Transcript Bound States of a Free Electron and

Surprising strong field dynamics in laser filaments
Misha Ivanov
• Lasing without inversion in the air (N2)
• Bound states of a free electron
• Lasing without inversion in the air
D.Kartashov, S. Haessler, G. Andriukaitis, A.
Pugžlys, A. Baltuška
A. Zheltikov
J. Möhring, M. Motzkus
M. Richter, F. Morales, O. Smirnova
M. Spanner
Laser filamentation: the bare basics
Kerr effect and Kerr lens
n( I )  n0  n2 I 
n(r )  n0  n2 I (r )
• Self-guided beam, can move very far
• Interplay of self-focusing and defocusing
d plasma (t )  n(t )
1

2
F cos t
Laser filamentation: the bare basics
• Looks pretty
•Broad spectrum: UV- IR
Strong field molecular alignment: the bare basics
F cost
Q
Induced dipole:
d(E)= a x E cost
- oscillates with the field
Cycle-averaged interaction energy:
U(q)=- ¼ [Da] E2cos2q
N2 Field-free alignment after a short pulse
Key facts for today
• Air is made of molecules, mostly N2
Key facts for today
• Air is made of molecules, mostly N2
• Filamentation by-product I:
They rotate
Key facts for today
• Air is made of molecules, mostly N2
• Filamentation by-product I:
They rotate
• Filamentation by-product II: molecular ions N2+
8
N2+
2
B u
4
0

2
1
2
2
2
0
X g
1.0
A u
354,89
391,44
358,21
427,81
388,43
356,39
Energy, eV
Energy, eV
6
R, Å

1
0
1.2
1.4
1.6
1.8
2.0
Key facts for today
• Air is made of molecules, mostly N2
• Filamentation by-product I:
They rotate
• Filamentation by-product II: molecular ions N2+
• Filamentation by-product III : broad spectra, one-photon transitions can saturate
8
N2+
2
B u
B(v=0) -> X(v=0): 391 nm
4
0

2
1
2
2
2
0
X g
1.0
A u
354,89
391,44
358,21
427,81
388,43
356,39
Energy, eV
Energy, eV
6
R, Å

1
0
1.2
1.4
1.6
1.8
2.0
Key facts for today
• Air is made of molecules, mostly N2. Filamentation makes them rotate
• You do not even need to saturate X-> B to make it lase !
8
N2+
2
B u
B(v=0) -> X(v=0): 391 nm
4
0

2
1
2
2
2
0
X g
1.0
A u
354,89
391,44
358,21
427,81
388,43
356,39
Energy, eV
Energy, eV
6
R, Å

1
0
1.2
1.4
1.6
1.8
2.0
Inversion without inversion
• Inversion without inversion:
B
X
• More X molecules than B molecules:
PX>PB
B
X
• But more aligned B molecules than X molecules:
PB (Q=0)>PX(Q=0)
• B -> X is a parallel transition
Inversion without inversion
• Inversion without inversion:
B
B
Wup ~ <cos2Q>X PX
Wdown ~ <cos2Q>B PB
X
X
Gain: Wup - Wdown < 0
Transient inversion induced by rotations
Wup - Wdown
R=PB/PX=1/2
Almost transient inversion
Transient inversion induced by rotations
Wup - Wdown
R=PB/PX=1/2
Almost transient inversion
R=PB/PX=3/4
Transient inversion
• Lasing without inversion: transient inversion during rotational revivals
• Better alignment – smaller R is needed for transient inversion
Experiment I: Bright emission
391 emission in N2+
50000
Spectral intensity
40000
9th
4 mm
pump
30000
391 nm beam
20000
11th
10000
0
300
350
400
450
500
wavelength, nm
• Forward, well collimated
• Needs a seed:
Appears only when filamentation generates spectrum around 390
• Universal: has been observed for a single pump pulse @
• 400 nm, 800 nm, 1 mm, 2 mm, 4 mm
Another candidate ?
• Emission due to coherent polarization
•a.k.a. Wave mixing, Parametric emission,...
DXB(t)= < YX(t)|d|YB(t) >
DXB(W)= FT (DXB(t))
• General
• only needs coherence between N2+ (X) and N2+(B)
• all it needs is a seed around 390 nm
• will happen for all pump wavelengths that make filaments
• Will last after the filament is gone, as long as X-B coherence lasts
• Natural sensitivity to rotations
Coherent polarization / Wave mixing: Effect of rotations
• DXB(t)= <YX(t)|d| YB(t)> + c.c.
• Requires overlap of YX(t) and YB(t)
• Rotations with different period kill the overlap and DXB(t)
Wup - Wdown
Opposite temporal patterns
Inversion without
inversion
‘Wave mixing’
• Need
time-resolved measurements !
Experiment II: Time-resolved measurements
• Experiment @ 1.03 mm, 240 fsec
• Starts immediately,
• Lasts ~ 15 psec
• Follows revivals in N2+ B state
Time-resolved signal: Experiment vs Theory
Experimental FROG Spectra
‘Wave mixing’ FROG (Theory)
Time-resolved signal: Experiment vs Theory
Experimental FROG Spectra
Excellent Disagreement !
Time-resolved signal: complementary patterns
Experimental FROG Spectra
Transient Inversion
R=1
‘Wave Mixing’
Experiment vs Theory
Experimental FROG Spectra
Transient Inversion
‘Wave Mixing’
R=3/4
• Lasing without inversion:
• Threshold effect: better alignment – smaller R=PB/PX is needed
• Let us optimize alignment!
3 bar
Experiment III: Optimized alignment
Optimal sequence
N2+ emission: more
than 104 brighter
for optimal pulse
sequence
x 10-4
delay,ps
The smoking gun?
Bound states of a free electron
NRC Canada
Maria Richter
Serguei
Patchkovskii
Felipe Morales
Olga Smirnova
What is common between these?
Ilya Repin: Barge haulers on Volga
Laser filamentation in the air
Laser filamentation: the bare basics
Kerr effect and Kerr lens
d ()  [a ()  (3) () F * F ]F ()
n( I )  n0  n2 I 
n(r )  n0  n2 I (r )
d plasma (t )  n(t )
1

