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Coherent quantum phase slip, Nature, 484, 355 (2012). RIKEN/NEC: O. V. Astafiev, S. Kafanov, Yu. A. Pashkin, J. S. Tsai Rutgers: L. B. Ioffe Jyv ä skyl ä : K. Yu. Arutyunov Weizmann: D. Shahar, O. Cohen. Coherent Quantum Phase Slip. Oleg Astafiev

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slide1

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

RIKEN/NEC: O. V. Astafiev, S. Kafanov, Yu. A. Pashkin, J. S. Tsai

Rutgers:L. B. Ioffe

Jyväskylä: K. Yu. Arutyunov

Weizmann: D. Shahar, O. Cohen

Coherent Quantum Phase Slip

Oleg Astafiev

NEC Smart Energy Research Laboratories, Japanand

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

slide2

Outline

  • 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
slide3

Coherent Quantum Phase Slips (CQPS)

  • 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)
slide4

What is phase slip?

Cooper pair tunneling

Flux tunneling

Space

Superconductor

Superconductor

Superconductor

Space

Space

Superconducting

Wire

Insulating

Barrier

Space

Superconductor

2e

F0

Josephson Effect: tunneling of Cooper pairs

CQPS: tunneling of vortexes (phase slips)

slide5

Thermally activated phase slips

Superconductivity does not exist in 1D-wires:

Width  coherence length 

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

V

Phase can randomly jump by 2

I

slide6

Thermally activated and Quantum phase slip

Thermally activated phase slips

Are phase slips possible at T = 0?

V

Signature of QPS?

T

Quantum phase slip

kT 

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

slide7

Quantum Phase Slip (QPS)  Coherent QPS

Incoherent quantum process  coherent quantum process

incoh< 

Spontaneous emission:

Open space  infinite number of modes

Dissipative transport measurements:

P = IV

I

Coherent coupling to a single mode:

Resonator, two-level system  single mode

Nanowire in a closed superconducting loop

slide8

Duality between CQPS and the Josephson Effect

Mooij, Nazarov. Nature Physics2, 169-172 (2006)

Josephson junction

Phase-slip junction

Z  Y L  C 0  2e

The CQPS is completely dual to the Josephson effect

slide9

Exact duality

Mooij, Nazarov. Nature Physics2, 169-172 (2006)

[nq,f] = -i

nq = normalized charge alongthe wire

f = Phase across junction

CQPS Voltage: Vc sin(2pnq)

Kinetic Capacitance: 2e(2p Vc cos(2pnq))-1

Shapiro Step: DI =n2en

Josephson Current: Ic sinf

Kinetic Inductance: F0(2pIc cosf)-1

Shapiro Step: DV =nF0n

Shapiro Step

Shapiro Step

IC

VC

Supercurrent

CQPS voltage

slide10

A loop with a nano-wire

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

Flux is quantized: N0

Hamiltonian:

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

the phase slip qubit
The Phase-Slip Qubit

Degeneracy

1

0

-

-

-

-

EL

>> ECQPS

+

+

+

+

1

0

E

0

1

2

3

4

ext

Magnrtic energy:

EL

>> kT

ECQPS

Phase-slip energy:

CQPS qubit:

slide12

Duality to the charge qubit

L  C 0  2e extqext

Cg

Cg

Box

C

Vg

EJ

Reservoir

Charge is quantized: 2eN

Hamiltonian:

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

slide13

Choice of materials

  • 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
slide14

107

106

105

Sheet resistance R□ ()

104

103

102

101

0

5

10

15

T (K)

Superconductor-insulator transition(SIT)

Requirements: high sheet resistance > 1 k

InOx, TiN, NbN

High resistance  high kinetic inductance

The materials demonstratingSIT transition are the most promising for CQPS

slide15

The device

N0

(N+1)0

E

Amorphous InOx film:

R□ = 1.7 k

Es

ext

(N+1/2)0

MW in

Gold ground-planes

InOx

MW out

0.5 mm

InOx

Step-impedance resonator:

High kinetic inductance

40 nm

5 m

slide16

Measurement circuit

Network

Analyzer

output

input

4.2 K

1 K

Low pass filters

Isolator

-20 dB

40 mK

-20 dB

Isolator

resonator

Phase-slip qubit

Coil

slide17

B

Transmission through the step-impedance resonator

Z0

Z0

Z1

Current field the resonator

2nd

Current amplitudes: maximal for evenzero for odd modes

Z1 >> Z0

1st

Transmission at 4th peak

4

3

5

250 MHz

slide18

Two-tone spectroscopy

We measure transmission through the resonator at fixed frequency fres Another frequency fprobe is swept

f =

260 MHz

arg(t) (mrad)

0

-5

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

slide19

Ip

M

I0

Current driven loop with CQPS

ES

|1

|0

RWA:

Transitions can happen only when ES 0

slide20

The result is well reproducible

Three identical samples show similar behaviorwith energies 4.9, 5.8 and 9.5 GHz

After “annealing” at room temperature InOxbecomes more superconducting.

The samples were loaded three times with intervals about 1 months. Es is decreased with time.

slide21

=

D

E

/

h

(

)

2

+

2

d

F

2

I

E

p

s

=

h

Wide range spectroscopy

2 fprobe + fres

(3-photons)

fprobe + fres

(2 photons)

fprobe

Linear inductance!

slide22

Decoherence

Gaussian peak 

low frequency noise

f =

260 MHz

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?

slide23

NbN thin films

R 2 k

In MW measurements Tc 5 K

L 1.6 nH/sq

20 different loops with wires of 20-50 nm width

Many qubits can be identified

General tendency: the higher resistance, the higher ES

slide24

NbN qubits

Transmission amplitude

f (GHz)

slide25

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
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