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
!!!!! "!
=
#=
!!!!! "!
$
$$
$$$
$
$%
IN
OUT
Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)
June 4, 2007 Asilomar
Spectral Pulse Shaping. Implementation
shaped pulselens
grating
spatial lightmodulatorinput pulse lens
grating
Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)
Asilomar
Shaped pulses. Examples
780 785 790 795 800 805 810 815 820
1
-1-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Wavelength (nm) Time (ps)
780 785 790 795 800 805 810 815 820
π/2
-π/2
-1 -0.5 0 0.5 1
old phasenew phase
original pulseshaped pulse
Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)
Asilomar
Application I. Quantum control
Non-adiabatic population transfer between two quantum states
)(0e)(tti
tE!" +
1
2
Constant phase0)( !t"
h/)(
)(cos
12
22
2
tE
t
µ
!
="
"= -250 -200 -150 -100 -50 0 50 100 150 200 2500
0.2
0.4
0.6
0.8
1
1
2
Time (fs)
Rabi oscillations:
+ Fast- Sensitive to precise timing- Sensitive to exact frequency- Sensitive to phase coherence
Bloch Sphere
2
1
Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)
Application I. Quantum control
Adiabatic population transfer between two quantum states
1
2
)(
)(
0 tdt
d
t
!"
""
+=
#
time
Adiabatic passage:
+ Slower but still fast+ Much more robust
( )2)()( ttdt
d!<<"
Adiabaticity: pulses arelong on the time scale ofsystem’s evolution
Frequency chirping
tttt !"! )()( 2 #$
)(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
Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)
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
Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)
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
Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)
June 4, 2007 Asilomar
Presented at the PITP/SpinAps Asilomar Conference in June 2007 Brought to you by PITP (www.pitp.phas.ubc.ca)