Overview

2. Overview • attosecond transient absorption spectroscopy: • probe the system by spectrally resolved absorption of the EUV pulse • powerful technique, can be applied to molecules and solid state • they have shown that strong field ionisation can create long-lived coherences • they have measured wave-packet motion in a simple open system: Kr+ ion

3. Probing intra-atomic electron motion by transient attosecond absorption spectroscopy • few-cycle pulse creates Kr ions in the superposition of states 4p3/2-1 and 4p1/2-1 • Are these states populated coherently? • EUV pulse creates core-hole in state 3d−1 • transmitted spectrum is measured as a function of time delay

4. Transient absorption spectroscopy: experimental setup EUV spectrometer • Pump: ~750 nm, sub-4 fs, CEP stable, 3 kHz, 7 x 1014 W/cm2 , intensity adjusted with iris • Probe: ~80 eV, bandwidth 15 eV, <150 as, generated in Ne filled tube • Target: Kr in quasi-static cell, 80mbar, interaction length 1mm Figure 1: Probing intra-atomic electron motion by attosecond absorption spectroscopy

5. Measured transient absorption spectra of krypton ions • Absorbance is defined as A(E, τ) = ln(Itrans(E, τ)/I0(E)) • Kr2+ lines appear with a well-resolved delay of TL/2 ≈ 1.25 fs after the Kr+ lines • they analyse dynamics at long delays, after the NIR field is vanished Figure 2: Transient absorption spectra of krypton ions

6. Theory: strong-field ionisation of krypton • strong field populates ground state 4p3/2-1 (mj = 3/2 = −3/2, −1/2, 1/2, 3/2) and excited state 4p1/2-1 (mj = 1/2 = −1/2, 1/2) • spin orbit splitting 0.67 eV g wave-packet evolves with period 6.2 fs • Kr+ is an open system – describe with density matrix rjj’(mj) • diagonal elements – population of states • off-diagonal elements – coherences • coherence is defined as: Figure 3: Build-up of electronic coherence in Kr+ produced by optical field ionization (theory). • for 3.8 fs pulse: g(t) = 0.6

7. Probing the coherence by attosecond absorption spectroscopy • EUV pulse promotes the ions from the coherent superposition of 4p3/2-1 and 4p1/2-1 to 3d3/2−1 • two pathways result in interference • (transition 4p1/2-1 to 3d5/2−1 is forbidden, therefore there is no interference in the 4p3/2-1 to 3d5/2−1 transition) • phase between 4p3/2-1 and 4p1/2-1 : Figure 4: Attosecond absorption spectroscopy reveals intra-atomic electron wave-packet motion in Kr+. • wave-packet evolves with period TSO = 6.2 fs

8. Modulations in the absorption spectra Experiment Theory • coherence between 4p3/2-1 and 4p1/2-1 results in modulation of the absorption lines 4p3/2-1g 3d3/2−1 and 4p1/2-1 g 3d3/2−1 • they fit their model (rand TSO) to get the best agreement with experiment • very good agreement for TSO = 6.3 +- 0.1 fs and degree of coherence g = 0.63+-0.17, not so good agreement for populations (e.g. 2r3/23/2 = 0.23 from fit, 0.05 from calculation)

9. Reconstruction of valence-shell electron wave-packet motion • absorbance at photon energies 81.20–81.45 eV corresponds to 4p3/2-1g 3d3/2−1 transition • they retrieved phase with resolution 0.6 fs • time 0: when Kr+ reaches 95% of its stationary value • can measure the phase with attosecond streaking (?) Figure 5: Reconstruction of valence-shell electron wave-packet motion.

10. Summary and outlook • Transient attosecond absorption spectroscopy is a powerful technique, can be extended to study processes in atoms, molecules and solid state • Should work for many materials with arbitrary ionisation potential • Can study (de)coherences in complex systems in real time • Quantum chemistry: long-lived electron wave packet can affect nuclear motion, molecular bond breaks where the hole migrates Remacle F , Levine R D PNAS 2006;103:6793-6798 Snapshots of the densities of the hole as a function of time for TyrAla3 for ionization of the HOMO (Left) and HOMO-1 (Right).