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
Harmonic Oscillator
Anharmonic 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.
Pendulum frequency Vs. amplitude
[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
wdrive=w0-at
Amplitude, a
Phase Mismatch F
{ L. Friedland et al. Phys. Plasmas. 5 (645) }

11. Ladder climbing in a quantum systems
Morse Potential D
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 / TR=2.8
Ts / TR=1
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 molecule: requirements from the radiation source
In the IR regime
To bring the population to the 4th level
Ladder climbing threshold

27. Theoretical curve of phase matching for PPKTP with period of 27
Theoretical curve of phase matching for PPKTP with period of 27.1m pumped by wide-band Ti:Sapphire Laser
Idler spectrum 2-3m
Signal spectrum 1-1.5m

28. The Experiment
Collimated Ti:Sapphire

29. The Signal & 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 Standard deviation Avg. Number of photons
Conditions:
4.6
11.16
10 torr HF
0.7
0.5
10 torr Air
0.57
0.33
Continually evacuated
1.1
1.5
10 torr HF & filtered spectra

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