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)

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

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!

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

June 4, 2007 Asilomar

Spectral Pulse Shaping. Principle

Amplitude & Phase mask for individual spectralcomponents

)()(

e)()(

)()()(

)()(

TransformFourier

)(

TransformFourier

tEE

TH

HEE

EtE

outout

i

inout

inin

!!!!! "!

=

#=

!!!!! "!

$

$$

$$$

$

$%

IN

OUT

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

June 4, 2007 Asilomar

Spectral Pulse Shaping. Implementation

shaped pulselens

grating

spatial lightmodulatorinput pulse lens

grating

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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

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

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

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

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

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

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

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

June 4, 2007 Asilomar

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 !

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

Very preliminary results

Rb 5p population as a function of chirp

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

June 4, 2007 Asilomar

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)

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

Simulations for Na

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

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

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 !

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

June 4, 2007 Asilomar

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!+"

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

June 4, 2007 Asilomar

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 "

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

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

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

June 4, 2007 Asilomar

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

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June 4, 2007 Asilomar

“Cheap” shaping for NASCARS

multi-mode fiber

ToluenePreliminary results

Temporal randomization(noise) by means of fibermode dispersion

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

June 4, 2007 Asilomar

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.

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

June 4, 2007 Asilomar

Acknowledgements

Experiment

Valery Milner Stas KonorovXiaoji XuSergey Zhdanovich

Theory

Moshe Shapiro Evgeny ShapiroCian Menzel-Jones

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

June 4, 2007 Asilomar

Alternate formulation of dark state (1)

Hamiltonian for 3 states:

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June 4, 2007 Asilomar

Alternate formulation (2)

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June 4, 2007 Asilomar

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

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June 4, 2007 Asilomar

UBC, Vancouver

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June 4, 2007 Asilomar

a

- 2

- 1

! p

! S

! 0

! 0 + - 2

! 0 + - 1CCD

Spectrometer

OrSLM

Sample

OPA

Filter

Fibre

b

(i) (ii)

PS

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June 4, 2007 Asilomar

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