prl ,106, 257003 (2011)

ABSTRACTQuasiparticle Trapping in Andreev Bound States

Maciej Zgirski*, L. Bretheau, Q. Le Masne, H. Pothier, C. Urbina, D. Esteve

Quantronics Group, SPEC, CEA Saclay, France*presently: Institute of Physics, PAN, Warsaw

Electron transport through superconducting weak links can be understood in terms of Andreev bound states. They originate from conduction channels with each conduction channel giving rise to two Andreev bound states. In order to get access to single Andreev bound states we have used a system with a few conduction channels at most – quantum point contact. We have studied supercurrent across such a phase-biased atomic size contacts. For broad phase interval around p we have found suppresion of supercurrent – effect attributed to quasiparticle trapping in one of the discrete subgap Andreev bound states formed at the contact. Since single Andreev bound state can sustain supercurrent up to 50nA, such a trapping has a sound influence on the response of the atomic contact. Next to single Cooper-pair devices in which parity of the total number of electrons matters, it is another demonstration of a situation, when a single quasiparticle leaves a macroscopic trace. However, unlike a single Cooper device, atomic contact contains no island at all. The trapped quasiparticles are long-lived, with lifetimes up to hundreds of ms. Trapping occurs essentially when the Andreev energy is smaller than half the superconducting gap D. The origin of this sharp energy threshold is presently not understood.

PRL ,106, 257003 (2011)

PRL ,106, 257003 (2011)

Quasiparticle Trapping in Andreev Bound States

Maciej Zgirski*, L. Bretheau, Q. Le Masne, H. Pothier, C. Urbina, D. Esteve Quantronics Group, SPEC, CEA Saclay, France*presently: Institute of Physics, PAN, Warsaw

L. Bretheau

Q. Le Masne

D. Esteve

C. Urbina

H. Pothier

MOTIVATION• Josephson effect in superconducting weak

links – unified approach

• Spectroscopy of Andreev Levels

• Andreev Qubit

S SIL R

L R

tS SL R

E()

-EA

+EA+D

-D

0

ANDREEV REFLECTION

COUPLING OF eh AND h$

D

D

for E

a E, 1

Earg a E, arccos

SN

N-S interface ,a E

PHASE-BIASED SHORT, BALLISTIC SINGLE CHANNEL

L x

p arg , arg , 0 mod 2R La E a E

Fabry-Perot resonator

L R

L R

, La E , Ra E

t1

ANDREEV BOUND STATESin a short ballistic channel (t1 )

Andreev spectrumE()

2pp

+D

-D

0

E→

E←

D cos 2E

2 resonances

E

+D

-D

0 p 4

t= 1

L R

ANDREEV BOUND STATESin a short reflective channel (t1 )

tD 21 sin 2AEFurusaki, TsukadaC.W.J. Beenakker (1991)

E()

-EA

+EA+D

-D

0tD 2 1

2p

Andreev spectrumt< 1

Central prediction of the mesoscopic theoryof the Josephson effect

E

+D

-D

0 p 4

SUPERCONDUCTING WEAK LINKS

S SIL R

Tunnel junction:N infinityt->0

L R

tS SL R

Atomic contact:N ~ 10t< 1

J 0I I sin

N – number of transmission channelst- transmission

Current phase-relation

= L - R

Weak link = ensamble of independent transmitting channels,each characterized by transmission t(Landauer picture)

Iac() = ?

FROM ANDREEV BOUND STATESTO SUPERCURRENT

E()

-EA

+EA+D

-D

0

AI

p

2p

Current-phase relation

Ground state :

0

1( )AAE

I

Current – phase relation…

0

1( )AAE

I

…is a probe of a configuration of Andreev bound states

p

E()

+D

-D

0

tD 21 sin 2AE

TOWARDS ANDREEV QUBITS

Chtchelkatchev and Nazarov, PRL (2003)

Use quasiparticle (spin ½) states

E()

-EA

+EA+D

-D

02p

Zazunov, Shumeiko,Bratus’, Lantz and Wendin, PRL (2003)

