconductors

a) One optical photon creates ~100–1000 excited electrons (superconducting gap ~ 2 meV for NbN).

b) Relaxation times are picosecond.

c) Extremely low dark counts.

d) No gating required, simple biasing source.

Low temperature environment reduces background noise and thermal fluctuations responsible for dark counts.

(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. 9 4205 ©1999 IEEE).

Transition-edge detector

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. 1995 Appl. Phys. Lett. 66 3203)

Hot-electron microcalorimeter based on superconducting tunnel junction

(Nahum M. and Martinis J. M. 1993 Appl. Phys. Lett. 63 3075)

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.

STJ microbolometer with Andreev reflection of quasiparticles

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

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

Energy Relaxation Process

e-e interactionPhoton h

Debyephonons

Cooperpairs

e-e interaction

Quasi particles2

kbT

10-3

10-1

100

eV

Schematic description of relaxation process in an optically excited superconducting thin film.

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) 349-356

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 () are shown along lines crossing the normal spot (a) and the sidewalk (b).

Semenov A., Gol'tsman G., Korneev A., Physica C 351 (2001) 349-356

Phase Slip Center

SSPD response mechanism

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) 705Korneev A. et al, Appl. Phys. Lett. 84 (2004) 5338

SSPD placed inside a cryostat

meander

5 mm

Au contacts

10 m

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

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

0 1 2 3 40

5

10

15

20

25

Resistivestate

Superconducting state

50 load line

MetastableRegion

B

AIc

cu

rren

t,

A

Voltage, mV

Time-resolved SSPD photoresponse signal

The measured FWHM of the response signal is about 150 ps and includes both the risetime and falltime jitter

Jitter of a NbN SSPD at 1.55 m and 778 nm wavelengths is below 18 ps

Oscilloscope: 50-GHz bandwidth Tektronix TDS-8000BLaser source: Pritel OptiClock 1 GHz rate, 1.6 ps pulses, 70 fs jitter, Signal amplifiers: Miteq JS3-00101800-24, 0.1-18 GHz bandwidth

0.0

0.2

0.4

0.6

0.8

1.00.0

0.2

0.4

0.6

0.8

1.0

1550 nm

FWHM

~18 ps

778 nm

FWHM

~18 ps

Korneev et al., APL, 84, 5339 (2004)c

Counting speed of 3.5-nm-thick SSPDs is above 2 GHz for 1.55-m photons

1-GHz-rate photoresponse train (real-time oscilloscope picture).

T = 4.2 K

Detector photoresponse speed is limited by the acquisitionelectronics: = 134 ps.

Korneev et al., APL, 84, 5339 (2004)

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

10 12 14 16 18 20 2210-5

10-4

10-3

10-2

10-1

100

101

102

100

101

102

103

104

105

106

107

Dar

k co

unts

, s-1

QE

, %

Ib, A

, T=4.2 K, Ic=16.9A

, T=3.2 K, Ic=19.5A

, T=2.2 K, Ic=21.5A

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

0.4 0.5 0.6 0.7 0.8 0.9 1.010-3

10-2

10-1

100

101

102

10-4

10-2

100

102

104

106

1.26 m

0.94 m

1.55 m

0.56 m

QE

, %

Ib/I

c

Dar

k co

unts

, cps

Spectral dependencies of the quantum efficiency measured for a NbN SSPD at 3 K temperature and different bias currents

1 2 3 4 5 610-6

10-5

10-4

10-3

10-2

10-1

100

101

I

b/I

c=0.94

Ib/I

c=0.88

Ib/I

c=0.82

Ib/I

c=0.78

T=3K

QE

,%

,μm Ic =29.7A at 3 K

The NEP and the dark counts (inset) measured at 1.26, 1.55 and 5.6 m wavelengths at 2 K.

RDE

NEP 2

0.88 0.92 0.96 1.0010-21

10-20

10-19

10-18

10-17

10-16

Normalized bias current

1.26 m 1.55 m 5.6 m

NE

P, W

/Hz1/

2

0.88 0.92 0.96 1.0010-4

10-2

100

102

104

Dar

k co

unts

per

sec

ond

Normalized bias current

Detector Model Counting rate (Hz)

QE (%)

Jitter (ps)

Dark Counts (s-1)

NEP (W/Hz1/2)

InGaAs PFD5W1KS APD (Fujitsu)

5 106 20 200 6 103 310-17

R5509-43 PMT (Hamamatsu)

9 106 1 150 1.6 104 10-16

Si APD SPCM-AQR-16 (EG&G)

5 106 0.01 350 25 10-16

W bolometer- 0.1 K (NIST)

2 104 90 N/A <10-4 <210-21

Superconducting Tunnel Junction

5 103 60 N/A N/A N/A

SSPD - 2 K 2 109 30 18 <10-4 510-21

Comparison of traditional single-photon detectors and superconducting single-photon detectors at ~1.3 m wavelength







Application: CMOS Device Debug

• Normally operating nMOS transistor emits near IR photons (0.9-1.4um) when current passes through the channel

• Time-correlated photon emission detection measures transistor switching time

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

Vdd (1)

Vss (0)

Vdd (1)

Vdd (1)

Vss (0)

Vss (0)

TRPE system setup

TRPE: Time-Resolved Photon Emission

OptiCA® System with NbN SSPD commercialized by NPTest, Inc.

For more information:http://www.nptest.com/products/probe/idsOptica.htm

VacuumManipulators

CouplingOptics

FiberCold

Shield

CompressedHe Lines

Single-photon emission from CMOS transistors

0.35-m linewidth, 3.3-V bias CMOS circuit running at 100 MHz

Mepsicron IIdetector

NbN SSPDdetector


Good

0 5 10 15 20Time (ns)

Cou

nts

Single-photon emission from bothnMOS and pMOS transistors


Zhang et al., El. Lett, 39, 1086 (2003)

Quantum Cryptography (QC) based onsingle-photon communication assures unconditional security

• 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.

Alice(Sender)

Bob (Receiver)

[from Simon Benjamin, Science 290, 2273 (2000)]

Free-space, satellite-based quantum key distribution will provide us with high-speed

and unconditional security communications

(from www.space-technology.com)

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.

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.

Andreev reflection

0.04 0.06 0.08 0.10

5

10

15

20

SuppressionEnhancement

max

min

, G

Hz

1/l, Å-1

Enhancement and suppression of superconductivity by microwaves

l is electron mean free path

)/( 111

eephephephep

pheee pp 1

Probabilities of quasiparticles relaxation due to electron-phonon interaction (EPI) and electron-electron interaction (EEI).

Al bridges 1 m wide and 100 m long

E.M. Gershenzon, G.N. Gol'tsman, V.D. Potapov, A.V. Sergeev, Physica B 169(1991) 629-630

Equilibrium at T

11

)/( /0 TkEkk Bke

TEff

Equilibrium state of superconductor at temperature T

Quasi-particle disequilibrium

Energy-mode disequilibrium

Charge-mode disequilibrium

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.

Enhancement by extraction of quasi-particles

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

a b

Phase-slip centers

Documents

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