2
F cos t
Is ionization needed for filamentation?
Kerr effect, n(I), in
air @ 800 nm
n(I)
Intensity
1013 W/cm2
• Is this really possible, and if possible – when, why, and how?
Acceleration of neutrals: ‘free’ electron pulling the parent ion
k
He, 800 nm, ~1016 W/cm2
Very strong laser field:
Up=F2/42~ KeV
e-
+
~ mm
r
But how is the rope made?
How the rope is made: frustrated ionization
What happens when the laser intensity is very high?
-zFcost
Oscillation amplitude
a0=F/2 >> Angstrom
-zFcost
Does above-barrier decay necessarily mean ionization?
Again NO!
How the rope is made: The Kramers-Henneberger atom
Idea: W. Henneberger PRL, 1968
Bound electron
Very strong laser field:
nearly free oscillations
Include both:
Bound again!
+
Bound states of the KH potential make the rope
Bound states of the free electron
-zFcost
6.1014 W/cm2
800 nm
The electron is placed at
the exit from the barrier,
simulating tunnel
ionization. It refuses to
behave ionized in 1520% of cases.
Kerr response in strong low-frequency laser fields
-zFcost
Kr, Xe, Ar, O2, N2, @1013 W/cm2
- zFcost
Note:
• at I~1013 W/cm2 all excited states are way above barrier, and ground state
is well below
• Oscillation amplitude a0> 6 a.u is large
Pertinent to all phenomena which include response of bound states in strong
fields, e.g. Kerr effect around and above 1013 W/cm2
Analysis
d (t )  F cost 2
n
| zng ( F , t ) |2
En ( F , t )  E g ( F , t )
In the KH regime for the excited states,
En(F)=En+Up+DEn
The ground state still goes down:
Eg(F)=Eg-DEg
Energy
En (F,) – bound states of a ‘free’
electron
Eg(F,)
ainst(I,)
Intensity ,>1013W/cm2
Intensity
Can this be seen with everything else (ionization, real excitation) piling up on top?
Any signatures of this physics? TDSE for 3D Hydrogen
Grid
1:
2:
2x:
3:
1600 a.u.
r
Z Time step
0-100 +/-200 0.005
0-100 +/-400 0.005
0-200 +/-800 0.005
0-100 +/-400 0.00125
800 a.u.
2
2x
Spacing
0.2
0.2
0.2
0.1
r axis
1
400 a.u.
Field, z axis
Role of box size
Role of the box size:
• Absorb more, or less, free electrons
• See how this changes the Kerr response
1600 a.u.
800 a.u.
2
2x
r axis
1
400 a.u.
Field, z axis
High order Kerr effect: TDSE for 3D Hydrogen
Short pulse: sin2 with 4 cycles turn-on and turn-off, l=0.9 mm
High order Kerr effect: TDSE for 1D Hydrogen
Short pulse: sin2 with 4 cycles turn-on and turn-off, l=1.8 mm
High order Kerr effect: TDSE for 1D Hydrogen
Short pulse: Gaussian FWHM=4 cycles, l=1.8 mm
Saturation of the Kerr response
• Happens just before ionization kicks in
• Once ionization kicks in, it takes over
• HOKE is real, but is important in a very
narrow intensity window
• KH states are playing major role
Conclusions: Lasing without inversion
• Laser filamentation leads to
• Very broad spectrum
-> Easy saturation of 1-photon transitions in the ion: IR-nearUV
• Ionization
• Molecular alignment
• Rotational revivals naturally create time-windows with population inversion
• Better alignment – better lasing ‘without inversion’
Conclusions: HOKE
• In general, saturation of the Kerr effect comes from:
• Ionization (major player)
• Real excitations to ‘bound states of the free electron’
• Modification of the instantaneous response (i.e. virtual transitions) due to
restructuring of the dressed atom.
• Restructuring of the atom leads to saturation and – partly – to the onset of
the reversal of the Kerr effect
• This happens just before ionization kicks in
• Ionization starts to dominate as soon as it kicks in
• The interplay of the three effects is strongly pulse-shape dependent
Proposal for HOKE Consensus
Misha and Rob agreed to build a Russian wet-sauna.
But they could not agree on what floor is best
Rob :
We should shave and sand the floor
Misha: No, we shouldn’t. Sanded floors get slippery when wet,
we can slip and fall
Rob:
No, Misha, we should. If we don’t sand the floor, we’ll get
splinters into our bare feet!
Proposal for HOKE Consensus
Misha Ivanov and Bob Levis agreed to build a Russian wet-sauna.
But they could not agree on what floor is best
Rob :
We should shave and sand the floor
Misha: No, we shouldn’t. Sanded floors get slippery when wet,
we can slip and fall
Rob:
No, Misha, we should. Otherwise we’ll get splinters!
They went to ask the Rabbi.
Rabbi, who is right?
Proposal for HOKE Consensus
Misha and Rob agreed to build a Russian wet-sauna.
But they could not agree on what floor is best
Rob :
We should shave and sand the floor
Misha: No, we shouldn’t. Sanded floors get slippery when wet,
we can slip and fall
Rob:
No, Misha, we should. Otherwise we’ll get splinters!
They went to ask the Rabbi.
You are both right!
Rabbi, who is right?
Proposal for HOKE Consensus
Misha and Rob agreed to build a Russian wet-sauna.
But they could not agree on what floor is best
Rob :
We should shave and sand the floor
Misha: No, we shouldn’t. Sanded floors get slippery when wet,
we can slip and fall
Rob:
No, Misha, we should. Otherwise we’ll get splinters!
They went to ask the Rabbi.
You are both right!
We can’t both be right!
Proposal for HOKE Consensus
Misha and Rob agreed to build a Russian wet-sauna.
But they could not agree on what floor is best
Rob :
We should shave and sand the floor
Misha: No, we shouldn’t. Sanded floors get slippery when wet,
we can slip and fall
Rob:
No, Misha, we should. Otherwise we’ll get splinters!
They went to ask the Rabbi.
We can’t both be right!
Yes you can!
Proposal for HOKE Consensus
Misha and Rob agreed to build a Russian wet-sauna.
But they could not agree on what floor is best
Rob :
We should shave and sand the floor
Misha: No, we shouldn’t. Sanded floors get slippery when wet,
we can slip and fall
Rob:
No, Misha, we should. Otherwise we’ll get splinters!
They went to ask the Rabbi.
Yes you can!
OK, Rabbi, we can’t argue
with you.
But what shall we do with
the floor?
Shall we sand the
floorboards or not?
Proposal for HOKE Consensus
Misha and Rob agreed to build a Russian wet-sauna.
But they could not agree on what floor is best
Rob :
We should shave and sand the floor
Misha: No, we shouldn’t. Sanded floors get slippery when wet,
we can slip and fall
Rob:
No, Misha, we should. Otherwise we’ll get splinters!
They went to ask the Rabbi.
You should sand the
floorboards,
But put them sanded side
down
Conclusions
•Looking inside a dressed atom is not easy!
High order Kerr effect: TDSE for 3D Hydrogen
Short pulse: Gaussian FWHM=4 cycles, l=0.9 mm
5.6 1013 W/cm2
• Kerr is reversed
• Box-size dependence
4.3 1013 W/cm2
• Kerr is saturated
• No box size dependence!
Field, a.u.
High order Kerr effect: TDSE for 3D Hydrogen
Short pulse: Gaussian FWHM=4cycles, l=1.8 mm
5.6 1013 W/cm2
• Kerr is reversed
• Box-size dependence
4.3 1013 W/cm2
• Kerr is saturated
• No box size dependence!
Field, a.u.
High order Kerr effect: TDSE for 3D Hydrogen
Short pulse: Gaussian FWHM=4 cycles, l=1.8 mm
5.6 1013 W/cm2
• Kerr is reversed
• Box-size dependence
4.3 1013 W/cm2
• Kerr is saturated
• No box size dependence!
Saturation of the Kerr response
• Happens just before ionization kicks in
• Once ionization kicks in, it takes over
• HOKE is real, but is important in a very
narrow intensity window
Field, a.u.
Are the KH states really there? TDSE for 1D Hydrogen
Flat-top pulse: sin2 Turn-on/off in Ncycles=4 cycles, 40 cycles flat top
l0.5mm
l=3mm
Resonances are still present, even for l=3 mm
• Deviations from standard model are
much more prominent for flat-top pulses
• KH states are responsible for resonances
Field, a.u.
Photo-electron spectroscopy of the KH atom
free electron oscillations
+ harmonics Vn
(,2, ,...)
‘The KH atom exists’ means ‘Only few Vn matter’
If the KH harmonics act like perturbative fields, we can use standard
Photo-Electron Spectroscopy idea: En,kphoto=En+k;
The system: Potassium atom
Ip = 4.34 eV : Barrier suppression intensity I=1.5 x 1012 W/cm2
Barrier suppression regime is easily achieved with routine setup
Laser wavelength 800 nm, 3D, linear polarization, TDSE
How the rope is made: frustrated ionization
-zFcost
Oscillation amplitude
a0=F/2 >> Angstrom
-zFcost
Suppose the electron tunneled out.
Does this really mean ionization? – No!
• T. Nubbemeyer, K. Gorling, A. Saenz, U. Eichmann, and W. Sandner,
Phys. Rev. Lett. 101, 233001 (2008)
• G. Yudin and M. Ivanov, Phys. Rev. A, 63, 033404 (2001)
Kerr response in strong-field limit
En (F,t,) – bound states of a ‘free’ electron;
On average, go up as Up=F2/42
-zFcost
Eg
Instantaneous response (virtual transitions only!) – almost like usual linear
susceptibility – only for dressed states.
d (t )  F cost 2
n
| zng |
2
En  E g
d (t )  F cost 2
n
| zng ( F , t ) |2
En ( F , t )  E g ( F , t )
Experimental setup
Yb, Na:CaF2
Regen.
SLM
SHG
spectrometer
FROG
UVspectrometer
SHG
1,03 mm, 500 Hz, 7 mJ, 240 fs
Pharos
(Light Conversion)
UVspectrometer
Experimental setup
Yb, Na:CaF2
Regen.
SLM
SHG
spectrometer
FROG
UVspectrometer
SHG
1,03 mm, 500 Hz, 7 mJ, 240 fs
Pharos
(Light Conversion)
UVspectrometer
3 bar
Optimal pulse sequence
N2 fluorescence
N2 fluorescence
delay,ps
Spectroscopy of N2+
8
2
B u
Observed lines
4
0

