Olga Smirnova Max-Born Institute, Berlin Attosecond Larmor clock: how long does it take to create a hole?

Olga SmirnovaMax-Born Institute, Berlin

Attosecond Larmor clock: how long does it take to create a hole?

Jivesh KaushalMBI, Berlin

Misha Ivanov,MBI Berlin, Imperial College

Lisa Torlina,MBI, Berlin

Work has been done with:

Work has been inspired by:

Alfred Maquet

Armin Scrinzi

PhD studentsPhD students

Goal:Observe & control electron dynamics at its natural time-scale (1asec=10-3fsec)

One of key challenges: • Observe non-equilibrium many-electron dynamics

• This dynamics can be created by photoionization• Electron removal by an ultrashort pulse creates coherent hole

ħ

Ionization by XUV

ħħħħ

Ionization by IR

Attosecond spectroscopy: Goals & ChallengesAttosecond spectroscopy: Goals & Challenges

X 2g~

A 2u~

B 2u

~4.3eV

3.5 eV

CO2

CO+2

Coherent population of several ionic states

Can we find a clock to measure this time?

Attosecond spectroscopy: QuestionsAttosecond spectroscopy: Questions

distance

The Larmor clock for tunnellingThe Larmor clock for tunnelling

Beautiful but academic ? – No! There is a built-in Larmor-like clock in atoms!

Beautiful but academic ? – No! There is a built-in Larmor-like clock in atoms!

I. Baz’, 1966 S SH

• Based on Spin-Orbit Interaction• Good for any number of photons N• Based on Spin-Orbit Interaction• Good for any number of photons N

Eg

Spin-orbit interaction: the physical pictureSpin-orbit interaction: the physical picture

• For e-, the core rotates around it• Rotating charge creates current• Current creates magnetic field• This field interacts with the spin• Results in ESO for nonzero Lz

Lz => HLz => H

S+ -

Take e.g. L=Lz=1xħ

Gedanken experiment for Calibrating the clockGedanken experiment for Calibrating the clock

One-photon ionization of Cs by right circularly polarized pulseDefine angle of rotation of electron spin during ionizationOne-photon ionization of Cs by right circularly polarized pulseDefine angle of rotation of electron spin during ionization

ħħ

+

S

Cs5s

S

No SO interaction in the ground stateNo SO interaction in the ground state

SO Larmor clock as InterferometerSO Larmor clock as Interferometer

• Looks easy, but … -- the initial and final states are not eigenstates, thanks to the spin-orbit interaction

Initial state

Final state

• Record the phase between the spin-up and spin-down pathways• Record the phase between the spin-up and spin-down pathways

SO Larmor clock as InterferometerSO Larmor clock as Interferometer

Radial photoionization matrix element

j=3/2 j=1/2j=3/2 A crooked interferometer: arm + double arm

A crooked interferometer: arm + double arm

U. Fano, 1969 Phys Rev 178,131

SO Larmor clock as InterferometerSO Larmor clock as Interferometer

Radial photoionization matrix element

j=3/2 j=1/2j=3/2

Wigner-Smith time hides hereWigner-Smith time hides here

A crooked interferometer: arm + double arm

A crooked interferometer: arm + double arm

U. Fano, 1969 Phys Rev 178,131

The appearance of Wigner-Smith timeThe appearance of Wigner-Smith time

SOWS

SORR

E

EEE

)()(31

EEWS /)(

0.38 eV

J. Cond. Matter 24 (2012) 173001

?31 RR

We have calibrated the clock We have calibrated the clock

Wigner-Smith time Wigner-Smith time

Strong Field Ionization in IR fieldsStrong Field Ionization in IR fields

Multiphoton Ionization: N>>1Multiphoton Ionization: N>>1

xFLcost

Adiabatic (tunnelling) perspective (/Ip << 1) Adiabatic (tunnelling) perspective (/Ip << 1)

-xFLcost

ħħħħ

Keldysh, 1965

Find time it takes to create a hole in general case for arbitrary Keldysh parameter

Starting the clock: Ionization in circular fieldStarting the clock: Ionization in circular field

N>>1 ionization preferentially removes p- (counter-rotating) electronN>>1 ionization preferentially removes p- (counter-rotating) electron

Closed shell, no Spin-Orbit interaction Closed shell, no Spin-Orbit interaction

NħNħ

P electrons

Kr4s24p6

+

P +

Kr+

4s24p5+

P -

Open shell, Spin-Orbit interaction is on Open shell, Spin-Orbit interaction is on

