Coherent Quantum Phase Slip

Oleg Astafiev

NEC Smart Energy Research Laboratories, Japanand

The Institute of Physical and Chemical Research (RIKEN), Japan

RIKEN/NEC: O. V. Astafiev, S. Kafanov, Yu. A. Pashkin, J. S. TsaiRutgers: L. B. Ioffe Jyväskylä: K. Yu. ArutyunovWeizmann: D. Shahar, O. Cohen

Coherent quantum phase slip, Nature, 484, 355 (2012)

Introduction. Phase slip (PS) and coherent quantum phase slip (CQPS)

Duality between CQPS and the Josephson Effect CQPS qubits Superconductor-insulator transition (SIT) materials Experimental demonstration of CQPS

Outline

Very fundamental phenomenon of superconductivity (as fundamental as the Josephson Effect) Exactly dual to the Josephson Effect

• Flux interference (SQUID) Charge interference• Charge tunneling Flux tunneling

Applications Quantum information

• Qubits without Josephson junctions Metrology

• Current standards (dual to voltage standards)

Coherent Quantum Phase Slips (CQPS)

Flux tunnelingFlux tunneling

SpaceSpace SpaceSpace

SuperconductorSuperconductor

SuperconductorSuperconductor

SuperconductingSuperconducting WireWire

SuperconductingSuperconducting WireWire

Cooper pair tunnelingCooper pair tunneling

SuperconductorSuperconductor SuperconductorSuperconductor

SpaceSpace

SpaceSpaceInsulating Insulating

BarrierBarrierInsulating Insulating

BarrierBarrier

2e2e

What is phase slip?

Josephson Effect: tunneling of Cooper pairs

CQPS: tunneling of vortexes (phase slips)

Superconductivity does not exist in 1D-wires:

Thermally activated phase slips

I

V

PSe

h

teV

22

Phase-slips at T close to Tc are known for long time

I

VR

Width coherence length

Phase can randomly jump by 2

Thermally activated phase slips

Quantum phase slip

V

T

kT

Thermally activated and Quantum phase slip

Signature of QPS?

At T = 0: Phase slips due to quantum fluctuations(?)

Are phase slips possible at T = 0?

Incoherent quantum process coherent quantum process

Quantum Phase Slip (QPS) Coherent QPS

Spontaneous emission:Open space infinite number of modes

I

Dissipative transport measurements:P = IV

Coherent coupling to a single mode:Resonator, two-level system single mode

Nanowire in a closed superconducting loop

incoh <

Duality between CQPS and the Josephson Effect

Josephson junction Phase-slip junction

cos0JJ EE qSS EE cos0

02

22

0

~21

JJ

J

EE

L

02

22

~2

21S

q

S

k

EE

eC

The CQPS is completely dual to the Josephson effect

Z Y L C 0 2e

0

2

e

q

2

2

Mooij, Nazarov. Nature Physics 2, 169-172 (2006)

Exact dualityExact duality

Josephson Current: Ic sinKinetic Inductance: (2Ic cos)-1

Shapiro Step: V = n

CQPS Voltage: Vc sin(2nq)Kinetic Capacitance: 2e(2 Vc cos(2nq))-1

Shapiro Step: I = n2e

= Phase across junction = Phase across junction nq = normalized charge alongthe wire

nq = normalized charge alongthe wire

Mooij, Nazarov. Nature Physics 2, 169-172 (2006)

IICC

VVCC

Shapiro Step

Shapiro Step

[nq,] = -i

Supercurrent CQPS voltage

NNNNE

NNEH SN 11

2

Flux is quantized: N0

A loop with a nano-wire

Hamiltonian:

L

NE extN 2

20

The loop with phase-slip wire is dual to the charge qubit

BSext

(PS qubit proposed by Mooij J. E. and Harmans C.J.P.M ）

Magnrtic energy:

Phase-slip energy: ECQPS

E

Degeneracy

>> kT

0 2 31 4

The Phase-Slip Qubit

ext

EL

>> ECQPS

ELCQPS qubit:

