Presentation on theme: "Attosecond Larmor clock: how long does it take to create a hole?"— Presentation transcript:
1 Attosecond Larmor clock: how long does it take to create a hole? Olga SmirnovaMax-Born Institute, Berlin
2 Work has been inspired by: Alfred MaquetArmin ScrinziWork has been done with:Jivesh KaushalMBI, BerlinMisha Ivanov,MBI Berlin, Imperial CollegeLisa Torlina,PhD students
3 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 dynamicsThis dynamics can be created by photoionizationElectron removal by an ultrashort pulse creates coherent holeX 2Pg~A 2PuB 2S+u4.3eV3.5 eVħwCO+2ħWħwħwħwCO2Ionization by XUVIonization by IRCoherent population of several ionic states
4 Attosecond spectroscopy: Questions How long does it take to remove an electron and create a hole?– the time scale of electron rearrangementExperiment & 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?
5 The Larmor clock for tunnelling I. Baz’, 1966SSHdistanceDE=gH/2Beautiful but academic ? –No! There is a built-in Larmor-like clock in atoms!Based on Spin-Orbit InteractionGood for any number of photons N
6 Spin-orbit interaction: the physical picture Take e.g. L=Lz=1xħLz => HFor e-, the core rotates around itRotating charge creates currentCurrent creates magnetic fieldThis field interacts with the spinResults 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 knownWigner-Smith timeE. Wigner Phys. Rev. 98, (1955)F. T. Smith Phys. Rev. 118, (1960)Find angle of rotation of the spin in one-photon ionization
7 Gedanken experiment for Calibrating the clock One-photon ionization of Cs by right circularly polarized pulseDefine angle of rotation of electron spin during ionizationCs5sSSħw+No SO interaction in the ground state
8 SO Larmor clock as Interferometer Initial stateFinal stateRecord the phase between the spin-up and spin-down pathwaysLooks easy, but … -- the initial and final states are not eigenstates, thanks to the spin-orbit interaction
9 SO Larmor clock as Interferometer U. Fano, 1969Phys Rev 178,131j=1/2j=3/2Radial photoionization matrix elementA crooked interferometer:arm + double armj=3/2
10 SO Larmor clock as Interferometer U. Fano, 1969Phys Rev 178,131j=1/2j=3/2Radial photoionization matrix elementA crooked interferometer:arm + double armj=3/2Wigner-Smith time hides here
11 The appearance of Wigner-Smith time 0.38 eVJ. Cond. Matter 24 (2012)Wigner-Smith timeWe have calibrated the clock
12 Strong Field Ionization in IR fields Keldysh, 1965Multiphoton Ionization: N>>1xFLcoswtAdiabatic (tunnelling) perspective (w/Ip << 1)-xFLcoswtħwFind time it takes to create a hole in general case for arbitrary Keldysh parameter
13 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, 2012P electronsKr4s24p6+P +Kr+4s24p5+NħwP -Closed shell, no Spin-Orbit interactionOpen shell, Spin-Orbit interaction is onIonization turns on the clock in Kr+Clock operates on core states: P3/2 (4p5,J=3/2) and P1/2 (4p5,J=1/2)
14 SO Larmor clock operating on the core electronAt the moment of separationcoreJ=3/2J=3/2J=1/2Ionization amplitude
15 The SFI Time One photon, weak field Many photons, strong field - Looks like a direct analogue of tWSDESO- Does f13 /DESO correspond to time?
16 The appearance of SFI time Kr+P3/2Kr+P1/2e-Part of f13 yields Strong Field Ionization timeWhat about Df13 ?
17 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-packetProper time delay in hole formationTime is phase, but not every phase is time!
18 Stopping the clock: filling the p- hole Final s - stateP +4s24p64s24p54s 4p6Asec XUV,Left polarizedJ=3/2J=1/2Kr+4s24p5ssFew fs IR,Right polarizedPump: Few fs IR creates p-hole and starts the clockProbe: Asec XUV pulse fills the p-hole and stops the clockObserve: Read the attosecond clock using transient absorption measurement
19 Strong-field ionization time & tunnelling time Larmor tunneling time :VHauge,E. H. et al, Rev. Mod Phys, 61, 917 (1989)-xFLcoswtIpSFI time:We can calculate this phase analytically (Analytical R-Matrix: ARM method):L. Torlina & O.Smirnova, PRA,2012, J. Kaushal & O. Smirnova, arXiv:
20 Delays : Results and physical picture Exit point, BohrKr atom:Ip=14 eVKr+DESO=0.67 eV2.5x1014W/cm2Approaches WS delay as N -> 1WS-like delayIp-3/2Number of photons-xFLcoswtN>10N=4N=2Delay, asApparent ‘delay’0.4F2/DESOIp5/2Number of photonsPhase and delays are accumulated after exiting the barrierLarger N – more adiabatic, exit further outPhase accumulated under the barrier signifies current created during ionization
21 Conclusions Using SO Larmor clock we defined delays in hole formation: Actual delay in formation of hole wave-packetLarmor- and Wigner-Smith – like,Applicable for any number of photons, any strong-field ionization regimeApparent ‘delay’ – trace of electron-hole entanglement:Clock-imparted ‘delay’ (encodes electron – hole interaction )Analogous to spread of an optical pulse due to group velocity dispersiondoes not depend on clock periodAbsorbing many photons takes less time than absorbing few photons, but not zeroThe SO Larmor clock allowed simple analytical treatment, but the result is generalMoving hole = coherent population of several states: This set of states is a clockReading the clock = finding initial phases between different statesNot all phases translate into time! This will be general for any attosecond measurements of electronic dynamics.