Spectroscopy and Control with Ultra-Short Laser Pulses

June 4, 2007 Asilomar

Spectroscopy and Control with Ultra-Short Laser PulsesJohn Hepburn

University of British Columbia

Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)

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logo


Controlled coherent excitation

• The large bandwidth and high coherence of femtosecondpulses can be exploited for controlled excitation ofquantum systems.

• The subsequent evolution of those systems results fromthe combination of the mixture of states coherentlyexcited and the phase and amplitude pattern of theexciting field.

• This can be used to control system behaviour, or probethe system spectrum.

• Two examples:– Femtosecond adiabatic passage– Coherent Raman spectroscopy



Outline

Spectral Shaping of Ultra-short Pulses1. Main tools

3. Spectroscopy

Coherent spectroscopy withincoherent pulses

2. Quantum Control

Control of adiabatic dynamicswith non-adiabatic pulses



Broadband pulses

Long(cw)

time

Short(<100 fs)

frequency

Narrowband(<0.001 nm)

Broadband(>10 nm)

We would like to modulate field on a femtosecond time scale

)()()( tHtEtEinout

!=

Electro-optics too slow!



Spectral Pulse Shaping. Principle

Amplitude & Phase mask for individual spectralcomponents

)()(

e)()(

)()()(

)()(

TransformFourier

)(

TransformFourier

tEE

TH

HEE

EtE

outout

i

inout

inin

!!!!! "!

=

#=

!!!!! "!

$

$$

$$$

$

$%

IN

OUT



Spectral Pulse Shaping. Implementation

shaped pulselens

grating

spatial lightmodulatorinput pulse lens

grating


Asilomar

Shaped pulses. Examples

780 785 790 795 800 805 810 815 820

1

-1-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Wavelength (nm) Time (ps)

780 785 790 795 800 805 810 815 820

π/2

-π/2

-1 -0.5 0 0.5 1

old phasenew phase

original pulseshaped pulse


Asilomar

Application I. Quantum control

Non-adiabatic population transfer between two quantum states

)(0e)(tti

tE!" +

1

2

Constant phase0)( !t"

h/)(

)(cos

12

22

2

tE

t

µ

!

="

"= -250 -200 -150 -100 -50 0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1

2

Time (fs)

Rabi oscillations:

+ Fast- Sensitive to precise timing- Sensitive to exact frequency- Sensitive to phase coherence

Bloch Sphere

2

1


Application I. Quantum control

Adiabatic population transfer between two quantum states

1

2

)(

)(

0 tdt

d

t

!"

""

+=

#

time

Adiabatic passage:

+ Slower but still fast+ Much more robust

( )2)()( ttdt

d!<<"

Adiabaticity: pulses arelong on the time scale ofsystem’s evolution

Frequency chirping

tttt !"! )()( 2 #$

)(0e)(tti

tE!" +

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Bloch Sphere

Time (ps)

1

2


Piecewise Adiabatic Passage

What if the dynamics is fast even on a picosecond scale ?

populationtransfer intooscillating wavepacket

)(t! )(tE

T

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Time (ps)

We use pulse shaping tocreate a “Pulse train”with a piecewisequadratic phase or a“piecewise chirp”

T



Piecewise Adiabatic Passage

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1

2

Time (ps)1

3

2

Bloch Sphere

!!"

!!#

$

=%

&=

'=

%=(

)(ˆˆˆ

)(ˆˆ

)(ˆˆ

ˆˆˆ

),(

3

1

)

*

+

,-*

*

*

RRR

RR

RR

RRR

Rabi

Rabi

Rabi

Dynamics of the state vectoris a series of rotations:

!!!

"

!!!

#

$

%

&±=

%'±=

%+&=

(

)*

(+,

()-

)tan(

2/2/

2/)(2/)( 22

!"#$

!"#$

"#$

=%&<<'

=%&>>'

=%&<<'

:End .3

2/ :Middle .2

0 :Start .1

State vector adiabatically follows the axis of rotation !



Preliminary results: 85Rb 5s→5p PiecewiseAdiabatic Passage



Very preliminary results

Rb 5p population as a function of chirp



Stimulated Raman population transfer

• To reach optically inaccessible states, or to cool highlyvibrationally excited molecules– Example: cooling ultracold molecules formed by

photo-association• Need to use Raman type transitions:ΩP connects Ψ1 and Ψ2 (pump)

ΩS connects Ψ2 and Ψ3 (Stokes)



Stimulated Raman Adiabatic Passage: STIRAP

Create a state that evolves from|1> to |2> without developingamplitude in |3> Do this by starting with ω23, thenapplying ω13: counter-intuitiveordering



Simulations for Na

Again, to avoid problems caused by longer pulses, can use a pulse sequences.



Piecewise Adiabatic Passage. Summary

• Spectral pulse shaping enables creation of femtosecond pulse trains

with predefined temporal amplitude and phase

• Tailoring the amplitude and phase of the pulses in the train allows to

mimic traditional (continuous) adiabatic passage in a piecewise

manner

• Piecewise adiabatic passage is as robust (vs intensity and timing) as

the traditional adiabatic passage

• Piecewise adiabatic passage offers new possibilities of controlling

quantum dynamics of complex systems on a femtosecond time scale

• Theory: accepted to PRL

• Experiment: underway



Application II. Ultrafast Spectroscopy

Delay τ

Vibrational excitation Probe scattering

CARSsignal

)(!pE)(!

