ABSTRACT Quasiparticle Trapping in Andreev Bound States Maciej Zgirski ABSTRACT 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 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)

Quasiparticle Trapping in Andreev Bound States Maciej Zgirski. , L 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 D. Esteve L. Bretheau H. Pothier Q. Le Masne C. Urbina PRL ,106, 257003 (2011)

MOTIVATION Josephson effect in superconducting weak links – unified approach Spectroscopy of Andreev Levels Andreev Qubit S I t S E(d) d -EA +EA +D -D

ANDREEV REFLECTION COUPLING OF eh AND h$ S N N-S interface

PHASE-BIASED SHORT, Ballistic Fabry-Perot resonator SINGLE CHANNEL L < x t =1 fL fR Fabry-Perot resonator

in a short ballistic channel (t =1 ) ANDREEV BOUND STATES in a short ballistic channel (t =1 ) E +D -D t = 1 fL fR Andreev spectrum E(d) d 2p p +D -D E→ E← 2 resonances

ANDREEV BOUND STATES t < 1 in a short reflective channel (t <1 ) Andreev spectrum t < 1 E(d) d -EA +EA +D -D Furusaki, Tsukada C.W.J. Beenakker (1991) Central prediction of the mesoscopic theory of the Josephson effect

SUPERCONDUCTING WEAK LINKS Weak link = ensamble of independent transmitting channels, each characterized by transmission t (Landauer picture) N – number of transmission channels t - transmission Atomic contact: N ~ 1 0 < t < 1 Tunnel junction: N infinity t ->0 t S S I g = gL - gR Current phase-relation Iac(d) = ?

FROM ANDREEV BOUND STATES TO SUPERCURRENT E(d) d -EA +EA +D -D Ground state : Current-phase relation

Current – phase relation… E(d) d +D -D …is a probe of a configuration of Andreev bound states

Towards ANDREEV QUBITS E(d) d -EA +EA +D -D Use even states Use quasiparticle (spin ½) states Zazunov, Shumeiko,Bratus’, Lantz and Wendin, PRL (2003) Chtchelkatchev and Nazarov, PRL (2003)

ATOMIC CONTACT = SIMPLEST WEAK LINK fabrication & characterization V 1 atom contact = few conduction channels (Al: 3) Stable system Can be completely characterized

MICROFABRICATED BREAK-JUNCTIONS insulating layer counter- support Flexible substrate metallic film pushing rods

PIN code of the atomic contact Scheer et al. PRL 1997

Current bias in not enough…

Atomic Squid… or V IAC

…allows to determine channels transmissions… measurement Ib OPEN V I transmissions {ti}

…and impose phase on atomic contact measurement IJJ >> IAC Ib g “Strength” of the weak link ~ critical current SHORT

Switching of the Atomic Squid Ib switching V retrapping or IAC d g

SWITCHING MEASUREMENTS Ib (nA) V (µV) <Isw> Supercurrent branch Ib Pulse height Switching probability Ib (nA) P « s curve » tp Tr time N V time n usually Tr=20µs tp=1µs N=5000

Flux Modulation pattern for ATOMIC SQUID = I(d) of the atomic contact 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 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,j) Switching probability map with normal leads P s = Ib/I0 1 A vertical cut is an s-curve s = Ib/I0 I0 - critical current of JJ alone

SAMPLE

Sample design bias line e-beam lithography designed to be 50W antenna bias line designed to be 50W at T < 1K e-beam lithography

Switching probability map with superconducting electrodes T=40mK, Period= 20µs tp Tr t={0.95, 0.445, 0.097} time N j1 j2 As we increase dead time between pulses plateau gets higher meaning higher probability of finding our contact in the ground state. It suggests that there is some relaxation going in the system. So we are in ground state or in an another state with different probability dependent on dead time between pulses. To avoid playing with conditional probabilities and test the system always in statistically the same state we use prepulse to erase memory and prepare system in the statistically same state (= definite probability of being in the ground state just after switching). Height of plateau is period dependent => some relaxation going on in the system

Switching curve with prepulse {0.95, 0.45 , 0.10} Erase memory of the previous history before each measurement: P1(Ib) pP1(Ib)+(1-p)P2(Ib) ~ 0.1µs 1 1.3 1ms P2(Ib) {0.45 , 0.10} delay « prepulse » After switching, system is where we expect it to be with probability p

Blocking the most transmitting channel {0.45 , 0.10} {0.95 , 0.45 , 0.10}

QUASIPARTICLES IN A SUPERCONDUCTING POINT CONTACT E D -D EA -EA Ground state 1-qp states 2 qps E(d) d +D -D

Excitation picture The smallest excitation All electrons paired breaking parity = one unpaired quasiparticle Excited Cooper pair

1. 2. Two scenarios Initial state QP nQP Weight = p Channel switched on E nQP 2. Weight = 1 - p Channel switched off Switching probability is the weighted average of these 2 scenarios.

