THE ANDREEV QUBIT. Landry BRETHEAU Quantronics Group, CEA-Saclay, FRANCE now at MIT, Cambridge, USA

Transcription

1 THE ANDREEV QUBIT C. JANVIER L. TOSI Ç. GIRIT M. STERN H. POTHIER M. GOFFMAN D. VION P. BERTET P. JOYEZ D. ESTEVE C. URBINA Landry BRETHEAU Quantronics Group, CEA-Saclay, FRANCE now at MIT, Cambrid, USA

2 TUNNEL JOSEPHSON JUNCTION-BASED QUBITS 2 Josphson junction Q -Q E 2> 1> > ω 1 φ,q = i! H = E J cos + Q2 2C Suprconductin è no dissipation Anharmonic è Us 2 lowst lvls as a qubit

3 JOSEPHSON EFFECT IN ALL TYPES OF WEAK LINKS 3 I I SIS nanotub I I S F S S N S brid I()

4 THE FERMIONIC SIDE OF JOSEPHSON EFFECT 4 wll-transmittin phas-biasd Josphson junction φ +E A H = E A () σ z E A π ANDREEV BOUND STATES

5 JOSEPHSON EFFECT FROM THE MESOSCOPIC VIEW 5 S Wak link S Landaur channls { } τ i Kulik and Oml yanchuk 1975, Furusaki and Tsukada 1991, Bnakkr 1991

6 SHORT SINGLE CHANNEL 6 Short, sinl channl τ L < ξ

7 SHORT SINGLE CHANNEL 7 Short, sinl channl τ L < ξ = E E E Δ Δ Δ -Δ -Δ -Δ

8 THE ANDREEV BOUND STATES 8 Short, sinl channl τ L < ξ I E E E Δ Δ Δ -Δ -Δ -Δ

9 A LOCALISED «ANDREEV COOPER PAIR» 9 Short, sinl channl τ L < ξ E E E Δ Δ Δ -Δ -Δ -Δ

10 PHASE DEPENDENCE OF ABS 1 E A =Δ τ ( ) 2 1 sin 2

11 THE ANDREEV QUANTUM DOT 11

12 FROM ABS TO STANDARD JOSEPHSON EFFECT 12 τ i = 1 n 1 channls SIS E n A i = 1 with τi τi =Δ 1 + cos 4 4 E A E J = E Δ = 4 J cos n i = 1 τ i : cos Only considr th round stat, not th xcitd stat

13 ANDREEV QUANTUM DOT 13 Δ o -Δ π 2π A TWO LEVEL SYSTEM AS LONG AS PARITY IS CONSERVED A. Zazunov t al, PRL (23) N. M. Chtchlkatchv and Yu. V. Nazarov, PRL (23)

14 SPECTROSCOPY OF ANDREEV STATES 14 Silvr wir Lsuur, PRL 28 Atomic Contact Brthau, Natur 213 InAs nanowir Chan, PRL 213 Carbon Nanotub Pillt, Natur Physics 21

15 COHERENT MANIPULATION OF ANDREEV QUBIT 15 Δ 2Δ o hf = 2 E (, τ ) A A nry 2Δ 1 τ -Δ π 2π π 2π In a HYBRID cqed ARCHITECTURE

16 ATOMIC CONTACTS WITH BREAK JUNCTIONS 16 2 µm Fw conduction channls (Al: 3) Stabl Mchanical control of in situ { } τ i

17 PHASE BIASING WITH AN ATOMIC RF-SQUID 17 L om = L A φ = 2π φ φ φ = h 2 Atomic rf-squid

18 ATOMIC RF-SQUID COUPLED TO A COPLANAR MICROWAVE RESONATOR 18 IN OUT f C f R! 1GHz M φ RESPONSE DEPENDS ON STATE OF ANDREEV SYSTEM

19 EXPERIMENTAL REALIZATION 19 Nb 2 µm 5 µm Al loop

20 EXPERIMENTAL SETUP 2 I masurmnt f! f R Q driv f 1 Nb 2 µm T! 3 mk 5 µm Al loop

21 CW RESONATOR CHARACTERIZATION 21 f IN A OUT R (db) -1-2 f R! GHz Q tot! 22 Q xt! f (GHz) 1

22 GETING ONE-ATOM CONTACTS 22 ν R φ opnnin Closd loop Opn loop

23 SINGLE-TONE SPECTROSCOPY 23 f 1.16 R (db) f (GHz) 1.14 f R MHz.92π π 1.8π H = hf R (a + a ) + hf A 2 σ z + h(aσ + + a+ σ - )

24 TWO-TONE SPECTROSCOPY 24 A 3 f R χ 2 1 f 1 f 3 f R + χ f A 2 1 f 1 (GHz) A (mv) 2-2 f R 13µs driv 1µs masurmnt f A hf A = 2Δ 1 τ sin 2 ( / 2) 8 with τ = Δ = 44.3 GHz.92π.96π π 1.4π 1.8π

25 SINGLE-SHOT DETERMINATION OF STATE 25 Dnsity plot masurmnts at =π in absnc of driv Q (V).1. o I (V) n photons! 3 NUMBER OF POINTS IN EACH CLOUD GIVES POPULATION OF EACH STATE

