Molecular excitation by chirped laser radiation in ladder climbing and autoresonance regimes

1
Molecular excitation by chirped laser radiation
in ladder climbing and autoresonance regimes
Gilad Marcus, Arie Zigler and Lazar
Friedland Racah Institute of Physics, Hebrew
University, Jerusalem, Israel
2
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

3
Basics of Auto-Resonance

• Anharmonic Oscillator

• Harmonic Oscillator

4
Pendulum frequency Vs. amplitude
w/w0
q/p
5

• How to excite nonlinear systems into
• high energy ?
• Changing the drive frequency will keep it in
  resonance.

q/p
6

• 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

7
Few method to excite nonlinear oscillator

• Feedback control.
• (requires a real time feedback)
• Exact tailoring of the force.
• (requires pre-knowledge of the system)
• Ladder-climbing autoresonance

8
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

9
Threshold-chirp relation
10
Auto-Resonance simulation
L. Friedland et al. Phys. Plasmas. 5 (645)
11
Ladder climbing in a quantum systems

• Energy levels in Morse potential.

Ladder of energy levels with decreasing gaps.
12
Two levels with constant frequency drive
constant frequency drive force
13
Two level with chirped drive
Efficient conversion when
Ts / TR2.8
Ts / TR1
chirped drive force
time
14
The validity of the two level approximation
Which means the width of resonance is
small enough to include only two levels
15
Characteristic times
16
The limit between quantum mechanics and
classicality
In terms of the three characteristic times
17
The condition for efficient ladder-climbing
In terms of the three characteristic times
18
Efficient classical autoresonance
.
In term of the characteristic times
19
P1-P2 parameters
Quantum limit
Efficient transfer between 2 levels
Efficient Autoresonance
20
P1-P2 parameters
.
21
Ladder climbing-below threshold
22
Ladder climbing-above threshold
23
Autoresonance-below threshold
24
Autoresonance-above threshold
25
Design consideration for experiment
.
26
Experiment with HF moleculerequirements from
the radiation source
In the IR regime
To bring the population to the 4th level
Ladder climbing threshold
27
Theoretical curve of phase matchingfor PPKTP
with period of 27.1m pumped by wide-band
TiSapphire Laser

• Idler spectrum 2-3m
• Signal spectrum 1-1.5m

28
The Experiment
29
The Signal Laser spectrum
Laser spectrum
Signal spectrum O Non collinear --- Collinear
30
Delay as a function of wave-length
31
Chirp measurement
32
IR specifications

• Bandwidth 25
• Pulse length 185 psec
• Spot size 60m x 700m
• Energy up to 200mJ

33
P1-P2 parameters
- Witte et al. Cr(CO) 6
- Maas et al. - NO
- Our experiment - HF
.
34
Demonstration of ladder climbing on HF molecule.
35
IR spectrum
36
HF experiment results
37
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

38
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

39
The end