2
1
2
2
2
0
X g
1.0
A u
354,89
391,44
358,21
427,81
388,43
356,39
Energy, eV
6

1
0
1.2
1.4
1.6
1.8
2.0
internuclear distance, A
Bright coherent emission in forward direction
What is the physical origin?
Physical origin: Possible Candidates
• Stimulated emission due to population inversion in N2+: more B than X
• Universal mechanism for creating population inversion @
400 nm, 800 nm, 1 mm, 2 mm, 4 mm ???
• Ionization into N2+ X state dominates
• Requires seed – but seed can’t create inversion
• Collisions – why >104 enhancement by optimizing alignment ?
Transient inversion induced by rotations
R=PB/PX=3/4
Wdown - Wup
Transient inversion
R=PB/PX=1/2
Almost transient inversion
• Lasing without inversion: transient inversion during rotational revivals
• Better alignment – smaller R is needed for transient inversion
Filamentation-based remote sensing of bad guys
Filament
Lasing
backward
Send laser
beam
Collect information
Make a laser in the air, detect backward emission
Filamentation-based remote sensing of bad guys
Filament
Lasing
backward
Send laser
beam
Collect information
Laser in the air that shoots backwards – not yet, not today 
Laser in the air that shoots forward & without inversion - today 
Time-resolved measurements
• Experiment @ 1.03 mm, 240 fsec
Frequency-integrated cross-correlation
0.1
Cross-Correlation Intensity
Theory
P(N2)=1.8 bar (June 28)
P(N2)=2.1 bar (June 27)
Revival of the
excited ionic
2
state B 
-1
B=2.073 cm
(anti-Stokes branch)
0.0
-2
0
2
4
6
Revival of the
ground ionic
2
state X 
-1
B=1.92 cm
(Stokes branch)
8
10
Delay, ps
Starts immediately, Lasts ~ 15 psec
Sensitive to rotations – but in N2+ B state!
12
14