Use even states

ATOMIC CONTACT = SIMPLEST WEAK LINK

fabrication & characterization

IS SV

1 atom contact = few conduction channels (Al: 3)Stable system

Can be completely characterized

2 µm

insulating layer counter-

support

Flexiblesubstrate

metallic film pushing rods

MICROFABRICATED BREAK-JUNCTIONS

PIN code of the atomic contact

Scheer et al. PRL 1997

Current bias in not enough…

Atomic Squid…

b JJ ACI I I

JJIor

V

IAC

p

0

2

…allows to determine channels transmissions…

IbI

V

measurement( )I V

transmissions {ti}

OPEN

…and impose phase on atomic contact

“Strength” of the weak link~ critical current

( )I measurement

IJJ >> IAC

Ib

SHORT

b JJ ACI I I

JJIorIAC

Ib

V

)2

(0 p AC

JJsw III

0

2

p

switching

retrapping

Switching of the Atomic Squid

Ib Pulse height

V

time

time

tp Tr

N

Tr=20µstp=1µsN=5000

usually Sw

itchi

ng

prob

abili

ty

Ib (nA)

P « s curve »

SWITCHING MEASUREMENTS

-400 -200 0 200 400-1000

-500

0

500

1000

Ib (nA)

V (µV)

<Isw>Supercurrent branch

NnPsw

n

Flux Modulation pattern for ATOMIC SQUID= I() of the atomic contact

0.0 0.5 1.0

480

520

560

Sw

itchi

ng c

urre

nt [n

A]

magnetic flux [/0]

I0-switching current of junction alone

When SQUID switches, phase across JJ is approx. the same independently of applied magnetic flux => interference pattern is current-phase relation of atomic contact

)2

(0 p AC

JJsw III

The ground Andreev state is well-known…

Theses in Quantronics:M. Chauvin,

B. Huard,Q. Le Masne

Della Rocca et al., PRL 2007

P (Ib,)

A vertical cut is an s-curve

P = 0

P = 1

P1

0

s = Ib/I0I0 - critical current of JJ alone

Switching probability map with normal leads

SAMPLE

Sample design

antenna

bias line

designed to be 50W at T < 1K

e-beam lithography

T=40mK,Period= 20µs

t={0.95, 0.445, 0.097}

Switching probability map with superconducting electrodes

0.80 0.85 0.90 0.95 1.000.0

0.2

0.4

0.6

0.8

1.0

= 2

= 3

.05

rad

Psw

s

= 1

= 0

.62

rad

j1 j2timetp Tr

N

Height of plateau is period dependent => some relaxation going on in the system

0,80 0,85 0,900,0

0,2

0,4

0,6

0,8

1,0

P sw

s

P1(Ib)

P2(Ib)

pP1(Ib)+(1-p)P2(Ib)

Switching curve with prepulse

After switching, system is where we expect it to be with probability p

{0.45 , 0.10}

{0.95, 0.45 , 0.10}Erase memory of the previous history before each measurement:

1

0

1.3

delay

~ 0.1µs

1ms

« prepulse »

0.80 0.85 0.900.0

0.2

0.4

0.6

0.8

1.0

Psw

s

Blocking the most transmitting channel

{0.95 , 0.45 , 0.10}

{0.45 , 0.10}

QUASIPARTICLES IN A SUPERCONDUCTINGPOINT CONTACT

E

D

-D

0

Ground state 1-qp states

energy 0 DAenergy > -E + Aenergy E

Aenergy E

EA

-EA

2 qps

E()

+D

-D

0 AE

AE

Excitation picture

All electrons paired The smallest excitationbreaking parity= one unpaired quasiparticle

Excited Cooper pair

Two scenariosQP

E

nQP

1.

2.E

nQP

Weight = p

Weight = 1 - p

Channel switched off

Channel switched on

Switching probability is the weighted average of these 2 scenarios.

