Looking inside the tunneling process Nirit Dudovich Physics of Complex Systems, Weizmann Institute of Science

Looking inside the tunneling process

Nirit Dudovich

Physics of Complex Systems, Weizmann Institute of Science

Co- authorsCo- authorsDror ShafirOren RazHadas SoiferOren PedazurMichal DaganBarry Bruner

Collaborations:Olga Smirnova Misha IvanovYann MairesseSergueiPatchkovskiiCaterina VozziSalvatore Stagira2

The free electron probes the process

Time resolved measurements in the Time resolved measurements in the attosecond regimeattosecond regime

The optical pulse pump/probe the process

Attosecond pulse

IR pulse

Production Measurement

The recollision process

Attosecond ScienceAttosecond Science

Acceleration by the electric field

Re-collision

Tunnel ionization

E>100eV

kp EI

High harmonics generation

Re-collision as a pump – probe schemeRe-collision as a pump – probe scheme

pump probe

Re-collision

Tunnel ionization

Optical cycle

H. Niikura, et al., Nature 421, (2003).X. M. Tong et al., Phys. Rev. Lett. 91 (2003).M. Lein, Phys. Rev. Lett. 94, (2005).M. Lein, J. Phys. B, 40 (2007). S. Baker et al., Science 312, (2006).O. Smirnova, et al. Nature 460 (2009).O. Smirnova et al., PNAS 106, (2009).B. K. McFarland et al., Science 322, (2008).

Field induced tunnel ionizationField induced tunnel ionization

Tunneling through a static barrierTunneling through a static barrier

Field induced tunnelingField induced tunneling

L. V. Keldysh Sov. Phys. JETP 20 1307 (1965)

• When does an electron leave the tunneling barrier?

• What is the instantaneous probability?

• Does the process evolve in an adiabatic manner?

• Can we resolve multi-channels ionization?


Distan

ceTime [cycle]

Electric field

P. B. Corkum,, Phys. Rev. Lett. 71, 1994 (1993).

How does the time of ionization map into our experiment?How does the time of ionization map into our experiment?


The induced dipole moment is described by:

003

0

0 ,,exp,, ttpiSttppCddttxt

2

0

02

1,,

t

t

ApdttpS

0

,, 0

p

ttpS

The semi-classical action

The main contribution to the integral comes from the stationary points:

0

2

20

0

pp ItAp

It

SThe solution is found in the complex plane of t0

• When does an electron leave the tunneling barrier?




Re(t0)

Im(t0)

c• The recollision process provides an Angstrom-attosecond resolution

• Any deviations are mapped to the properties of the recolliding electron

Recollision as a measurementRecollision as a measurement

X(t0)=0

V(t0)=0

X(t)=0

• Can we keep it simple?

• The output is the high harmonic spectrum

- We need additional information

We add a weak second harmonic field

If the field is much weaker than the fundamental field it acts as an amplitude gate

““kicking” the recollision processkicking” the recollision process

““kicking” the recollision processkicking” the recollision process

Gate

max (t0)

Gating the recollision process - HeliumGating the recollision process - Helium

[cycle]

Ene

rgy

(har

mon

ic n

umbe

r)

-0.1 0 0.1 0.3 -0.4

20

30

40

50

60

70

0.2

Reconstructing the ionization timesReconstructing the ionization times

Har

mon

ic o

rder

D. Shafir, H. Soifer, B. D. Bruner, M. Dagan, Y. Mairesse, Serguei Patchkovskii, M. Yu. Ivanov, O. Smirnova and N. Dudovich, Nature 485, 343 (2012).


The induced dipole moment is described by:

003

0

0 ,,exp,, ttpiSttppCddttxt

2

0

02

1,,

t

t

ApdttpS

0

,, 0

p

ttpS

The semi-classical action

0

2

20

0

pp ItAp

It

S

• When does an electron leaves the tunneling barrier?




Re(t0)

Im(t0)

• We can add a parallel perturbation

• This perturbation adds a small phase shift and perturbs the ionization step.

• In the limit of a small Keldysh parameter we are left with a phase shift

• How do we perform the measurement? How can we separate the two

mechanisms?

