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