Ionization turns on the clock in Kr+ Clock operates on core states: P3/2 (4p5,J=3/2) and P1/2 (4p5,J=1/2)Ionization turns on the clock in Kr+ Clock operates on core states: P3/2 (4p5,J=3/2) and P1/2 (4p5,J=1/2)

- Theoretical prediction: Barth, Smirnova, PRA, 2011 - Experimental verification: Herath et al, PRL, 2012

SO Larmor clock operating on the coreSO Larmor clock operating on the core

electron

J=1/2J=3/2J=3/2Ionization amplitude

coreAt the moment of separation

The SFI TimeThe SFI Time

• One photon, weak field• One photon, weak field

• Many photons, strong field• Many photons, strong field

- Looks like a direct analogue of WSESO - Looks like a direct analogue of WSESO

- Does 13 /ESO correspond to time? - Does 13 /ESO correspond to time?

SRpc I ,33 )(

SRSOpc EI ,11 )(

SRpcSOpc IEI ,1313 )()(

SOp

c EI

p

cSFI I

The appearance of SFI timeThe appearance of SFI time

Kr+

P3/2

e-

Kr+

P1/2

e-

- Part of 13 yields Strong Field Ionization time- What about 13 ?- Part of 13 yields Strong Field Ionization time- What about 13 ?

SRSOSFI E ,1313

Time is phase, but not every phase is time! Time is phase, but not every phase is time!

The phase that is not timeThe phase that is not time

-13 does not depend on SO

- Trace of electron – hole entanglement

p

cSFI I

Proper time delay in hole formationProper time delay in hole formation

SR,13 ‘Chirp’ of the hole wave-packet imparted by ionization: compression / stretching of the hole wave-packet‘Chirp’ of the hole wave-packet imparted by ionization: compression / stretching of the hole wave-packet

Stopping the clock: filling the p- holeStopping the clock: filling the p- hole

4s24p6

4s24p5

4s 4p6

• Pump: Few fs IR creates p-hole and starts the clock• Probe: Asec XUV pulse fills the p-hole and stops the clock• Observe: Read the attosecond clock using transient absorption

measurement

• Pump: Few fs IR creates p-hole and starts the clock• Probe: Asec XUV pulse fills the p-hole and stops the clock• Observe: Read the attosecond clock using transient absorption

measurement

Few fs IR, Right polarized

Asec XUV, Left polarized

J=3/2 J=1/2

Final s - state

P +

Kr+

4s24p5ss

Strong-field ionization time & tunnelling timeStrong-field ionization time & tunnelling time

p

cSFI I

SFI time:SFI time: -xFLcost

Ip

Larmor tunneling time : Larmor tunneling time : Vc

L

V

Hauge,E. H. et al, Rev. Mod Phys, 61, 917 (1989)

We can calculate this phase analytically (Analytical R-Matrix: ARM method): L. Torlina & O.Smirnova, PRA,2012, J. Kaushal & O. Smirnova, arXiv:1302.2609

pI /13

Number of photons

Del

ay, a

s WS-like delay

Apparent ‘delay’

Delays : Results and physical pictureDelays : Results and physical picture

-xFLcost

N>10

N=4N=2

• Phase and delays are accumulated after exiting the barrier• Larger N – more adiabatic, exit further out• Phase accumulated under the barrier signifies current created during ionization

• Phase and delays are accumulated after exiting the barrier• Larger N – more adiabatic, exit further out• Phase accumulated under the barrier signifies current created during ionization

Number of photons

Exit point, Bohr

F2/ESOIp5/2

Ip-3/2

Kr atom:Ip=14 eVKr

ESO=0.67 eV

2.5x1014W/cm2

Approaches WS delay as N -> 1

Conclusions Conclusions

• Using SO Larmor clock we defined delays in hole formation:• Using SO Larmor clock we defined delays in hole formation:

• The SO Larmor clock allowed simple analytical treatment, but the result is general• The SO Larmor clock allowed simple analytical treatment, but the result is general

• Actual delay in formation of hole wave-packet• Larmor- and Wigner-Smith – like, • Applicable for any number of photons, any strong-field ionization regime

•Apparent ‘delay’ – trace of electron-hole entanglement:• Clock-imparted ‘delay’ (encodes electron – hole interaction )• Analogous to spread of an optical pulse due to group velocity dispersion• does not depend on clock period

•Absorbing many photons takes less time than absorbing few photons, but not zero

• Moving hole = coherent population of several states: This set of states is a clock• Reading the clock = finding initial phases between different states• Not all phases translate into time! This will be general for any attosecond measurements of electronic dynamics.