Laser-assisted Autoionzation

Z. X. Zhao

X. M. Tong and C. D. Lin

KSU AMO Seminar, 3/10/04

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

Aautoionization / Fano profile

Reduced energy:

q parameter: ratio of direct ionization and autoionization.measure the strength of interference.

Resonance width:

Shifted resonance position:

q Tr

Vc*T

T

Tr

Vc

Illustration of pump-probe schemes

Time-resolved spectra

Pump X-ray

Probe laser

Initiate atomic process

Linear or circular

Cross-correlation Probe atomic dynamics

Can be attosecond pulse!

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.

1. Hentschel et al, Nature 414, 5092. Drescher et al, Science 291, 19233. Drescher et al, Nature 419, 803

Example of attosecond metrology: Laser-assisted Photoionization

t

AL(t)

X-ray

W/o Laser Delay=0 Delay=T/4

Kitzler et al, PRL88, 173904

x //

L

Spectrum:

Formulation of Laser-assisted PI

Strong field approximation

depletion of ground state

0 exp(iIpt) d3 pb(p , t)

p

Stationary phase equation: ts: Saddle point

Electron amplitude:

Free electron: Coulomb field, laser field, X-ray field

Bound electron: excitation

Photoionization: Laser field, X-ray field

px IW 0

Kinetics

1

2[p

A (t)]2 W0

Linear polarization:

p

p 0

A (t)

x

y

A Asin(t)

e x

Or:

Electron energy at observation angle :

:energy conservation

Laser-assisted autoionization: Lorentzian shape

Virtual three-step process:1. Resonance state excited by X-ray at time t1;2. Decay at time t2 giving birth to continuum electrons;3. Propagation of electrons in the laser field.

Laser-assisted: electron spectrum under strong field approximation (SFA):

f (E) dtf (t)exp(iEt) 1

i(E E r) 2

f (t) exp( iE rt 2

t)Field-free:

Time profile:

Energy domain:

Laser-assisted autoionization: Fano shape

Profile in energy domain:

Profile in time domain:

,E ,q

bL (p , t)

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

Feshbach resonance: two-ch potential with coupling

Ch1:Only 1 deeply bound state to exclude excitation

Coupling

Ch 2

X-ray

Laser

Xray pulse: 0.5 fs, 1x1012 W/cm2, 38.1 eVLaser: 10 fs, 2x1012 W/cm2. Phase:0 and frequency 0.04 a.u.(1 eV).

Energy gap 27.21 eVResonance 23 eVGround state -16.1 eV

Lx //

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).

Laser

X-ray

Show agreement between analytical-model and num-simulation

Angle-Integrated spectra

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).

1 resonance case

Two pulses on top of each other for positive q (delay zero)

Laser

X-ray

q=4.2 –only change

Laser freq:1eV

Laser freq:2eV

Zero angle, no delayTotal

Resonance only

interference from direct and resonance

Laser

X-ray

better sideband developed

Time resolved spectra in forward direction

dr tEE )(

Measuring lifetime

Electron counts within sideband from 0.5 a.u. to 0.7 a.u. are plotted verse time delays.

Laser phase 0

Laser phase pi/2

ecc 10

2 resonances case

Parameters:(0, 1)+6 with energy 64.96eV, lifetimeof 667 fs and (0, 1)+7 with energy 65.08 eV, lifetime of 1000 fs. q=-2.6Xray pulse: duration 4 fs with intensity 1x1012 W/cm2.

No laser field

Energy (a.u.)

Laser-modified spectra for 2 resParameters:(0, 1)+6 with energy 64.96eV, lifetimeof 667 fs and (0, 1)+7 with energy 65.08 eV, lifetime of 1000 fs. q=-2.6Xray 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

Measuring energy separation from quantum beat

Phase difference:(E2-E1)tdelay

E=0.1 EV correspondent to 34.5 fs

)cos(2/)(1221

2121 Etececec ttt Fiting by:

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?

2 resonances case

Energy (a.u.)

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.

2 resonances case

Only first resonance

Only second resonance

Two resonances

)cos(2/)(1221

2121 Eececec

(0,1)+6 : 64.96 eV,667 fs

(0,1)+7 : 65.08 eV, 1000 fs

Energy separation:0.12 eV (34.5 fs)

Drescher et al, Nature 419, 803

Fano profile

Center of gravity:

x //

L

Observation angle 900

Hentschel et al, Nature 414, 509Drescher, Science 291, 1923

Zero observation angle

P P0 A

P P0 A

A P P

2

P2 P P

P P

Forward direction

Backward direction

Measuring laser pulse

Measuring duration of X-ray Bandrauk et al, PRA 68, 041802

Measuring instantaneous field of laser pulses

‘Measured’

‘Real’

Absolute phase measurement: Shot to shot varying phase: asymmetry of electron counts from PI,Nature 414, 182Phase stabilized laser: structure of soft X-ray emission, Nature 421, 611

Total photoelectron spectrum

IL=2x1012, IX=1012 W/cm2,wL=1 eV, L=10fs, X=0.5 fs, delay=0

Measuring atto pulse duration

Bandrauk et al, PRA 68, 041802

Measurement of lifetime in time-domain

ecc 10

Angular distribution of photoelectron spectrum