““kicking” the recollision process – kicking” the recollision process – parallel perturbationparallel perturbation

J M Dahlstr¨om, A L’Huillier and J Mauritsson, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 095602x

Can we measure the imaginary time?

exp(i)

Interferometry in High Harmonic Interferometry in High Harmonic GenerationGeneration

exp(-i )

exp(i ) exp(i )

exp(-i )

Odd harmonics Even harmonics

A(N)

A(N)

A(N)

A(N)

17 19 21 23 25 27 29

exp(i)


exp(-i )

exp(i ) exp(i )

exp(-i )


A(N)

A(N)

A(N)

A(N)

Two color delay

π

Odd harmonics

Even harmonics

N. Dudovich, O. Smirnova, J. Levesque, M. Yu. Ivanov, D. M. Villeneuve and P. B. Corkum, Nature Physics 2, 781 (2006).

exp(i)


exp(-i )

exp(i ) exp(i )

exp(-i )


A(N)

A(N)

A(N)

A(N)

Two color delay

π

Odd harmonics

+

exp(-i -)

exp(i +)

exp(-i -)

exp(i +)

Even harmonics


odd- even

Harmonic Order

30

40

50

60

70

0.05 0.1 0.15 0.2

Har

mon

ic o

rder

Time [rad]

Reconstruction of the imaginary timesReconstruction of the imaginary times

Mapping the tunneling processMapping the tunneling process

30

40

50

60

70

0.05 0.1 0.15 0.2

Har

mon

ic o

rder

Time [rad]

Moment of Ionization Probability

The link between ionization and recollisionThe link between ionization and recollision

Ionization time:

270 attoseconds

250 attoseconds

230 attoseconds

210 attoseconds

190 attoseconds

170 attoseconds

Destructive interference

Multiple channel ionizationMultiple channel ionization


O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum and M. Y. Ivanov, Nature 460, 972 (2009)

Gating multi channels ionization Gating multi channels ionization H

HG

Ionization times [attosecond]

Ionization gate

Phase jump

[cycle]

HOMO

HOMO-2

Ene

rgy

(har

mon

ic n

umbe

r)

Single channel - 90 degrees

red-blue delay (radians)

harm

onic

ord

er

90 deg, low I

0.5 1 1.5 2 2.5 3

10

15

20

25

30

35

40 0.4

0.5

0.6

0.7

0.8

0.9

1

Gating multi channels ionization Gating multi channels ionization


harm

onic

ord

er

0 deg, low I

0.5 1 1.5 2 2.5 3

10

15

20

25

30

35

40 0.4

0.5

0.6

0.7

0.8

0.9

1

Two channels - 0 degrees

[cycle]

HH

G

We observe a clear signature to two channels ionization , probing a delay of 50 attoseconds in the ionization times.

[cycle]

HH

GE

nerg

y (h

arm

onic

num

ber)

Ene

rgy

(har

mon

ic n

umbe

r)



• Recollision processes provide temporal information with attosecond

resolution.

• We have measured the tunneling ionization time in simple systems,

directly confirming the analysis based on the path integral formalism.

• We can measure a delay related to multiple orbitals tunneling

• In more complex molecular systems the tunneling process involves

attosecond core rearrangements leading to a real time-delay associated

with different tunneling channels.

Gating multi channels ionization Gating multi channels ionization

Classical solution

Stationary solution

M. Lewenstein et al., Phys Rev A 49, 2117 1994.



0 200 400 600 800 1000 1200 1400 1600 1800 200010

20

30

40

50

60

70

80

Time [asec]

Ha

rmo

nic

Ord

er

Tunneling - stationary solutionTunneling - stationary solution

• We have linked the real part to the time at which the electron leaves the Coulomb barrier

• The imaginary part is linked to the instantaneous tunneling probability

• Can we measure it?

The stationary solution is complex

0

2

20

0

pp ItAp

It

S

0 200 400 600 800 1000 1200 1400 1600 1800 200010

20

30

40

50

60

70

80

Time [asec]

Ha

rmo

nic

Ord

er

0 200 400 600 800 1000 1200 1400 1600 1800 200010

20

30

40

50

60

70

80

Time [asec]

Ha

rmo

nic

Ord

er

ClassicalExperimentPath integraln

ReturnIonization

Gating the recollision processGating the recollision process


t0

2D Gate

GLmax(t0,t)

Gmax(t0,t)

t

Displacement Gate: GLmax(N) Angular Gate: G

max(N)

Gating the recollision processGating the recollision process

[cycle]

HH

G

-0.1 0 -0.2 -0.3 -0.4

20

30

40

50

60

70

Gating the recollision processGating the recollision processDisplacement gateDisplacement gate

How do we reconstruct the dynamics?There are two unknown parameters – t0 and tHow do we reconstruct the dynamics?There are two unknown parameters – t0 and t

Recollision as a measurementRecollision as a measurement

The optimal gate The optimal gate

1. Perturbative manipulation

2. A window in the ionization time

3. Can be shifted

• Can we keep it simple?

