Transcript Attosecond Larmor clock - Weizmann Institute of Science

Attosecond Larmor clock:
how long does it take to create a hole?
Olga Smirnova
Max-Born Institute, Berlin
Work has been inspired by:
Alfred Maquet
Armin Scrinzi
Work has been done with:
Jivesh Kaushal
MBI, Berlin
Lisa Torlina,
MBI, Berlin
PhD students
Misha Ivanov,
MBI Berlin, Imperial College
Attosecond spectroscopy: Goals & Challenges
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
~
B 2S+
3.5 eV
ħW
ħw
ħw
ħw
ħw
~
u
~
A 2P
X 2Pg
4.3eV
u
CO+2
CO2
Ionization by XUV
Ionization by IR
Coherent population
of several ionic states
Attosecond spectroscopy: Questions
• How long does it take to remove an electron and create a
hole?
– the time scale of electron rearrangement
Experiment & Theory:
Nirit’s talk:
Eckle, P. et al Science 322, 1525–1529 (2008).
Goulielmakis, E. et al, Nature 466 (7307), 700-702 (2010)
Schultze, M. et al. Science 328, 1658–1662 (2010).
Klunder, K. et al., Phys. Rev. Lett. 106, 143002 (2011)
Pfeiffer, A. N. et al. Nature Phys. 8, 76–80 (2012)
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?
The Larmor clock for tunnelling
I. Baz’, 1966
S
S
H
distance
EgH/2
  E
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
Spin-orbit interaction: the physical picture
Take e.g. L=Lz=1xħ
Lz => H
+
-
S
• 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
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
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
S
ħw
Cs
+
5s
No SO interaction in the ground state
S
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
SO Larmor clock as Interferometer
U. Fano, 1969
Phys Rev 178,131
Radial
photoionization
matrix element
j=3/2
j=3/2
j=1/2
A crooked
interferometer:
arm + double arm
SO Larmor clock as Interferometer
U. Fano, 1969
Phys Rev 178,131
Radial
photoionization
matrix element
j=3/2
j=3/2
j=1/2
A crooked
interferometer:
arm + double arm
Wigner-Smith time
hides here
The appearance of Wigner-Smith time
   ?
R
1
R
3
J. Cond. Matter 24 (2012) 173001
1R  3R   ( E + ESO )   ( E )
  WS ESO
0.38 eV
WS   (E) / E
Wigner-Smith time
We have calibrated the clock
Strong Field Ionization in IR fields
Keldysh, 1965
Multiphoton Ionization: N>>1
Adiabatic (tunnelling) perspective (w/Ip << 1)
ħw
ħw
ħw
ħw
xFLcoswt
-xFLcoswt
Find time it takes to create a hole in general case for arbitrary Keldysh parameter
Starting the clock: Ionization in circular field
N>>1 ionization preferentially removes p- (counter-rotating) electron
- Theoretical prediction: Barth, Smirnova, PRA, 2011
- Experimental verification: Herath et al, PRL, 2012
P electrons
P+
Nħw
Kr
4s24p6
+
Closed shell, no Spin-Orbit interaction
Kr+
4s24p5
P-
+
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)
SO Larmor clock operating on the core
electron
At the moment of separation
core
J=3/2
J=3/2
J=1/2
Ionization amplitude
The SFI Time
• One photon, weak field
• Many photons, strong field
- Looks like a direct analogue of WSESO
- Does 13 /ESO correspond to time?
The appearance of SFI time
Kr+
e-
P3/2
Kr+
e-
P1/2
3  c (I p ) + 3,SR
1  c (I p + ESO ) + 1,SR
13  c (I p + ESO )  c (I p ) + 13,SR
c
ESO
I p
 SFI
c

I p
- Part of 13 yields Strong Field Ionization time
- What about 13 ?
The phase that is not time
13   SFI ESO + 13,SR
13,SR
 SFI
c

I p
- 13 does not depend on ESO
- 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!
Stopping the clock: filling the p- hole
Final s - state
P+
4s 4p6
Asec XUV,
Left polarized
J=3/2
J=1/2
4s24p5
s
Kr+
4s24p5
s
Few fs IR,
Right polarized
4s24p6
• 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
Strong-field ionization time & tunnelling time
Larmor tunneling time :
 c
L 
V
V
Hauge,E. H. et al, Rev. Mod Phys, 61, 917 (1989)
SFI time:
 SFI
c

I p
-xFLcoswt
Ip
We can calculate this phase analytically (Analytical R-Matrix: ARM method):
L. Torlina & O.Smirnova, PRA,2012, J. Kaushal & O. Smirnova, arXiv:1302.2609
Delays : Results and physical picture
Exit point, Bohr
Kr atom:
Ip=14 eV
Kr+
ESO=0.67 eV
  13 / I p
Approaches WS
delay as N -> 1
Delay, as
2.5x1014W/cm2
WS-like delay
Ip-3/2
Apparent ‘delay’
0.4F2/ESOIp5/2
Number of photons
Number of photons
-xFLcoswt
N=2
N=4
N>10
• 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
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.