Olga Smirnova

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

• Olga Smirnova
• Max-Born Institute, Berlin

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Work has been inspired by
Alfred Maquet
Armin Scrinzi
Work has been done with
PhD students
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Attosecond spectroscopy Goals Challenges

• Goal
• Observe control electron dynamics at its
  natural time-scale (1asec10-3fsec)
• 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

CO2
hw
hW
hw
hw
hw
CO2
Ionization by XUV
Coherent population of several ionic states
Ionization by IR
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Attosecond spectroscopy Questions

• How long does it take to remove an electron and
  create a hole?
• the time scale of electron rearrangement
• Experiment Theory Eckle, P. et al
  Science 322, 15251529 (2008).
• Goulielmakis, E. et al, Nature 466 (7307),
  700-702 (2010)
• Schultze, M. et al. Science 328, 16581662
  (2010).
• Klunder, K. et al., Phys. Rev. Lett. 106, 143002
  (2011)
• Pfeiffer, A. N. et al. Nature Phys. 8, 7680
  (2012)
• Nirits talk Shafir, D. et al. Nature
  485 (7398), 343-346 (2012)
• How does this time depend on the number of
  absorbed photons (strong IR vs weak XUV)?
• How does electron-hole entanglement affect this
  process and its time-scale?

Can we find a clock to measure this time?
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The Larmor clock for tunnelling
I. Baz, 1966
H
distance
Beautiful but academic ? No! There is a
built-in Larmor-like clock in atoms!

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

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Spin-orbit interaction the physical picture
Take e.g. LLz1xh
Lz gt H

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

S
-

We have a clock! ... But we need to calibrate
it How rotation of the spin is mapped into
time? Consider one-photon ionization, where the
ionization time is known Wigner-Smith time E.
Wigner Phys. Rev. 98, 145-147 (1955) F. T. Smith
Phys. Rev. 118, 349-356 (1960) Find angle of
rotation of the spin in one-photon ionization
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Gedanken experiment for Calibrating the clock
One-photon ionization of Cs by right circularly
polarized pulse Define angle of rotation of
electron spin during ionization
 
 
 
hw

 
No SO interaction in the ground state
 
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SO Larmor clock as Interferometer
 
 
Initial state
 
 
 
Final state
 
 

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

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

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SO Larmor clock as Interferometer
U. Fano, 1969 Phys Rev 178,131
 
 
A crooked interferometer arm double arm
j3/2
 
 
 
 
 
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SO Larmor clock as Interferometer
U. Fano, 1969 Phys Rev 178,131
 
 
A crooked interferometer arm double arm
j3/2
 
 
 
 
 
Wigner-Smith time hides here
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The appearance of Wigner-Smith time
Wigner-Smith time
We have calibrated the clock
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Strong Field Ionization in IR fields
Keldysh, 1965
Multiphoton Ionization Ngtgt1
Find time it takes to create a hole in general
case for arbitrary Keldysh parameter
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Starting the clock Ionization in circular field
Ngtgt1 ionization preferentially removes p-
(counter-rotating) electron
- Theoretical prediction Barth, Smirnova, PRA,
2011 - Experimental verification Herath et al,
PRL, 2012
Nhw
P -
Closed shell, no Spin-Orbit interaction
Open shell, Spin-Orbit interaction is on
Ionization turns on the clock in Kr Clock
operates on core states P3/2
(4p5,J3/2) and P1/2 (4p5,J1/2)
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SO Larmor clock operating on the core
electron
 
 
 
At the moment of separation
 
 
 
core
 
 
 
J1/2
J3/2
J3/2
Ionization amplitude
 
 
 
 
 
 
 
 
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The SFI Time

• One photon, weak field

• Many photons, strong field

- Looks like a direct analogue of tWSDESO
- Does f13 /DESO correspond to time?
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The appearance of SFI time
e-
Kr P3/2
e-
Kr P1/2

• Part of f13 yields Strong Field Ionization time
• What about Df13 ?

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The phase that is not time
- Df13 does not depend on DESO - Trace of
electron hole entanglement
Chirp of the hole wave-packet imparted by
ionization compression / stretching of the hole
wave-packet
Proper time delay in hole formation
Time is phase, but not every phase is time!
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Stopping the clock filling the p- hole
Final s - state
P
Asec XUV, Left polarized
J1/2
J3/2
Kr 4s24p5
s
s
Few fs IR, Right polarized

• 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

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Strong-field ionization time tunnelling time
V
Larmor tunneling time
Hauge,E. H. et al, Rev. Mod Phys, 61, 917 (1989)
SFI time
 
We can calculate this phase analytically
(Analytical R-Matrix ARM method) L. Torlina
O.Smirnova, PRA,2012, J. Kaushal O. Smirnova,
arXiv1302.2609
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Delays Results and physical picture
Exit point, Bohr
Kr atom Ip14 eV Kr DESO0.67 eV 2.5x1014W/cm2
Approaches WS delay as N -gt 1
Ip-3/2
WS-like delay
Number of photons
Delay, as
Apparent delay
0.4F2/DESOIp5/2
Number of photons

• 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

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Conclusions

• Using SO Larmor clock we defined delays in hole
  formation

• 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

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

• 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.