0

1 0

1

L

NE extN 2

20

NNNNE

NNE

H JN 1122

Charge is quantized: 2eN

Duality to the charge qubit

Hamiltonian:

C

qeNE extN 2

2 2

The loop with phase-slip wire is dual to the charge qubit

EJ

Reservoir

BoxC

Cg

Vg

ggext CVq

Cg

L C 0 2e extqext

Loops of usual (BCS) superconductors (Al, Ti) did not show qubit behavior BCS superconductors become normal metals, when superconductivity is suppressed Special class of superconductors turn to insulators, when superconductivity is suppressed Superconductor-insulator transition (SIT) High resistive films in normal state high kinetic inductance

Choice of materials

R

RaE Q

S exp

Superconductor-insulator transition

(SIT)

InOx, TiN, NbN

Requirements: high sheet resistance > 1 k

n

k

RL

High resistance high kinetic inductance

107

106

105

104

103

102

101

0 5 10 15

T (K)

Sh

ee

t re

sist

an

ce R

□ (

)

The materials demonstratingSIT transition are the most promising for CQPS

40 nm

Es

N0 (N+1)0

E

ext(N+1/2)0

Gold ground-planes InOx

5 m

0.5 mmInOx

MW in MW out

Amorphous InOx film:R□ = 1.7 k

The device

Step-impedance resonator:High kinetic inductance

Measurement circuit

NetworkAnalyzer

-20 dB

-20 dB

Isolator

Isolator

resonator

Phase-slip qubit Coil

Low

pas

s fil

ters

output

input4.2 K

1 K

40 mK

Transmission through the step-impedance resonator

1st

2nd

Z0 Z1

Z0

Current field the resonator

Current amplitudes: maximal for evenzero for odd modes

6 7 8 9 10 11 120.0

0.5

1.0

t (a.

u.)

f (GHz)

34

5250 MHz

-0.10 -0.05 0.00 0.05 0.100.7

0.8

0.9

1.0

0.0

0.1

0.2

t

Bext

(mT)

arg

(t)

B

Z1 >> Z0

Transmission at 4th peak

5.0 5.5 6.0-6

-4

-2

0

arg

(t)

(m

rad

)

f (GHz)

f = 260 MHz

0

-5

arg

(t)

(mra

d)

Two-tone spectroscopy

We measure transmission through the resonator at fixed frequency fres

Another frequency fprobe is swept

The fitting curve: Ip = 24 nA, ES/h = 4.9 GHz

Current driven loop with CQPS

Transitions can happen only when ES 0

M

Ip

I0

|1

|0

tacosa

tIMIE

H axpxS

z cos

22 0

a

Sp

EIMI

0

zH 2int

RWA:

22sa E

tH axza

cos22

ES

The result is well reproducibleThree identical samples show similar behaviorwith energies 4.9, 5.8 and 9.5 GHz

After “annealing” at room temperature InOx becomes more superconducting.The samples were loaded three times with intervals about 1 months. Es is decreased with time.

00.0 0.5 1.0

0

20

40

60

80

E/h

(G

Hz)

ext

/

fprobe

2 fprobe + fres

(3-photons)

h

EI

hE

sp22

2

/

fprobe + fres

(2 photons)

Wide range spectroscopy

Linear inductance!

Decoherence

5.0 5.5 6.0-6

-4

-2

0

arg

(t)

(m

rad

)

f (GHz)

f = 260 MHz

Gaussian peak low frequency noise

k

kSkS e

qiEE

2

2exp

Total PS energy:

Potential fluctuations along the chain of Josephson junctions leads to fluctuations of energy and decoherence

Potential equilibration (screening) in the wire? Mechanism of decoherence?

L 1.6 nH/sq

NbN thin filmsR 2 kIn MW measurements Tc 5 K

Many qubits can be identified

20 different loops with wires of 20-50 nm width

General tendency: the higher resistance, the higher ES

NbN qubitsf (

GH

z)

Tra

nsm

issi

on a

mp

litud

e

Conclusion

We have experimentally demonstrated Coherent Quantum Phase Slip

Phase-slip qubit has been realized in thin highly resistive films of InOx and NbN

Mechanism of decoherence in nano-wires is an open question