Laser-assisted Autoionzation

1. Laser-assisted Autoionzation Z. X. Zhao X. M. Tong and C. D. Lin KSU AMO Seminar, 3/10/04

2. Outline • Introduction • Autoionization • Time-resolved measurement • Analytical model • Laser-assisted photoionization • Lorentzian shape • Fano resonance • Numerical simulation • Discussion of results • Comparison of total spectra • Deduce lifetime • More than one resonance:quantum beat

3. Introduction

4. Vc Aautoionization / Fano profile Reduced energy: Shifted resonance position: Resonance width:  q parameter: ratio of direct ionization and autoionization. measure the strength of interference.

5. Can be attosecond pulse! Illustration of pump-probe schemes Linear or circular  Pump X-ray Initiate atomic process Probe laser • Cross-correlation • Probe atomic dynamics Time-resolved spectra

6. Time-resolved measurements: previous work With: attosecond soft-X-ray and fs laser pulse, • Cross-correlation can be built for laser assisted photoionization to: • Measure X-ray pulse duration[1,2] • Measure absolute phase of the laser pulse(?) • Measure the lifetime of a resonance: laser assisted auger decay [3] • Study Laser-assisted autoionization. Hentschel et al, Nature 414, 509 Drescher et al, Science 291, 1923 Drescher et al, Nature 419, 803

7. Example of attosecond metrology: Laser-assisted Photoionization X-ray AL(t) t Spectrum: W/o Laser Delay=0 Delay=T/4 Kitzler et al, PRL88, 173904

8. analytical model

9. Formulation of Laser-assisted PI Free electron: Coulomb field, laser field, X-ray field Strong field approximation Bound electron: excitation Assumptions depletion of ground state Photoionization: Laser field, X-ray field Electron amplitude: ts: Saddle point Stationary phase equation:

10. y   x  Kinetics :energy conservation Linear polarization: Electron energy at observation angle : Or:

11. Laser-assisted autoionization: Lorentzian shape Time profile: Field-free: Energy domain: Laser-assisted: electron spectrum under strong field approximation (SFA): Virtual three-step process: Resonance state excited by X-ray at time t1; Decay at time t2 giving birth to continuum electrons; Propagation of electrons in the laser field.

12. ? Laser-assisted autoionization: Fano shape Profile in energy domain: Profile in time domain:

13. Numerical model Two-channel TDSE to model two-e- system in a laser field: • Split-Operator propagation method used to solve TDSE • Two channel continuum constructed by applying scattering wave boundary condition

14. Laser Ch 2 Coupling X-ray Ch1:Only 1 deeply bound state to exclude excitation Feshbach resonance: two-ch potential with coupling Xray pulse: 0.5 fs, 1x1012 W/cm2, 38.1 eV Laser: 10 fs, 2x1012 W/cm2. Phase:0 and frequency 0.04 a.u.(1 eV). Energy gap 27.21 eV Resonance 23 eV Ground state -16.1 eV

15. results

16. X-ray Laser Angle-Integrated spectra Two pulses on top of each other for negative q Fano resonance: 22.9 eV (position), 0.055 eV (12 fs) (width) and -4.2 (q number). Xray: 0.5 fs, 1x1012 W/cm2, 38.1 eV Laser: 10 fs, 2x1012 W/cm2. Phase:0 and frequency 0.04 a.u.(1 eV). Show agreement between analytical-model and num-simulation

17. X-ray Laser 1 resonance case q=4.2 –only change Two pulses on top of each other for positive q (delay zero)

18. X-ray Laser Zero angle, no delay Laser freq:1eV Total Resonance only interference from direct and resonance better sideband developed Laser freq:2eV

19. Time resolved spectra in forward direction

20. Measuring lifetime Laser phase pi/2 Laser phase 0 Electron counts within sideband from 0.5 a.u. to 0.7 a.u. are plotted verse time delays.

21. 2 resonances case No laser field Parameters: (0, 1)+6 with energy 64.96eV, lifetime of 667 fs and (0, 1)+7 with energy 65.08 eV, lifetime of 1000 fs. q=-2.6 Xray pulse: duration 4 fs with intensity 1x1012 W/cm2. Energy (a.u.)

22. Laser-modified spectra for 2 res Parameters: (0, 1)+6 with energy 64.96eV, lifetime of 667 fs and (0, 1)+7 with energy 65.08 eV, lifetime of 1000 fs. q=-2.6 Xray pulse: duration 4 fs with intensity 1x1012 W/cm2. Laser: duration 50 fs with intensity 5x1011 W/cm2. Phase:pi/2 and frequency 1.55 eV (800nm). Energy (a.u.) Counts in sideband is 1% of total resonance population

23. Measuring energy separation from quantum beat Phase difference: (E2-E1)tdelay E=0.1 EV correspondent to 34.5 fs Fiting by:

24. Conclusions • Build an analytical model for laser-assisted AI • Justified by numerical simulation • Deduce lifetime and • Energy separation of two resonance • Q parameter?,and • other significance?

25. 2 resonances case Electron spectra from decay itself at fixed time delay with different laser pulse duration Width of individual sideband decreases as laser pulse duration increased. For long enough pulse, each sideband shows two sub-peaks correspondent to contribution from both resonances. For short pulse, it can’t be resolved, interference is expected. Energy (a.u.)

26. 2 resonances case Only first resonance Only second resonance

27. Two resonances (0,1)+6 : 64.96 eV,667 fs (0,1)+7 : 65.08 eV, 1000 fs Energy separation: 0.12 eV (34.5 fs)

28. Drescher et al, Nature 419, 803

29. Fano profile

30. Observation angle 900 Center of gravity: Hentschel et al, Nature 414, 509 Drescher, Science 291, 1923

31. Zero observation angle Forward direction Backward direction Measuring laser pulse Measuring duration of X-ray Bandrauk et al, PRA 68, 041802

32. Measuring instantaneous field of laser pulses ‘Measured’ ‘Real’ Absolute phase measurement: Shot to shot varying phase: asymmetry of electron counts from PI,Nature 414, 182 Phase stabilized laser: structure of soft X-ray emission, Nature 421, 611

33. Total photoelectron spectrum IL=2x1012, IX=1012 W/cm2,wL=1 eV, L=10fs, X=0.5 fs, delay=0

34. Measuring atto pulse duration Bandrauk et al, PRA 68, 041802

36. Measurement of lifetime in time-domain

37. Angular distribution of photoelectron spectrum