Initial state

Modulation curves on different contacts

{1,0.7,0.24,0.24,0.06}AC3

{1,0.072,0.072}AC1

{0.998,0.56,0.124}AC2

The most transmitting channel is sometimes switched off

1QP STATE RELAXATION MEASUREMENTS

0,76 0,78 0,80 0,82 0,84 0,86 0,880,0

0,2

0,4

0,6

0,8

1,0

P sw

1 µs 580 µs

s

0 100 200 300 400 500 6000,65

0,70

0,75

0,80

0,85

P0

waiting time (µs)

TR = 172 µs

P=0.815

Current line

waiting time0

Ib

TR() Pinf()

Flux line

i

w Phase across contacti

A few 100ms relaxation time

T=29mK

Symmetry around pMonotonous behaviour

{1,0.07,0.07}

1

10

100

T R(

µs)

-0.6p 0 0.6p phase across atomic contact

T=29mK

Relaxation as a function of phase across Atomic Contact for different transmissions

-0.9p -0.6p -0.3p 0.0p 0.3p 0.6p 0.9p0.75

0.80

0.85

0.90

0.95

1.00

{0.85,0.22,0.22}

p

p

{0.74,0.01}

{1,0.07,0.07}

{0.96,0.03,0.03}

1

10

100

{0.85,0.22,0.22}

{0.96,0.03,0.03}{1,0.07,0.07}

{0.74,0.01}

T R(µ

s)

200

-1,00 -0,75 -0,50 -0,25 0,000,75

0,80

0,85

0,90

0,95

1,00

{0.96,0.03,0.03}

{1,0.07,0.07}

{0.74,0.01}

p

Eground / D

{0.85,0.22,0.22}

Energy threshold for relaxation

21 sin 2 DE t

1

10

100

200

{0.74,0.01}

T R(µ

s)

{0.85,0.22,0.22}

{1,0.07,0.07}

{0.96,0.03,0.03}

E()

E-

2pp

+D

-D

0

Relaxation instantaneous only for Andreev Bound states with energies bigger than 0.5 D~25GHz ~1K

-1,00 -0,75 -0,50 -0,25 0,000,75

0,80

0,85

0,90

0,95

1,00

{0.96,0.03,0.03}

{1,0.07,0.07}

{0.74,0.01}

p

Eground / D

{0.85,0.22,0.22}

Energy threshold for relaxation

1

10

100

200

{0.74,0.01}

T R(µ

s)

{0.85,0.22,0.22}

{1,0.07,0.07}

{0.96,0.03,0.03}

E

nQP

E

nQP

D/2D

WHY?

Possible explanation

E

nQP

E

nQP

D/2D

hn ~ D/2

hn

Conclusions• Atomic contacts with tunable transmissions• Atomic Squid to measure current-phase relation of atomic contact

with switching measurements - for ground Andreev bound states excellent agreement with theory

• No evidence of excited Andreev state in 2 different experiments (switching measurements, coupling to resonator )

• Quasiparticle poisoning => disappearence of the most transmitting channel;

• long relaxation for Andreev Cooper pair binding energies smaller than 0.5D,sharp cut off for binding energies bigger than 0.5D?

• Dispersive measurements of resonant frequency of resonator + atomic squid

• Trials to observe avoided level crossing (atomic contact embedded in resonator)

• Current Status: Josephson Junction spectroscopy of Atomic Squid – observed avoided level crossing PLASMA FREQUENCY – ANDREEV GAP

1

10

100 29mK 66.5mK 101mK 129mK 150mK 168mK 184mK 202mK 214mK

T R(µ

s)

{1,0.07,0.07}

Temperature dependence

-0.6p -0.3p 0.0p 0.3p 0.6p0.75

0.80

0.85

0.90

0.95

1.00

p

p

Does excited Andreev state exist?(OPTIONAL)

Sample design

antenna

bias line

designed to be 50W at T < 1K

e-beam lithography

Capacitor + inductive lines

inductive lines, 900nm wide, 70 + 54 nm thick Al

680µm

10µm gap140µm

antenna (5µm wide short of CPW)

Capacitor C = 60 pF

Ltotal = 1.8nH

Andreevmon (or Andreevnium)

