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June 4, 2007 Asilomar
Spectroscopy and Control with Ultra-Short Laser PulsesJohn Hepburn
University of British Columbia
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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
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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
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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!
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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
!!!!! "!
=
#=
!!!!! "!
$
$$
$$$
$
$%
IN
OUT
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June 4, 2007 Asilomar
Spectral Pulse Shaping. Implementation
shaped pulselens
grating
spatial lightmodulatorinput pulse lens
grating
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Asilomar
Shaped pulses. Examples
780 785 790 795 800 805 810 815 820
1
-1-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Wavelength (nm) Time (ps)
780 785 790 795 800 805 810 815 820
π/2
-π/2
-1 -0.5 0 0.5 1
old phasenew phase
original pulseshaped pulse
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Asilomar
Application I. Quantum control
Non-adiabatic population transfer between two quantum states
)(0e)(tti
tE!" +
1
2
Constant phase0)( !t"
h/)(
)(cos
12
22
2
tE
t
µ
!
="
"= -250 -200 -150 -100 -50 0 50 100 150 200 2500
0.2
0.4
0.6
0.8
1
1
2
Time (fs)
Rabi oscillations:
+ Fast- Sensitive to precise timing- Sensitive to exact frequency- Sensitive to phase coherence
Bloch Sphere
2
1
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Application I. Quantum control
Adiabatic population transfer between two quantum states
1
2
)(
)(
0 tdt
d
t
!"
""
+=
#
time
Adiabatic passage:
+ Slower but still fast+ Much more robust
( )2)()( ttdt
d!<<"
Adiabaticity: pulses arelong on the time scale ofsystem’s evolution
Frequency chirping
tttt !"! )()( 2 #$
)(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
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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
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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 !
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June 4, 2007 Asilomar
Preliminary results: 85Rb 5s→5p PiecewiseAdiabatic Passage
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June 4, 2007 Asilomar
Very preliminary results
Rb 5p population as a function of chirp
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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)
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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
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June 4, 2007 Asilomar
Simulations for Na
Again, to avoid problems caused by longer pulses, can use a pulse sequences.
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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
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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 !
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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!+"
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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 "
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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
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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
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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
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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
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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
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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
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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.
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June 4, 2007 Asilomar
Acknowledgements
Experiment
Valery Milner Stas KonorovXiaoji XuSergey Zhdanovich
Theory
Moshe Shapiro Evgeny ShapiroCian Menzel-Jones
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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
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