experiments with fluxon...

.

Experiments with

Fluxon ratchet

Edward Goldobin

Dubna Winter School 05.02.2011

Physikalische Institut — Experimentalphysik II, University of Tubingen, Germany

E.Goldobin -- Fluxon ratchet

What is a Ratchet?

Reimann, Phys. Rep. 361, 57 (2002). P. Hänggi, F. Marchesoni, and F. Nori, Ann. Phys. (N.Y.) 14, 51 (2005). P. Hänggi and F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009).

Po

ten

tial

coordinate

random force

Point-like Brownian particle in

asymmetric periodic potential

Aim: to rectify fluctuations


Ratchet effect

Transport

in biological

systems

Classical ratchet system

Separation of macromolecules


What is a Josephson Vortex Ratchet

(JVR)?

M. Beck, et al. Phys. Rev. Lett. 95, 090603 (2005)

Directed motion voltageBand up to 100GHzoverdamped underdampedquantum ratchet

Advantages of “Josephson”

Particle fluxonPotential w(x), h(x), j(x)

Periodic annular LJJ (n periods)

JVR Principle (Pert. theory approx.)

Peculiarities

E. Goldobin, et al. Phys. Rev. E 63, 031111 (2001)

Carapella, PRB 63, 54515 (2001)

Carapella et al., PRL 87, 77002 (2001)

ac current

V

Particle relativistic soliton


Long Josephson junctions

1D model:

)(

11)(

xi

s enx

)(

22)(

xi

s enx

Solutions: 1. linear electromagnetic waves (plasma waves)

1D model:

2. Soliton=fluxon=Josephson vortex

phase field supercurrent


Different approaches to construct

Asymmetric Periodic Potential

Carapella, PRB 63, 54515 (2001)

Carapella et al., PRL 87, 77002 (2001)

Internal modes:

Willis et al., PRE 69, 056612 (2004)PRE 71, 016604 (2005)

Morales-Molina, et al., PRL 91, 234102 (2003)

Asymmetric substrate pot.+symm. drive: move soliton in some dir.

Salerno et al., PRE 65, 25602 (2002); Constantini et al., PRE 65, 51103 (2002)

Constantini, et al., PRL 87, 114102 (2001)


Asymmetric potential

E. Goldobin, et al. PRE 63, 031111 (2001)

x

Potential: w(x) h(x) j(x)

tunability? no yes yes

topo. limits? no yes no

I/H source? no yes yes



JJ width modulation – potential for

fluxon

Non-relativistic approx,

“slow” modulation


Asymmetry due to non-uniform field

cos)( HxH

cos)( 0HxH

H 0

)(2)( 00 xwhxU

• Tunable potential• Topological limitations

h(x)


-8 -6 -4 -2 0 2 4 6 8

-1.0

-0.5

0.0

0.5

1.0

h0

c

with fluxon

w/o fluxon

Simulation

How an injector can create

strongly asymmetric saw-tooth

potential?h(x) 0 l

x 0 l

x,

x0...)(... xasyt

Sinus-Gordon

Iinj

1hx,

asy

U(x0)

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3 with fluxon

without fluxon

I c

[mA

]

Iinj1 [mA]

Experiment

sample C3

6,6m

m

E. Goldobin, et al. Phys. Rev. E 63, 031111 (2001)


M. Beck, et al. PRL 95, 090603 (2005)

For experimentalistsFor theorists

damping (

h(x) potential profile (saw-tooth)

ac amplitude of ac drive

dc dc force (usually =0)

System under investigation:

Relativistic Deterministic JVR

E. Goldobin et al, PRE 63, 031111 (2001) G. Carapella et al., PRB 63, 054515 (2001).

ac current acsin( t) [+ dc]

V

potential h0 Iinj1

fluxon insert

t

One can derive eq. for x0(t) in the PT limit,

assuming rigid fluxon shape.


inserts fluxons R = 70µm, x = 5µm, w = 5µm

asymmeric

Geometry

ac current

V

potential

fluxon insert

M. Beck, E. Goldobin, et al. Phys. Rev. Lett. 95, 090603 (2005)


Insertion of a fluxon ( ): A. V. Ustinov, APL 80, 3153 (2002)

Insertion of fluxon

x

IRU

mA9,3

if 2

2injI

B. Malomed, et al. PRB 69, 64502 (2004)

E. Goldobin, et al. PRB 67, 224515 (2003); PRL 92, 57005(2005)

IL

IL0

2


Quasi-static drive (100Hz)

450 500 550 600

-10

-8

-6

-4

-2

0

Vd

c [µ

V]

Amplitude Iac

[µA]

ALJJ C3:

Iinj1

= 0.2 mA

Iinj2

= 3.9 mA

I-V Characteristic Rectification curve Vdc(Iac)

Asymmetric fluxon steps!