26 COHERENT MANIPULATION AT d=p 26 f = 1 fa Rabi oscillations Q (V).1. o o counts I (V) I (V).5 B r populations Puls π puls duration (ns) 8 1

27 RELAXATION TIME AT =π 27 Rlaxation (T 1 ).5 π dlay population T T 1 = 4 µs 1 = dlay aftr π puls (ns)

28 A f 1 (GHz) D I, Q (V) RELAXATION AWAY FROM =π π.96π π 1.4π 1.8π f A A (mv) f R B C Q (V) f (GHz) < E Γ 1 (MHz) f R 1.12 o 1 no driv I (V).1 Purcll limitation whn f A clos to f R.92π π 1.8π o π puls I (V) R (db) counts.96π π 1.4π Empirical phas-indpndnt rat of 18 MHz Tim (µs) o A priori not du to phonons QP? offst by hand A. Zazunov t al., PRL 9, 873 (23) F. Kos t al. PRB 87, (213) D. G. Olivars t al., PRB 89, 1454 (214)

29 COHERENCE TIMES 29 Ramsy frins r B Δf dlay π/2 π/2 population T * 2 = 38 6 ns intrval btwn π/2 pulss (ns) 8 Hahn cho r B π/2 dlay π π/2 population T2 = 565 ns. 1 2 intrval btwn π/2 pulss (ns) 3

30 SPECTRAL LINEWIDTH AWAY FROM =π 3 C< 15 Dcohrnc rat FWHM (MHz) π π 1.4π At =π à Transmission nois Mchanical vibrations/atomic motion 1/f nois ~ / Hz at = π à corrspond to 1 5 in τ!!! Away from π à Flux nois 1/f nois ~ 5µ φ / Hz Whit flux nois 48 n φ / Hz à unknown oriin

31 p FW p.1 A f1 5 COMPARING CONTACTS D T1 = 4 µs dlay aftr π puls (µs) FB population T2* = 38 ns T1 = 8.4 µs intrval π/2 pulss dlaybtwn aftr π puls (µs) (ns) B D D population 5.32 * = 57 ns.9986 M=4.1 MHz 5 π π.96π 1 BB G G π π 1.4π1.4π T1=1.3 µs 8.4µsµs T1T= = T2 =T565 ns 2 = 565 ns 2 4 dlay aftr π puls (ns) aftr 2(µs) dlay 1π πpuls 2 dlayaftr puls (µs) C intrval btwn π/2 pulss (ns) intrval btwn π/2 pulss (µs)(µs) pulss (ns) intrval btwn π/2 intrval btwn π/2 pulss CC G.4 DD population population population 5 * ns FWHM=14 FWHM=14 T2*MHz =TMHz = 38 ns f (GHz) f(ghz) 4 π fπ 1.4π 1 (GHz) MHz π1 1.4π dlay aftraftr π puls (µs)(µs) dlay π puls FWHM=4.1 MHz AA.6.3 F F.2.6 E f1 (GHz) population τ population population population population population Γ1 (MHz) 7.94 B.1.1 T2T=1= µs µs * * = *2 =57 T2T*2T= nsnsns µsµs T2T= = puls duration (ns) intrval btwn π/2 pulss (ns) intrval btwn π/2 pulss (ns) intrval btwn π/2 pulss (µs).5 E intrvalbtwn btwnπ/2 π/2pulss pulss(µs) (µs) intrval T2* = 188 ns T2=78 ns π puls 6 8 dlay aftr (ns) intrval btwn π/2 pulss (ns) intrval btwn π/2 pulss (ns)

32 QUANTUM JUMPS AT =π 32 D < I, Q (V).92π.96π π 1.4π 1.8π.1. o o f A =6.57 GHz n photons! Hiddn Markov modl toolbox (rats in khz) M. Grnfld, t al., PLoS ONE (212) Tim (µs) 2 2 o 28 3 o Zirsky t al., PRL 16, 2573 (211)

33 CONCLUSIONS 33 Cohrnt manipulation of a sinl localizd Coopr pair Diffrnt contacts 3 GHz< f A (τ,π) < 8 GHz Liftim of xcitd stat : T 1 ~ 1-14 µs Cohrnc tim of suprpositions: T 2 * ~ 1-18 ns T 2 ~ µs No clar dpndnc on τ LIMITATION OF LIFETIME? Parity chans Poor control on th nvironmnt? SOURCES OF DECOHERENCE? Transmission nois Stup vibrations / Atomic motion Flux nois Andrv quantum dots à tst-bd to invstiat QP dynamics Multipl Andrv qubits in multichannl contact? Andrv qubit with othr systms? Manipulatin spin à Majorana stats? Zirsky t al., PRL 16, 2573 (211) Janvir t al., Scinc (215) Brthau t al., Natur, 499, 312 (213) Brthau t al., PRX (213) Brthau PhD thsis, on Quantronics wbsit

34 IT S A TEAM WORK! Ç. GIRIT P. SENAT 34 P. ORFILA C. JANVIER P. BERTET M. STERN D. ESTEVE P. JOYEZ L. TOSI L. BRETHEAU H. POTHIER D. VION M. F. GOFFMAN C. URBINA Quantronics Group, CEA Saclay, Franc