molecular excitation by chirped laser radiation in ladder climbing and autoresonance regimes gilad...
TRANSCRIPT
Molecular excitation by chirped laser radiation in ladder climbing
and autoresonance regimes
Gilad Marcus, Arie Zigler and Lazar FriedlandRacah Institute of Physics, Hebrew University, Jerusalem, Israel
Outlines for the Lecture
• Definition of the problem
• Ladder climbing and the Auto-Resonance
concepts
• Ladder-climbing experiment on HF molecule Radiation source for Excitation of the molecule
Basics of Auto-Resonance
Anharmonic Oscillator Harmonic Oscillator
krrm
m
k0
!3
sin3 g
ggl
)( 00 fl
g
Pendelum frequancy Vs. amplitude
0.98
0.985
0.99
0.995
1
1.005
0 0.1 0.2 0.3 0.4 0.5 0.6
Amplitude
0
pendulum
Pendulum frequency Vs. amplitude
• How to excite nonlinear systems into
high energy ?
• Changing the drive frequency will keep it in resonance.
Pendelum frequancy Vs. amplitude
0.98
0.985
0.99
0.995
1
1.005
0 0.1 0.2 0.3 0.4 0.5 0.6
Amplitude
Pendulum frequency Vs. amplitude
• How to excite nonlinear systems into
high energy ?
• Changing the drive frequency will keep it in resonance.
but we also have to
continually adjust
the phase
))(cos( 0 ttF
v
Few method to excite nonlinear oscillator
1. Feedback control.
(requires a real time feedback)
2. Exact tailoring of the force. (requires pre-knowledge of the system)
3. Ladder-climbing & autoresonance
Auto-Resonance• The drive frequency is slowly changed
(slow chirp)
• The oscillator is automatically phase locked(provided that the force exceed a certain threshold)
• The energy of the oscillator is a function of the drive frequency
Threshold-chirp relation
20 1)( aa c
ratechirp
2/1
4/3
082.0c
th m
forcedrive
tynonlineariOscillatorc
Auto-Resonance simulation
drive=t
Amplitude, a
Phase Mismatch
20 1 acoscillator
{L. Friedland et al. Phys. Plasmas. 5 (645)}
Ladder climbing in a quantum systems
• Energy levels in Morse potential.
Morse Potential
D
0
nn
qn
qn
n
nnE
1
0
20
21
2/12/1
Ladder of energy levels with decreasing gaps .
1
Two levels with constant frequency drive
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.0
0.5
1.0
lower level probability upper level probability
pro
ba
bili
ty
time
ERabi )exp( tiEE nconstant frequency drive force
R
Two level with chirped drive
))(exp( 21
0 ttiEE
Efficient conversionwhen 2/2 R
chirped drive force
2/ RS TT
/1ST
Ts / TR=2.8
Ts / TR=1
time
The validity of the two level approximation
qm 00 22/
Which means – the width of resonance is smallenough to include only two levels
Characteristic times
/2/1 0mT RR
/1ST
mT cqNL /2/2 0
The limit between quantum mechanics and classicality
qm 00 22/
In terms of the three characteristic times:
1/2 NLRs TTT
The condition for efficient ladder-climbing
2/ R
In terms of the three characteristic times:
2/ Rs TT
Efficient classical autoresonance
.
4/32/10 )/(82.0 cth m
48.1/2 NLSR TTT
In term of the characteristic times:
P1-P2 parametersRS TTP /1 SNL TTP /2
Quantum limit:
212 1/ PPTTT NLRs
Efficient transfer between 2 levels:
22/ 1 PTT Rs
Efficient Autoresonance: 2
122 /67.048.1/ PPTTT NLSR
P1-P2 parameters
RS TTP /1 SNL TTP /2
.
energy~
Ladder climbing-below threshold
Ladder climbing-above threshold
Autoresonance-below threshold
Autoresonance-above threshold
Design consideration for experiment
RS TTP /1 SNL TTP /2
.
energy~
~
2p
Experiment with HF molecule:requirements from the radiation source
54.20 In the IR regime
%16)(0
To bring the population to the 4th level
2700
cm
mJth Ladder climbing threshold
Theoretical curve of phase matchingfor PPKTP with period of 27.1pumped by wide-band Ti:Sapphire Laser
• Idler spectrum 2-3
• Signal spectrum 1-1.5
Signal & idler Vs. Pump
00.5
11.5
22.5
33.5
4
0.795 0.8 0.805 0.81 0.815
pump [ m icron]
S &
i
s1
s2
i1
i2
The Experiment
M on och rom ato r
B .S P P K T P I risG a :A s f i lter
S iP h otod iod e
I n :G a :A sP h o to d io d e
1 G H z O s cillo s co p e
S ign a l + Id lerC olim a ted T i:S ap p h ireCollimated Ti:Sapphire
The Signal & Laser spectrum
1 00 0 11 0 0 1 20 0 1 30 0 1 40 0 1 50 0
7 90 8 00 8 10 8 20
S ign a l w a velen g th [n m ]
P u m p w av elen g th [n m ]
Laser spectrum
Signal spectrumO Non collinear
---Collinear
Delay as a function of wave-length
Signal delay Vs. Wavelength
100010501100115012001250130013501400
0100200300400
Delay [pSec]
Wa
ve
len
gth
[ nm
]
Chirp measurement
0.796 0.800 0.804 0.808
1.0
1.5
2.0
2.5
3.0
3.5
sign
al a
nd id
ler
wav
elen
gths
(m
)
pump wavelength (m)
signal: first branch
IR specifications
• Bandwidth – 25%
• Pulse length – 185 psec
• Spot size 60x 700
• Energy – up to 200J
P1-P2 parameters
energy~
RS TTP /1
SNL TTP /2
.
-Witte et al. – Cr(CO) 6
-Maas et al. - NO
-Our experiment - HF
Demonstration of ladder climbing on HF molecule.
IR spectrum
HF experiment results
Conditions:Avg. Number of photons
Standard deviation
10 torr HF11.164.6
10 torr Air0.50.7
Continually evacuated
0.330.57
10 torr HF & filtered spectra
1.51.1
Summary
• We have shown theoretically a smooth transition from ladder-climbing to autoresonance
• We have generated a chirped, ultra wideband radiation source in the IR
• We have demonstrated ladder-climbing on HF molecule
Plans for the future
• Improving the optics to allow us to be above the threshold
• Check the transition from quantum-mechanics to classicality.
• Other molecules
The end