Modulation curves on different contacts {1,0.072,0.072} AC1 {0.998,0.56,0.124} AC2 {1,0.7,0.24,0.24,0.06} AC3 The most transmitting channel is sometimes switched off

1QP STATE RELAXATION MEASUREMENTS waiting time Ib Current line Flux line ji jw d Phase across contact di TR(d) Pinf(d)

A few 100ms relaxation time -0.6p 0 0.6p d phase across atomic contact {1,0.07,0.07} T=29mK Symmetry around p Monotonous behaviour

Relaxation as a function of phase across Atomic Contact for different transmissions T=29mK

Energy threshold for relaxation E(d) d E- 2p p +D -D Relaxation instantaneous only for Andreev Bound states with energies bigger than 0.5 D ~25GHz ~1K

Energy threshold for relaxation nQP E nQP D D/2 WHY?

Possible explanation hn E nQP hn ~ D/2 E nQP D D/2

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 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) No evidence of excited Andreev state in 2 different experiments (switching measurements, coupling to resonator ) Current Status: Josephson Junction spectroscopy of Atomic Squid – observed avoided level crossing PLASMA FREQUENCY – ANDREEV GAP

Temperature dependence {1,0.07,0.07}

Does excited Andreev state exist? (OPTIONAL)

Sample design bias line e-beam lithography designed to be 50W antenna bias line designed to be 50W at T < 1K e-beam lithography

Capacitor + inductive lines Andreevmon (or Andreevnium) Capacitor + inductive lines 10µm gap Capacitor C = 60 pF 140µm 680µm inductive lines, 900nm wide, 70 + 54 nm thick Al Ltotal = 1.8nH antenna (5µm wide short of CPW)

Electromagnetic environment is important d g R IB bias line RF line VB L

Trials to observe excited Andreev state 1 0.5 d / 2p Expected Peak position is frequency-dependent

Andreev Qubit in cavity Weak coupling

Cavity Quantum Electrodynamics VAC in VAC out strong coupling regime

Let 2 level system interact with resonator Andreev Gap Bare Resonator eigenfrequency Red – expected position of resonance Interaction “off” Interaction “on” avoided level crossing Coherent exchange of energy between resonator and artificial atom

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

Pollution of 2 channels {0.957, 0.948, 0.601, 0.344, 0.295, 0.291, 0.27, 0.262, 0.242, 0.2} All channels 2 channels blocked 1 channel blocked

Atomic SQUID in cavity

Flux pulse cleans excited Andreev state Flux line Vflux big enough Current line period delay RF line

MULTIPLE CHARGE TRANSFER PROCESSES V I t S Blonder, Tinkham, Klapwijk (‘82) 2D / 3 2D / 2 2D / 1

few channels, {ti} tunable Atomic contact 53/19 S Al film Δx pushing rod counter-support Elastic substrate Δz few channels, {ti} tunable {ti} measurable

QUASIPARTICLES IN A BULK SUPERCONDUCTOR Ground state 1-qp states 2 qps

QUASIPARTICLES AND SUPERCURRENT IN A SUPERCONDUCTING POINT CONTACT Ground state Lowest-lying 1-qp excitations 1-qp state Excited singlet E(d) d +D -D

correlated switching events V(t)  Need a ‘’reset’’ between pulses

MEASURING THE SWITCHING PROBABILITY meast hold 1µs sI0 Vb(t)/Rb V(t)

MEASURING THE SWITCHING PROBABILITY prepulse (reset) meast hold 1µs 1.3 sI0 sI0 Vb(t)/Rb Dt V(t)  Uncorrelated switching events

Reaching 1QP odd state QP nQP E 2QP state 1QP state (x2) Ground state for Al QP E nQP

RELAXATION VERSUS ANDREEV ENERGY