INTERACTION OF INTENSE SHORT LASER PULSES WITH GASES OF NANOSCALE ATOMIC .pdf
Atomic physics in Intense Laser Field
Transcript of Atomic physics in Intense Laser Field
Atomic physics in Intense Laser Field
M. A. BoucheneLaboratoire « Collisions, Agrégats, Réactivité »,
Université Paul Sabatier, Toulouse, France
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
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)
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-
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