Atomic physics in Intense Laser Field

M. A. BoucheneLaboratoire « Collisions, Agrégats, Réactivité »,

Université Paul Sabatier, Toulouse, France

“Popular”

Tradit.NLO

Extr.NLO:Reality

May be

OUTLOOKI- Free electron in an EM field: - Classical treatment

- Relativistic treatment- Quantum treatment

II- Atom is a strong Laser field: - Scenario with I- Experimental results

III- Above Threshold Ionisation

IV- Tunnel ionisation

I-Free electron in an EM field:Classical treatment

Drift motion

Oscillatory motion

magn0

elec

v BF vF qE ( 1); E E cos tF E c

×= = << = ω

E dv

2 2 2d 0

2k 2T

v q EdvF m E mdt 2 4m

π=ω

= → = +ω

PONDEROMOTIVE ENERGYUP

214 2

P m W /cmU (eV) 9.3410 I−

µ= λ

13 2

18 2P 2P

forU

fo1eV I 10 W / cm

100keV I 10 W /r (U 0.2mccm )

=

Force on the electron in a laser spot: PI I(r) F U= → = −∇

2 2x yρ = +

I

I−∇I−∇

The electron is ejected

I-Free electron in an EM field:Relativistic treatment( ) x 0 y 0F q E v B ; E E cos t; B B cos t= + × = ω = ω

E

Bk

electron at rest

e-

2pU /mc 1≤

ω2ω

ωPhoton dragging

Radiation pattern

Newton Relat. (pert reg. )

ω 2ω

General case: analytical solution

Periodic motionHARMONIC DECOMPOSITION

Fundamental oscillation frequency:

Fundamental emission frequency :

P2

e

4Um c

ε = t t;x kx;z kz= ω = =

osc2

20

111 sin

2 2

ω=

εω + + ξ

( )em

21

1 1 cos4

ω=

εω + − θ

0z(0) = −ξ

Zθ

0 0ξ =

I-Free electron in an EM field:Quantum treatment

Hamiltonian: ( )2

0

P qAH

2AE E c; os ttm

∂= − =

∂= ω

−

Schrödinger equation: (r, t)i H (r, t)t

∂Ψ= Ψ

∂Analytical solution!

( )d p p 0E U U sin 2 t qkEi k r t i i cos t 12 m

0(r, t) e e e + ω − − ω − ω ωΨ = Ψ

2 2

driftkE2m

=

VOLKOV STATE

- STATIONNARY STATE BUT TIME DEPENDENT ENERGY

VOLKOV STATE( )

d p 0pE U U sin 2 t qkEi k r t i i cos t 12 m

0(r, t) e e e ω − − ω − ω ω

+

Ψ = Ψ

Classical part

mi cos m im

mm

e i J ( )e=∞

α θ θ

=−∞

= α∑d pi k rE U

2t

i t m i t0 n m

n m

dP n P mU EU2

(r, t) e J e i J 2 2 e

−+

ω ω

Ψ =ω ω

Ψ − ∑ ∑

Even harmonics Odd + Even harmonics:Needs dE 0≠

New effects : p dU ,E ≥ ω

( )2k d p

00qEV V sin t

E E 2U si

m

t

;

n= −

= −ω

ω

ω

d pE E U n= + + ω

II- Atom in a strong laser fieldModel: Bound - Unbound transition for a single electron

Fundamental state

continuum

ionE

ionEω<<

Dynamics depends strongly on the laser intensity

12 2 NP ion ionI 10 W / cmU E ; P; I<< ω<< ∝≤

N ω

I

Perturbative multiphoton ionisation :

Above Threshold Ionisation

Scenario with I

P ionU Eω<< ≤

ion PE Uω<< ∼

)P p ioncrit.U U E> ≥ >> ω

VALID IF I < Isat (depletion of the ground state)

Experimental manifestation

Electron spectrum Radiation spectrum

p2U∼

Ee

p10U∼

PLATEAU

ion pE 3.17U+∼

PLATEAU2 ω

ω(2n 1)+ ω

- Quantification: transition into a Volkov state

- Cut-off energy? -Odd harmonics: inversion symmetry

-Cut-off energy?

ATI Tunneling→ Intra at.trans. ATI Tunneling→ +

Above Threshold Ionisation:Important features

Classical explanation.

P2U

0 0E E cos t;v(t ) 0 (electron created at rest)= ω =

2kin P 0 PE 2U cos t : 0 2U= ω →

1- Cut off energy

Drift motion even if v(t0)= 0 (phase shift effect)

2- Peak suppression

( ) Pelec. ion

U if conversion potential kineticE n s E

0 else≥ ↔

= + ω− ≥

PPeak sup ressi(1) long pulse on when U→ ≥ ω

(1)

(2)

(2) Short pulse

13 22 10 /I W cm×

12 22.2 10 /I W cm= ×

12 27.2 10 /I W cm= ×

12 27.2 10 /I W cm= ×

Tunnel Ionisation

Time dependent Barrier

Maximum of Ionisation when

0U(x) V(x) eE sin t x= + ω

t [ ]2π

ω = π

( )( ) ( )3/ 2ion ion

0

2Z m 13/ 2 22E 2E2 3Eion0ion n*l* ion3/ 2

0ion

2 2E3E C f (l,m)E eE2E

− −

− Γ = π

Tunnel Ionisation: Keldysh parameter

time needed t o escapeoptical period

γ = ion

P

E2U

γ =

1 Tunneling1 Multiphoton Ionisation

γ < →γ > →

Ionis. rate in the quasi-static regime (Amnosov, Delone, Krainov formula):

em c 1= = =1/ 2ioninitially electron n*,l,m ;l* n * 1;m Z(2E )= − =

( )( )( )m

2l 1 l mf (l,m)

2 m ! l m !

+ +=

−

ln*2

n*l*2C

n* (n * l* 1) (m* l*)=

Γ + + Γ −

Tunnel Ionisation: cut-off energies

Three-step model

Re-collision

0E E sin t= ω

0t t= ( )

( )

002

002

eEx sin t sin tm

eE t tm

−= ω − ω

ω

+ ω −ωω

1 0t t (t )=

0t [ ]2π

ω π

Force on e-

Force on e-

TRAJECTORIES

…. : No return

: Return

Several t0

0t [ ]2π≤ ω ≤ π π

00 t [ ]2π

≤ ω ≤ π

t / 2ω − π

Re-collision:

Diffusion ATI Plateau

Recombinaison HHG plateau

( )

1 12 2

20kin 1 02

0 0kin P

max io

0

n

1

P

t t x(t ) 0

e EE cos t cos t2m

maxwhen t E 3.17UN E 3.17U

108 t 342

= =

= ω − ωωω →ω =

→ = +

→

ω

( )

1 1 12

20drift 1 02

0 00 rift P1 d

t t x(t ) x(t ) (best situation)

eEE 2cos t cos t2m

maxwhen t 105 t 351. 1 U7 E 0

+ += = −

= ω − ωωω →ω → =

PERIOD T/2 2ω

FURTHER DEVELOMENTS

• Attosecond pulse generation (mode locking of HH)

• Coherent sources in the VUV and XUV• Cluster explosion :

neutron sourcesHighly energetic particles

CLUSTER EXPLOSION