SE

)(!prE

)()3( !PCoherent anti-Stokes Raman Scattering

• Coherent (directional): easy to detect• Non-resonant (electronic): low fluorescence

background• High efficiency: low average power, non-

invasive imaging in bio-applications• Low non-resonant background

Third-order polarization

)(!A

!

)( !+"aSE

Ultrafast CARS

• High time resolution (< 10-12 s) !

BUT

• Poor spectral resolution (>100 cm-1)

)(!prEImprove spectral resolution?

• Scan time delay, then do Fouriertransform (too long…)

• Reduce bandwidth (waste ofenergy or too many lasers)

• PULSE SHAPING !



CARS with shaped pulses

!!"!##

$+!"!+=!

%

&

dEAPE

i

CCA

praS

nn

nNR

)()()()(

)(

)3( ''')()()()(

)exp()(

)3(tEtAtPtE

ttiCCtA

praS

nnnNR

!!

"#$+= %

In time In frequency

time

)(tEaS

)( !+tEaS

n!

!

n!+"



CARS with shaped pulses

-π

π

2π

0

Vibration: amplitude; phaseProbe field: amplitude; phase CARS spectrum

Un-shaped

-50 0 50 100 150 200 250 300

-π

π

2π

0

Energy (cm-1)0 100 200 300 400 500 600

Energy (cm-1)

Shaped

2)()( !!

aSaSEI "



CARS with shaped pulses. Experiment

)()( !! SEpr " )(!prE

Shaping of Probe pulse

Prob

e tim

e de

lay

(ps)

Anti-Stokes wavelength (nm)

720 730 740 750

12

10

8

6

4

2

0

-2

11e11e21e31e41e5(a)

Raman shift (cm-1)900 1000 1100 1200 1300

0

2

4

6

8

10

012345

Raman spectrumof Toluene



Good news and bad news

• Recovery technique analogous to cross-correlationfrequency resolved optical gating (XFROG), standardtechnique used to measure femtosecond pulses.

• We recover full phase and amplitude information aboutthe system – locations and decoherence times of allresonances

• However, this technique requires knowledge of the probefield, and controlled phase coherence of that field

• Also, requires a scan of the time delay, resolutiondetermined by the maximum time delay

• A “scan-less” method would be better• Complex media (i.e. cells) introduce incoherence in the

probe that cannot be corrected for



Correlations in CARS spectrum

( )

)()()(2)(

:spectrum in the nscorrelatio new introduce resonances Thus,

)()()(

:ansformFourier tr Applying

)()()()(

:functionn correlatio field theof ansformFourier tr theis spectrumIntensity

)()()(

:resonances narrow infinitely twoAssuming

21

* 21

21

!"#+!+#+#=#

!++!+=

+$="=

+$=

!!

!!

%

&'&'''

'''

((( ((

prprpraS

praS

IIII

prpraS

ii

EaSaSE

titi

praS

GGGG

III

eeGdttEtEG

eetEtE

Amp. noise Phase noise



CARS with noisy pulses. Calculations

-50 0 50 100 150 200 250 300

)(

)(

!prE

A "

-50 0 50 100 150 200 250 300

)( !"aSIG

)(2)( !! "#"praS II GG

average over noiserealizations

0 100 200 300 400 500 600

)(!aSI

-50 0 50 100 150 200 250 300

!"

)( !"aSIG

one noise realization



CARS with noisy pulses. Experiment

-200 -100 0 100 200

-0.2

0

0.2

0.4

0.6

0.8

1

Toluene-1cm )1027 ,1000(=!

n

Resolution is determined by the granularity of noise (not by thepulse bandwidth)

Frequency (cm-1)

27 cm-1

0 20 40 60 80 100

0

0.2

0.4

0.6

0.8

Frequency (cm-1)

Toluene + Ortho-xylene-1cm )1049 ,1027 ,1000 ,982(=!

n

18 cm-1

22 cm-127 cm-1



What can we call this new method?

• Relies on Noise Autocorrelation• It is a Spectroscopy• Although general for non-linear spectroscopies, this

realization is based on Coherent Anti-Stokes RamanScattering

NASCARS



“Cheap” shaping for NASCARS

multi-mode fiber

ToluenePreliminary results

Temporal randomization(noise) by means of fibermode dispersion



Spectroscopy with Shaped Pulses. Summary

• Broad spectral bandwidth of ultra-short pulses offers new

ways of “interference spectroscopy”

• Pulse shaping technology enables design of “spectrally

incohererent” pulses with no correlation between separate

spectral components of the pulse

• Interference of noise, coherently produced via CARS, results

in the appearance of correlations in the Raman spectrum

• Identifying Raman resonances by the spectral correlations of

interference noise offers quick and easy way of doing

Raman spectroscopy with femtosecond pulses.



Acknowledgements

Experiment

Valery Milner Stas KonorovXiaoji XuSergey Zhdanovich

Theory

Moshe Shapiro Evgeny ShapiroCian Menzel-Jones



Alternate formulation of dark state (1)

Hamiltonian for 3 states:



Alternate formulation (2)



Experimental NASCARS spectrum of a mixture of toluene (782cm-1, 1000cm-1,1027cm-1) with ortho-xylene (982cm-1, 1049cm-1) mixture. Noise is introducedusing spectral pulse shaper. Result is averaged over 100 noise realizations.Red curve is autocorrelation of Raman spectrum as reference



UBC, Vancouver



a

- 2

- 1

! p

! S

! 0

! 0 + - 2

! 0 + - 1CCD

Spectrometer

OrSLM

Sample

OPA

Filter

Fibre

b

(i) (ii)

PS




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Spectroscopy and Control with Ultra-Short Laser Pulses