-100 -50 0 50 100

-1.0

-0.5

0.0

0.5

1.0

1.5

I [

mA

]

V [µV]

V0

ALJJ C3:

Iinj1

= 0.1 mA

)cos()(:Apply tItI ac)()(:Measure acacdc IVIV



Ratchet effect vs. potential height

0.6 0.8 1.0 1.2 1.4

-20

-10

0

10

20

Vd

c [

V]

Iac [mA]

Iinj1

= 0.2 mA

Iinj1

= 0.3 mA

Iinj1

= 0.4 mA

Iinj1

= 0.5 mA

Iinj1

= 0.6 mA

ALJJ C3

-4 -2 0 2 4

-1.0

-0.5

0.0

0.5

1.0

Cri

tical curr

ent

I c(I

inj1

)/I c

0

Potential height h0 Iinj1



Ratchet effect vs. driver shape

0.6 0.8 1.0 1.2 1.40

10

20

30

Vd

c [µ

V]

Amplitude Iac

[mA]

Waveform of Iac

Rect

Sine

Triang

ALJJ C3

Weighted

0.6 0.8 1.0 1.2 1.40

10

20

30

Vd

c [µ

V]

Amplitude Iac

[mA]

Waveform of Iac

Rect

Sine

Triang

ALJJ C3

t

t

t

Compact spectrum

does not imply

better rectification!


Figures of merit

0 200 400 600 800

-60

-40

-20

0

20

40

60

Iinj1= 200 A

Iinj1= 400 A

Iinj1= 600 A

V [

V]

Iac [ A]

Iminrect Imax

rect

Irect

V max

Figures of merit

min. Irect (aim: ,h0 ) max. Irect (aim: ,h0 ) Irect (aim: ,h0 ) V max(aim: ,h0 )


Adiabatic JVR: optimazation

0 100 200 3000.00

0.25

0.50

0.75

Irect/Imaxrect

Imaxrect /Ic

Iminrect/Ic

fig

ure

s o

f m

eri

tm [

dim

esio

nle

ss]

V max/Vstep

Iinj1 h0 [ A]

Figures of merit

min. Irect (aim: ,h0 ) max. Irect (aim: ,h0 ) Irect (aim: ,h0 ) V max(aim: ,h0 )

Result

One cannot optimize all figures at ones. Increasing h0 we optimize 3 out of 4:

most importantly Irect and V max.


Loaded quasi-static JVR

In adiabatic regime the result can be obtained

from the IVC:

How large should be the dc counter force

to stop the ratchet?

0.0

0.1

0.2

0.3

0.4

0.0 0.1 0.2 0.3 0.4 0.5

-0.10

-0.05

0.00

0.05

Ic+ Ic

vo

lta

ge

V(I

)

(Ic+ Ic )/2

Ic+ Iac(Ic+ Ic )/2

sto

pp

ing

dc c

urr

en

t Ist

op

dc

current Iac

uphill motion

-1.0 -0.5 0.0 0.5 1.0

-1.0

-0.5

0.0

0.5

1.0

+Ic+

vo

lta

ge

V(I

)

current I

Ic

Results for a simple step-like IVC model (Ic+,Ic )

stopping force grows linearly

it saturates in the middle of rect. window

saturation value is equal to rect. window size

make window as large as possible (large h0)

operate ratchet in the 2nd half of rect. window!


High frequency drive

– non Adiabatic JVR (nA-JVR)

Setup:• Resonator cupper box,

the first mode @ 6.0 GHz• Sender: rf-antenna• Receiver: JJ-Electrodes• Iac power P

What means high frequency?