• The output is the high harmonic spectrum

- We need additional information


Delay [fs]

16

18

20

22

24

26

17

19

21

23

25

27

N. Dudovich, O. Smirnova, J. Levesque, M. Yu. Ivanov, D. M. Villeneuve and P. B. Corkum, Nature Physics 2, 781 (2006).


Short trajectories

Long trajectories


Field induced tunnel ionizationField induced tunnel ionizationPioneering experimentsPioneering experiments

M. Uiberacker et al., Nature (2007).

P. Eckle et al., Science (2008) A. N. Pfeiffer et al., Nature Physics (2012).

HH

G

20

30

40

50

60

-0.1 0 -0.2 -0.3 -0.4

HH

G

[cycle]

Gating the recollision processGating the recollision processAngular gateAngular gate

x

y


Harmonic Order

odd- even




The link between ionization and recollisionThe link between ionization and recollisionrecollisionIonization

Ene

rgy

(har

mon

ic n

umbe

r)

Short trajectories

Long trajectories




phot

on e

nerg

y (e

V)

Kr - short_area - 110613\scan7

0 0.5 1 1.5 2 2.5 3

30

35

40

45

Scaling the gating mechanism – Scaling the gating mechanism – 1.41.4

• The interference between two adjacent half cycle leads to the

generation of odd harmonics.

• The second harmonic field breaks the symmetry and leads to

the generation of even harmonics.

““kicking” the recollision process – kicking” the recollision process – parallel perturbationparallel perturbation



• Can we study the internal dynamics? Can we link each trajectory to its ionization time?

• Such a measurement will provide a direct insight into one of the most fundamental strong

field phenomena – field induced tunnel ionization

We have an extremely accurate measurement – the electron is born at the origin, propagate

on an attosecond time scale and returns to the origion

Attosecond pulse generation processAttosecond pulse generation process

Acceleration by the electric fieldRe-collision

Tunnel ionization

E>100eV

Optical radiation with attoseconds duration

kp EI Ionization potential

Kinetic energy

H1523.3eV

H2132.6eV

H2741.9eV

H3960.5eV

Attosecond pulse trainAttosecond pulse train

The multi-cycle regime

High harmonics generation

max (t0) [cycle]

Ene

rgy

(har

mon

ic n

umbe

r)

-0.1 0 0.1 0.3 -0.4

20

30

40

50

60

70

He - normalized

0.2

[cycle]

-0.1 0 0.1 0.3 -0.40.2

Kicking the recollision process - HeliumKicking the recollision process - Helium

∆Y(t0)=0

Gate (“kick”)

max (t0)

Kicking the recollision process - HeliumKicking the recollision process - Helium

[cycle]

Ene

rgy

(har

mon

ic n

umbe

r)

-0.1 0 0.1 0.3 -0.4

20

30

40

50

60

70

He - normalized

0.2

∆Y()=0


Har

mon

ic o

rder

Why do we observe a significant deviation from the classical model?

Ene

rgy

(har

mon

ic n

umbe

r)


Har

mon

ic o

rder

Ene

rgy

(har

mon

ic n

umbe

r)


Stationary Phase approximationStationary Phase approximation

Weight

• Mapping objects from one dimension to another dimensions can lead to singularities:

• Singularities are classified according to Catastrophe theory

• This classification tells us about the shape, intensity, width and diffraction pattern of the caustic.

Think of how the density of the folded “ideal” paper is mapped to the plane!

Catastrophe TheoryCatastrophe Theory

The classical description links: t0 t E

The quantum picture approaches the classical at the stationary points 0

0

t

S

The quantum description:

000 ,exp, ttiSttAdttErt

t

t

pItAp

dtS0

2

''

2



Field induced tunnel ionizationField induced tunnel ionizationPioneering experimentsPioneering experiments

P. Eckle et al., “Attosecond Ionization and Tunneling Delay Time Measurements in Helium”, Science (2008) A. N. Pfeiffer et al., “Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms”, Nature Physics (2012).

M. Hentschel et al., Nature 414, (2001)Y. Mairesse, et al., Science 302, (2003).N. Dudovich et al., Nature Physics 2, (2006).

800 1000 1200 1400 1600 1800 200010

20

30

40

50

60

70

Return time [asec]

Har

mon

ic o

rder

ClassicalExperimental

Return timesReturn times

100 200 300 400 500 600 70010

20

30

40

50

60

70

Ionization time [asec]

Har

mon

ic o

rder

ClassicalExperimental

?

Ionization timesIonization times


Harmonic Order

odd- even

Multiple channel ionizationMultiple channel ionization

O. Smirnova, et al., Nature 460, 972 (2009).B. K. McFarland et al., Science 322, (2008).

-13.8 eV

-17.3 eV

-18.1 eV

0.2 0.6 1 1.430

50

70Classical solution


The link between ionization and recollisionThe link between ionization and recollisionrecollisionIonization

3 4 5 6

cc

Stationary solution

Energy (harmonic number) Real times

Time [rad] Time [rad]

c

0 0.4 0.8 1.2

30

50

70c

0 0.4 0.8 1.2

Imaginary times

Time [rad] Time [rad]

Documents

Looking inside the tunneling process Nirit Dudovich Physics of Complex Systems, Weizmann Institute of Science