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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: Jivesh Kaushal MBI, Berlin Misha Ivanov, MBI Berlin, Imperial College Lisa Torlina, PhD students

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**Attosecond spectroscopy: Goals & Challenges**

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 X 2Pg ~ A 2Pu B 2S+u 4.3eV 3.5 eV ħw CO+2 ħW ħw ħw ħw CO2 Ionization by XUV Ionization by IR Coherent population of several ionic states

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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, 1525–1529 (2008). Goulielmakis, E. et al, Nature 466 (7307), (2010) Schultze, M. et al. Science 328, 1658–1662 (2010). Klunder, K. et al., Phys. Rev. Lett. 106, (2011) Pfeiffer, A. N. et al. Nature Phys. 8, 76–80 (2012) Nirit’s talk: Shafir, D. et al. Nature 485 (7398), (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 S S H distance DE=gH/2 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. L=Lz=1xħ Lz => 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, (1955) F. T. Smith Phys. Rev. 118, (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 Cs 5s S S ħw + 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 j=1/2 j=3/2 Radial photoionization matrix element A crooked interferometer: arm + double arm j=3/2

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**SO Larmor clock as Interferometer**

U. Fano, 1969 Phys Rev 178,131 j=1/2 j=3/2 Radial photoionization matrix element A crooked interferometer: arm + double arm j=3/2 Wigner-Smith time hides here

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**The appearance of Wigner-Smith time**

0.38 eV J. Cond. Matter 24 (2012) Wigner-Smith time We have calibrated the clock

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**Strong Field Ionization in IR fields**

Keldysh, 1965 Multiphoton Ionization: N>>1 xFLcoswt Adiabatic (tunnelling) perspective (w/Ip << 1) -xFLcoswt ħw 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**

N>>1 ionization preferentially removes p- (counter-rotating) electron - Theoretical prediction: Barth, Smirnova, PRA, 2011 - Experimental verification: Herath et al, PRL, 2012 P electrons Kr 4s24p6 + P + Kr+ 4s24p5 + Nħw 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,J=3/2) and P1/2 (4p5,J=1/2)

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**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

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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**

Kr+ P3/2 Kr+ P1/2 e- 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 + 4s24p6 4s24p5 4s 4p6 Asec XUV, Left polarized J=3/2 J=1/2 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**

Larmor tunneling time : V Hauge,E. H. et al, Rev. Mod Phys, 61, 917 (1989) -xFLcoswt Ip SFI time: We can calculate this phase analytically (Analytical R-Matrix: ARM method): L. Torlina & O.Smirnova, PRA,2012, J. Kaushal & O. Smirnova, arXiv:

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**Delays : Results and physical picture**

Exit point, Bohr Kr atom: Ip=14 eV Kr+ DESO=0.67 eV 2.5x1014W/cm2 Approaches WS delay as N -> 1 WS-like delay Ip-3/2 Number of photons -xFLcoswt N>10 N=4 N=2 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.

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