Period of the drive is comparable with the time it takes for fluxon to move around the annulus

periodic dynamics integer number of turns

discrete average velocity=desctere average voltage steps

Underdamped system: inertial effects, chaos


GHzVnnV n

dc

2

20

nA-JVR: Quantized rectification

-10 -5 0 5

0

1

2

3

4

applied power P (dBm)

Vd

c (

V)

[email protected]

[email protected]

Non-monotonous steps!

experiment simulation


nA-JVR: Period-2 dynamics

0.0 0.1 0.2 0.3 0.4 0.5

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

2

dc v

oltage

rf current amplitude

averaging

over 1 period

of ac drive

1

3

4

pseudo 2

5


nA-JVR: half integer steps & current

reversal

3 4 5 6 7

-12

-8

-4

0

1

Vd

c [

µV

]

generator power P [dBm]

ALJJ C3

= 4GHz

1/2

-30 -20 -10 0 10 20

-10

0

10

Vd

c [

µV

]

ALJJ C2@5GHz

+1

1

Generator Ausgangsleistung P [dBm]

Particle„s (fluxon„s)current reversal, i.e. velocity reversali.e. voltage reversal

One turn takes two driving periods!

P. Jung, et al. Phys. Rev. Lett. 76, 3436 (1996)

J. Mateos, et al. PRL 84, 258 (2000)

Physica A 325, 92 (2003)

M. Barbi, et al. Phys. Rev. E 62, 1988 (2000)


nA-JVR: Half integer steps & current

reversal

0.0 0.1 0.2 0.3 0.4 0.5

-0.4

-0.2

0.0

0.2

0.4

dc v

oltage


averaging

over 1 period

of ac drive

1

+1

1/2

= 0.2

1 1

0.20 0.21 0.22 0.23 0.24 0.25

-0.20

-0.15

-0.10

1/2

dc v

oltage


averaging

over 1 period

of ac drive

= 0.2

zoom


nA-JVR: fluxon trajectories & period 2

dynamics

0.0 0.1 0.2 0.3 0.4 0.5

-0.4

-0.2

0.0

0.2

0.4

dc v

oltage


averaging

over 1 period

of ac drive

1

+1

1/2

= 0.2

1 1

0

20

40

60

80

100

0 2 4 6 8 10

-505

-1 0 1

ac=0.235

coordinate x

tim

e t

U(x

0)

Fac

l = 10, h0 = 1.0, = 0.2

subharmonic


nA-JVR: Period-1 dynamics: forward

step

0

20

40

60

80

100

0 2 4 6 8 10 -1 0 1

-505

coordinate, x

tim

e

t

ac=0.29

Fac

U(x

0)

l = 10, h0 = 1.0, = 0.2

0.0 0.1 0.2 0.3 0.4 0.5

-0.4

-0.2

0.0

0.2

0.4

dc v

oltage


averaging

over 1 period

of ac drive

1

+1

1/2

= 0.2

1 1

harmonic


nA-JVR: Period 1&2 dynamics,

current (voltage) reversal

l = 10, h0 = 1.0, = 0.2

0.0 0.1 0.2 0.3 0.4 0.5

-0.4

-0.2

0.0

0.2

0.4

dc v

oltage


averaging

over 1 period

of ac drive

1

+1

1/2

= 0.2

1 1

0

20

40

60

80

100

0 2 4 6 8 10 -1 0 1

-505

coordinate x

tim

e

t

ac=0.35

Fac

U(x

0)

Subharmonic

current reversal: period 1&2


nA-JVR: Peak velocities

-10 -5 0 5 10 15 20-20

0

20

40

60

Vd

c

[µ

V]

G3@12GHz

[email protected]

Generator output power P [dBm]

0

0

88.0

91.0

cu

cu

:C4

:G3

:velocity Average

0.0 0.2 0.4 0.6 0.8

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

= 0.3

dc v

olta

ge


averaging

over 1 period

of ac drive

+1

Simulation

Max. Average velocity

0.47 (?)

u @ : F. Mertens, et al. PRE 74, 66602 (2006)

u : G. Carapella, et al. Physica C 382, 337 (2002)

u : A. Ustinov, et al. PRL 93, 87001 (2004)


nA-JVR loaded by dc current

-50

0

50

-10 -5 0 5

-200

-100

0

100

200

V [

V]

n = 1

P [dBm]

f = 26.3 GHz

Iinj1 = 250 A

Isto

pd

c [

A]

