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Infrared X-ray pump-probe spectroscopy
Hans Ågren
Department of Theoretical Chemistry
Royal Institute of Technology, S-106 91 Stockholm, Sweden
http://www.theochem.kth.se
X-ray Free-Electron Lasers: Challenges for Theory,
Cambridge, Massachusetts, USA, June 19, 2006
8.9 million
450 000 km²
Contents
X-ray spectroscopies of molecules driven by strong IR fields
•
•
•
•
•
Principles of IR - X-ray pump-probe spectroscopy
Coherent laser induced electronic and nuclear wave packets
The phase dependence of the wave packets and the X-ray spectra
Role of molecular alignment
Recoil effect in the field of IR laser
Applications
• Diatomic Molecules
• Application on proton transfer in core ionized water dimer
• Role of vibronic coupling in pump-probe spectroscopy of Glyoxalmonoxime
Principles of X-ray pump probe spectroscopy
Pump (optical or IR) laser orients/aligns molecules: Structure
determination.
Laser excitation strongly modifies X-ray spectra. Many-electron
transitions are enhanced
Coherent laser radiation creates nuclear or electronic wave packets.
X-ray pulse probes the dynamics of wave packet
X-ray pump probe spectroscopy with electronic degrees of freedom
Optical or UV laser creates the electronic wave packet:
This electronic wave packet moves in molecule
ungerade MO
Optical or UV field
gerade MO
X-ray absorption
Optical laser mixes
gerade HOMO and ungerade LUMO
and creates electronic wave packet
core hole
OK X-ray absorption spectra of NO excited in ground state vibrational
levels: 0, 1, 2 (incoherent IR pump or heating)
Incoherent population by IR light
of ground state vibrational levels
results in strong change of
X-ray absorption spectrum
P()    P

X-ray
IR
One can use continuum wave
IR laser with rather small
intensity:
0.1-1 W/cm2
NO*(1s2p)
Coherent IR pulse induces wave packet dynamics
• IR field creates coherent superposition of vibrational
quantum states
 (t )   c (t )e i ( t  ) 
L

• Square of WP (and WP dynamics)
depends on the IR phase

)
 (t )  1  2 2c1 (t )( R  R0 ) cos(10t   L ) e
2
 ( R  R0 ) 2 / c02
Dynamics and phase effect disappear when IR field is incoherent
• Ehrenfest’s theorem (for the force)
F   (t )
d
E L  d( R ) cos( L t   L )  (t )
dR
Principle of X-ray + IR pump-probe spectroscopy (coherent IR field)
Formation of OK X-ray spectrum of NO driven by IR field
Origin of the phase dependence of X-ray spectra
interference of one- and two-photon channels
under core electron excitation:
EX (t)  EX (t) EL (t) cosωL t  L )
2-photon channel
depends on the phase
of IR field
X-ray photon
IR photon
X-ray photon
Some Theory
• General case of overlapping pump and probe pulses:
Coupled Schrödinger equations for nuclear WPs of ground
and core excited states
 

ˆ
i
  Φ(t )  H (t )Φ(t ),
 t

 0 
Φ(t )  
 

 c
• IR field interacts with molecules in both states
 h 0  VL00
VX0 c 

H (t )  
cc 
 Vc 0
h

V
X
c
L 

The interactions with IR (L) and x-ray (X) pulses
VL   d EL (t) cos(ωL t  L ), VX (rotating wave)
Schrödinger equation has to be solved for each frequency of x-ray field
Probe pulse is delayed (probe and pump pulses do not overlap)
The solution consists of three steps:
1. IR field interacts only with molecules in the ground state

i 0 (t )  h0  d  E L ) cos( L t   L )0 (t ).
t
2. Back propagation of the WP in
the core excited potential

i c ( , t )  hcc ( , t ).
t
 c( 0,t)
Now c(t) does not depend on the x-ray frequency
3. The spectrum is the norm of the WP
in the frequency domain
P()  c () c ()

c ()   dt e it E X (t ) c (t )

QUANTUM CONTROL OF THE SYSTEM
Dynamics of the wave packet after
the pump pulse leaves the system
and effect of the phase memory
Populations
Fast switching off of the IR field
compared with the Rabi period:
Molecule remains vibrationally
excited after IR pulse
Nuclear dynamics after IR pulse
Phase memory
IR field
Short IR pulse
Populations
Slow switching off of IR field
compared with the Rabi period:
Adiabatic depopultion
of vibrational states
IR field
Long IR pulse
No nuclear dynamics after IR pulse
No phase memory
Preparation of localized nuclear wave packet with higher mean energy
CO
Rabi period:
( R)
 
