Atomic physics in Intense Laser Field · Atomic physics in Intense Laser Field M. A. Bouchene...
Transcript of Atomic physics in Intense Laser Field · Atomic physics in Intense Laser Field M. A. Bouchene...
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