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

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Jivesh Kaushal MBI, 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 students

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Goal: Observe & control electron dynamics at its natural time-scale (1asec=10 -3 fsec) 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 ħħ ħħ Ionization by XUV ħħ ħħ ħħ ħħ ħħ ħħ ħħ ħħ Ionization by IR Attosecond spectroscopy: Goals & Challenges X 2 g ~ A 2 u ~ B 2 u ~ 4.3eV 3.5 eV CO 2 CO + 2 Coherent population of several ionic states

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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? Attosecond spectroscopy: Questions

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distance The 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 S H Based on Spin-Orbit Interaction Good for any number of photons N Based on Spin-Orbit Interaction Good for any number of photons N g

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Spin-orbit interaction: the physical picture 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 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 For e -, the core rotates around it Rotating charge creates current Current creates magnetic field This field interacts with the spin Results in E SO for nonzero L z L z => H S + - Take e.g. L=L z =1 x ħ

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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 One-photon ionization of Cs by right circularly polarized pulse Define angle of rotation of electron spin during ionization ħħ ħħ + S Cs 5s S No SO interaction in the ground state

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SO 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

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SO Larmor clock as Interferometer Radial photoionization matrix element j=3/2 j=1/2 j=3/2 A crooked interferometer: arm + double arm A crooked interferometer: arm + double arm U. Fano, 1969 Phys Rev 178,131

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

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

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Strong Field Ionization in IR fields Multiphoton Ionization: N>>1 xF L cos t Adiabatic (tunnelling) perspective ( /I p << 1) -xF L cos t ħħ ħħ ħħ ħħ ħħ ħħ ħħ ħħ Keldysh, 1965 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 Closed shell, no Spin-Orbit interaction Nħ P electrons Kr 4s 2 4p 6 + P + Kr + 4s 2 4p 5 + P - Open shell, Spin-Orbit interaction is on Ionization turns on the clock in Kr + Clock operates on core states: P 3/2 (4p 5,J=3/2) and P 1/2 (4p 5,J=1/2) Ionization turns on the clock in Kr + Clock operates on core states: P 3/2 (4p 5,J=3/2) and P 1/2 (4p 5,J=1/2) - Theoretical prediction: Barth, Smirnova, PRA, Experimental verification: Herath et al, PRL, 2012

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SO Larmor clock operating on the core electron J=1/2 J=3/2 Ionization amplitude core At the moment of separation

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The SFI Time One photon, weak field Many photons, strong field - Looks like a direct analogue of WS E SO - Does 13 / E SO correspond to time?

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The appearance of SFI time Kr + P 3/2 e-e- Kr + P 1/2 e-e- -Part of 13 yields Strong Field Ionization time -What about 13 ? -Part of 13 yields Strong Field Ionization time -What about 13 ?

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Time is phase, but not every phase is time! The phase that is not time - 13 does not depend on SO - Trace of electron – hole entanglement Proper time delay in hole formation ‘Chirp’ of the hole wave-packet imparted by ionization: compression / stretching of the hole wave-packet

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Stopping the clock: filling the p - hole 4s 2 4p 6 4s 2 4p 5 4s 4p 6 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 + 4s 2 4p 5 s s

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Strong-field ionization time & tunnelling time SFI time : -xF L cos t IpIp Larmor tunneling time : 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:

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Number of photons Delay, as WS-like delay Apparent ‘delay’ Delays : Results and physical picture -xF L cos t N>10 N=4 N=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 F 2 / E SO I p 5/ 2 I p -3/ 2 Kr atom: Ip=14 eV Kr E SO =0.67 eV 2.5x10 14 W/cm 2 Approaches WS delay as N -> 1

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Conclusions Using SO Larmor clock we defined delays in hole formation: 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.

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