1. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Ultrafast Electron Dynamics of non-thermal population in metals INFM and Università Cattolica del Sacro Cuore Dipartimento di Matematica e Fisica, Via Musei 41, Brescia. Claudio Giannetti

2. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Introduction ToF LINEAR PHOTOEMISSION: hν > Φ → mapping of EQUILIBRIUM ELECTRON DISTRIBUTION Femtosecond Light Pulses NON-LINEAR PHOTOEMISSION: hν < Φ → Mapping of NON-EQUILIBRIUM ELECTRON DISTRIBUTION CW Light 2-Photon Photoemission with P -polarized light hν=3.14eV Log Scale 10 6 sensitivity I abs =13 μJ/cm 2 Occupied states Non-equlibrium Distribution n=1 IPS Ag(100)

3. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Opened Problems NON-LINEAR PHOTOEMISSION on metals is a powerful tool to investigate 2 main physical questions: 1.PHOTON ABSORPTION MECHANISMS 2.NON-EQUILIBRIUM ELECTRON DYNAMICS

4. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Free-electron dispersion E k || Photon Absorption PHOTON ABSORPTION MECHANISMS PROBLEMS: ΔEΔE Δk || The intraband transition between s-s states within the same branch is FORBIDDEN for the conservation of the momentum. Recently the excitation mechanism has been attributed to: Laser quanta absorption in electron collisions with phonons. [ A.V. Lugovskoy and I. Bray, Phys. Rev. B 60, 3279 (1999)] Photon absorption in electron-ion collisions. [B. Rethfeld et al., Phys. Rev. B 65, 2143031 (2002)] THE ENERGY ABSORPTION IS DUE TO A THREE-BODY PROCESS AND NOT TO A DIPOLE TRANSITION

5. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Photon Absorption PHOTON ABSORPTION MECHANISMS RESULTS: E bin (eV)E-E f (eV) SCATTERING-MEDIATED ABSORPTION and PHOTOEMISSION scattering k || =0 E vac EFEF Z. Li, and S. Gao, Phys. Rev. B 50, 15394 (1994) Snapshot of the non-equilibrium electron distribution during the laser pulse duration (150 fs) DEPENDENCE ON POLARIZATION → The models predict a collision term: in agreement with the measured RATIO (C. Giannetti et al., in preparation.) (I P /I S ) 3 =0.69 R theor =0.29 R exp =0.22±0.1

6. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Introduction E vac E fermi occupied states empty states scattering hνhν hνhν photoemission decay dynamics of non-equilibrium electron distribution in Au film: PUMP: hν=1.84eV, I abs =120μJ/cm 2 PROBE: hν=5.52eV W.S. Fann et al., Phys. Rev B 46, 13592 (1992). Time Resolved 2-Photon Photoemission (TR-2PPE) pump probe delay time τ e–e– e–e– e–e– Φ NON-EQUILIBRIUM ELECTRON DYNAMICS PROBLEMS: This result is not compatible with Fermi-Liquid Theory

7. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Non-Equlibrium Electron Dynamics NON-EQUILIBRIUM ELECTRON DYNAMICS PROBLEMS: A.At our moderate laser intensities (I abs =13 μJ/cm 2 ), the electron relaxation time τ is consistent with Fermi-Liquid theory? B.Indirect population of empty states such as Image Potential States?

8. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Non-Equlibrium Electron Dynamics NON-EQUILIBRIUM ELECTRON DYNAMICS RESULTS: Time-Resolved Photoemission Spectroscopy Photemitted charge autocorrelation of different energy regions The Relaxation Time of the high-energy region is smaller than the pulse timewidth: τ<150 fs (C. Giannetti et al., in preparation.) This result is compatible with Fermi-Liquid Theory

9. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Non-Equlibrium Electron Dynamics NON-EQUILIBRIUM ELECTRON DYNAMICS RESULTS: G. Ferrini et al., Phys. Rev. Lett. 92, 2568021 (2004). Ag(100) Dipole selection rules Expected dipole selection rules: J=0 in S -pol J≠0 in P-pol Violated in non-resonant case EFEF EvEv occupied states empty states Φ n=1 Indirect population of IPS Scattering Assisted Population NO DIPOLE TRANSITION

10. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Conclusions NON-EQUILIBRIUM PHOTOEMISSION SPECTROSCOPY on Ag(100) Role of scattering in the photon absorption mechanism NON-EQUILIBRIUM electron dynamics at moderate laser intensities is well described by Fermi-Liquid theory Demonstration of indirect population of empty states such as IMAGE POTENTIAL STATES

11. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Responsibles: F. Parmigiani, G. Ferrini. Co-workers: F. Banfi, G. Galimberti, S. Pagliara, E. Pedersoli.

12. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. ToF e-e- UHV sample TOPG Tunability 1150-1500 nm (0.8-1.1 eV) Pulse width 150 fs Average power 50mW 4th 4.2eV 2nd 2.1eV Experimental Setup Amplified Ti:Sapphire Oscillator Pulse width: 130 fs Rep. rate: 1kHz Average power: 1W Wavelenght: 790nm ( 1.57eV ) Source : Travelling Wave Optical Parametric Generator TRANSLATOR BS pumpprobe delay τ 4th 6.28eV 2nd 3.14eV Energy resolution: 10 meV @ 2eV

13. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Introduction NON-LINEAR PHOTOEMISSION on METALS → IMAGE-POTENTIAL STATES (IPS) Ag(100) U. Hofer et al., Science 277, 1480 (1997). E bin = 0.5eV IPS: 2-dim electron gas in the forbidden gap of bulk states 2PPE: Population and Photoemission from IPS → Electronic Decay Dynamics

14. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. 2-PPE on Ag(100) Fermi Edge Direct Photoemission 2-Photon Photoemission with P -polarized light 2-P Fermi Edge Photoemission Spectra on Ag(100) single crystal hν=6.28eV E kin = hν-Φ hν=3.14eV E kin = 2 hν-Φ hνhν Log Scale 10 6 sensitivity E fermi E vac occupied states empty states Φ n=1 I abs =13 μJ/cm 2 P -polarized incident radiation

15. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. High-Energy Background HIGH ENERGY REGION: Non-linearity order REGION A: 2nd order process REGION B: 3rd order process EXPERIMENTAL EVIDENCES: Region B does not show a flat distribution The RATIO Region B/Region A is 10 -2 These results suggest that the 3rd order photoemission in the high energy region is not a coherent process Ag(100)

16. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Image Potential State Δ hν=0.39eV hν=3.15eVhν=3.54eV Shifting with photon energy m*/m  0.88  0.04 n=1 Fermi edge Dispersion of IPS in k || -space Ag(100) E kin = hν-E bin E bin  0.5 eV n=1 Ag(100) K || =0 IMAGE POTENTIAL STATE

17. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. 3-photon Fermi Edge 2 and 3 photon Fermi Edge: - ΔE = hν - Fermi-Dirac fitting Energy-shift with photon energy: ΔE 3PFE = 3 ·Δ hν Non-linearity order: 3-photon Fermi edge vs 2-photon Fermi edge 3-Photon Fermi Edge: Three experimental evidences... n=2 n=3

18. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Photoemission Process PHOTOEMISSION PROCESS PROBLEMS: E fermi E vac occupied states empty states Φ n=1 Upon the absorption of two photon the electron is already free. Which is the absorption mechanism responsible of the free-free transition? Evidence of ABOVE THRESHOLD PHOTOEMISSION on solids

19. IVC-16, Venice June 28-July 2, 2004 INFMD.M.F. Photoemission Process PHOTOEMISSION PROCESS RESULTS: To evaluate the cross section for an n -photon absorption involving the initial and final states: E fermi E vac occupied states empty states Φ n=1 is proportional to the Transition Matrix Element in the DIPOLE APPROXIMATION In this calculation we have to consider the mixing of the final free electron state with all the unperturbed Hamiltonian eigenstates→ is it difficult to evaluate the contribution of this mixing to T (3). Rough Estimate T (3) /T (2)  10 -6 Experimental Value T (3) /T (2)  10 -4 Is another mechanism involved? (F. Banfi et al., in preparation.)