-50

0

50

-15 -10 -5 0 5

-200

-100

0

100

200

V [

V]

f = 26.3 GHz

Iinj1 = 250 A

Isto

pd

c [

A]

n = 1

P [dBm]

Positive potential Negative potential


nA-JVR: stopping force (current)

experiment vs. simulation

-50

0

50

-10 -5 0 5

-200

-100

0

100

200

V [

V]

n = 1

P [dBm]

f = 26.3 GHz

Iinj1 = 250 A

Isto

pd

c [

A]

-0.5

0.0

0.5

-11 -10 -9 -8 -7 -6

-0.05

0.00

0.05

20 log(Iac / Ic) [dB]

= 0.23,

l = 10

n = 1

Isto

pd

c/I

c

n = +1

V /

Vst

ep

Experiment Simulation


JVR made of Intrinsic JJ stack

H. B. Wang et al., PRB 80, 224507 (2009)


Samples, I-V characteristic

Top view

N = 30 JJs

n = 20 teeth

L = 157 m

J = 0.4 m

T = 8.0 K

H. B. Wang et al., PRB 80, 224507 (2009)

no

flux-flow

T = 4.2 K

flux-flow

mvmax=2.3 107 m/s

mmax= 100 fluxons

mvmax=1.5 107 m/s

mmax= 15

flux-flowVmax= 40 V

Vmax= 300 V


Rectification

Experiment Simulation

V max= 100 V (record!)

random fluxon lattice

m ~ 40 fluxons

For large m and N the steps are smeared!

Why no (Shapiro) steps?

H. B. Wang et al., PRB 80, 224507 (2009)


Summary & Outlook

Fluxon (Josephson Vortex) ratchet

principles of operation (asymmetric periodic potential, particle=fluxon)

advantages

Quasi-static (adiabatic) drive:

rectification curves vs. potential height, driver shape

figures of merit

stopping force

Non-adiabatic drive:

quantized rectification

period 2 dynamics:

• subharmonic steps,

• pseudo-integer steps

current (voltage) reversal

loaded ratchet, stopping force

Intrinsic Josephson vortex ratchet

.

Thanks for your

attention!

Questions?


Can I rectify a white noise?

“white” noise cut off at 50MHz

0 50 100 150 200 250 300 350 400 450

-4

-2

0

2

4

Iinj1 = –240 A

Iinj1 = –170 A

Iinj1 = – 45 A

Vd

c,

µV

Iac, [mA]


Ratchet or just synchronization?

-0.10

-0.05

0.00

0.05

0.10

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Vdc

I dc


How do we measure?

)cos()(:Apply tItI ac

)()(:Measure acacdc IVIV

ac current

V

potential

fluxon insert


Josephson junction

1

1

i

s en

2

2

i

s en

)sin()sin( 12 ccs III

B. D. Josephson, Phys. Lett. 1, 251 (1962).

Fortgeschrittenen-Praktikum 2.11.2004

of overlapcI


Long Josephson junctions

1D model:

)(

11)(

xi

s enx

)(

22)(

xi

s enx

Solutions: 1. linear electromagnetic waves (plasma waves)

1D model:

2. Soliton=fluxon=Josephson vortex

phase field supercurrent


Content

Introduction

What is (long) Josephson junction?

What is a ratchet?

Why to build ratchets using long Josephson junctions?

How to create an efficient asymmetric periodic potential?

Results (experiment and simulations)

Everything under control: 1 injector, 2 injectors..(calibration)

Quasi-statically (adiabatically) driven ratchet

Non-adiabatic effects

Conclusions & outlook




Potential: w(x) h(x) j(x)

tunability? no yes yes

topological. limits? no yes no

current/field source? no yes yes


Asymmetry due to non-uniform field

cos)( HxH

)(2)( 00 xwhxU

• Tunable potential• Topological limitations

cos)( 0HxH

H 0

h(x)





dxh

xwH

L

xt

0

22

)cos1(2

)(

2)(

experiments with fluxon...

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