Electromagnetic environment is important

C

R IB

bias line

RF line

VB

L

n A1

1Re Z

T

Trials to observe excited Andreev state

Peak position is frequency-dependent

I

10.50/2p

Expected

Andreev Qubit in cavity

Weak coupling

strong coupling regime

VAC in

VAC out

Cavity Quantum Electrodynamics

Let 2 level system interact with resonator

avoided level crossingCoherent exchange of energy between resonator and artificial atom

Andreev Gap

E0=-Ea

E1=Ea

0-D

2pp

0

E()

Bare Resonator eigenfrequency

0|| resonator

1|0| ba

Interaction “on”

Interaction “off”Red – expected position of resonance

{0.95, 0.94, 0.60, 0.34, 0.30, 0.29, 0.27, 0.26, 0.24, 0.2}

2 CHANNELS POISONING

0.60 0.65 0.70 0.75 0.800.0

0.2

0.4

0.6

0.8

1.0

Psw

s

340 360 380 400 420 4400.00.20.40.60.81.0

Ib nAP

{0.957, 0.948, 0.601, 0.344, 0.295, 0.291, 0.27, 0.262, 0.242, 0.2}

Pollution of 2 channels

All channels

2 channels blocked

1 channel blocked

49/19

Atomic SQUID in cavity

460 480 500 5200.0

0.2

0.4

0.6

0.8

1.0

P

Ib (nA)

-0.61 x 2p -0.53 x 2p -0.44 x 2p -0.35 x 2p -0.26 x 2p -0.17 x 2p -0.09 x 2p no flux pulse

Flux pulse cleans excited Andreev state

Flux line

Vfluxbig enough

Current line

period

period

delayRF line

MULTIPLE CHARGE TRANSFER PROCESSES

eV

I

Blonder, Tinkham, Klapwijk (‘82)

2D / 12D / 22D / 3

VI

t

S S

52/19

S S

Atomic contact

few channels, {ti} tunableAl film

2 µm

Δx

pushing rod

counter-support

Elastic substrateΔz

i ii

I I{ , ,} t t {ti} measurable

53/19

QUASIPARTICLES IN A BULK SUPERCONDUCTOR

E

D

-D

0

Ground state 1-qp states 2 qps

Denergy > Denergy > 2energy 0

QUASIPARTICLES AND SUPERCURRENT IN A SUPERCONDUCTING POINT CONTACT

E()

+D

-D

0 AE

AE

AI

p

0i

0

1( )AAI

E

Lowest-lying 1-qp excitations

p

( ) 0AI

0

1( )AAI E

AI

p

0i

Aenergy E energy 0 DAenergy > -E + Aenergy E

Ground state 1-qp state Excited singlet

CORRELATED SWITCHING EVENTS

0 20 40 60 80 1001

10

100

# of

occ

uren

ces

D t / Tr

V(t)

0 5000 10 000 15 000 20 000

Need a ‘’reset’’ between pulses

V(t)

MEASURING THE SWITCHING PROBABILITY

1µs

sI0

swPNn

meast

hold

Vb(t)/Rb

pulsesN

eventsn

V(t)

MEASURING THE SWITCHING PROBABILITY

Dt

1µs

1.3 sI0

sI0

prepulse (reset)meast

hold

Vb(t)/Rb

pulsesN

eventsn

Uncorrelated switching events

QP

Reaching 1QP odd state

E1=0

E0=-Ea

E2=E

a

50GHzD

0-D

2pp

0

E()

τD 2 1

Ground state

1QP state (x2)

2QP state

1

0

2 I0=Ia

I2=-I

a

0

2pp

0

I()

I1=0

for Al

0.80 0.85 0.900.0

0.2

0.4

0.6

0.8

1.0

Psw

s

1

0

E

nQP

0

1

2

0.00 0.25 0.50 0.75 1.00

1

10

100

T1 (

µs)

0.0

0.1

0.2 {0.994, 0.10, 0.10}{0.96, 0.03, 0.03}{0.91, 0.62, 0.15}{0.85, 0.22, 0.22}{0.74, 0.01}

p

EA / D

/p

RELAXATION VERSUS ANDREEV ENERGY