T
2p
 ( R)
G 
G(R)  EL d 
d ( 1)  d 01   1
Time resolved x-ray probe spectra
Evolution of the wave packet in potential well ( as well as its phase
dependence) can be probed by short x-ray pulses
X-ray spectrum
r   (t ) r  (t )
Wave packet
The trajectories in
the coordinate and
frequency domains
coincide with high
accuracy.

Revival period
F   (t )
d P()


 d P()
d
E L  d( R ) cos( L t   L )  (t )
dR
Wave packet revival
Coupled oscillators with different frequencies experience beatings or revivals
Revival period is inversely proportional to the
anharmonicity constant of the system:
 r
10  21

p
10 xe
2
Wave packet
broadening

d P()


 d P()
}
}{
r
p
{
r 
2
TR 
Wave packet squeezing
Role of the duration of x-ray pulse
Neither ultra-short nor long x-ray pulses can ”see” nuclear dynamics and phase effect
Broadening of the spectrum
does not allow to see dynamics
 X
 1)
Long x-ray pulses
  0.4
Short x-ray pulses
Long x-ray pulse can not
probe fast nuclear dynamics
Role of molecular orientation
We discussed before pump-probe spectroscopy of oriented molecules
Spectra of oriented or fixed-in-space molecules can be measured
in the ion yield mode
X-ray
Ion detector
Role of molecular orientation
X-ray spectra averaged over molecular orientations
Smaller intensity of IR field:
IL = 1.5 x
1012
W/cm2
Larger intensity of IR field:
IL = 2.3 x 1012 W/cm2
NO
Small phase effect
Larger phase effect
The phase effect for randomly oriented molecules is small for small
IR intensity and it increases for higher IR intensity.
The reason for this is: The multi-photon absorption of the IR field
grows with the increase of the laser intensity.
Role of the molecular orientation versus pump level
Small IR intensity: 1+2 absorption (no interference-no phase effect)

(1)
Pint
  A1e i L d10  e L ) Dc 0  e X

2
 0
( 2)
Pint
  A2e 2i L d10  e L )d10  e L ) Dc 0  e X
2
 0
Higher IR intensity: 1+3 absorption (interference remains after orient. averag.)
X-Ray pump probe spectroscopy of water dimer
Ground state equilibrium structure of water dimer
Propagation of the wave packet in donor core ionized
potential surface of water dimer (no IR field !)
Proton transfer
region can be
studied using
x-ray fluorescent
or Auger
specroscopies
classical pathway
Proton transfer well
Potential curves of ground state and core ionized states
in donor and acceptor oxygens in water dimer
Ordinary XPS spectroscopy is
able to map the potentials
Only near equilibrium
XPS driven by IR allows
to study the proton transfer region
(far away from equilibrium)
IR field
Formation of O1s X-ray photoelectron spectrum of water dimer in a strong IR field
Phase dependence of the trajectory of the wave packet in
the ground state potential of water dimer created by a strong IR field
IR - X-ray pump-probe spectrum of water dimer for
different phases (L ) and time delays (t )
L = 3.8 rad
IL = 5.4 x 1014 W/cm2
Proton transfer band
L = 3.8 - p/2.
Role of vibronic coupling on proton transfer
in core ionized glyoxalmonoxime
driven by field of strong IR pulses
Role of vibronic coupling (VC) on proton transfer in core
ionized glyoxalmonoxime (GM)
Hydrogen
donor
Hydrogen
acceptor
q
Core ionization of O2 results in the formation
of the tautomer 2-nitrosoethenol (NE)
VC
Trajectory of nuclear wave packet in the ground state
X-ray photoionization
W
I L  2.3 10
cm 2
ωL  ω10  0.33 eV
14
τ L  10 fs
Populations by IR pulse of the ground state
vibrational levels of GM
 L  4.44
 L  4.34
L  3.17
W
I L  2.3 10
2
cm
ωL  ω40  0.88 eV
14
L  4.18
L  2.75
X-ray +IR pump-probe maping of proton transfer dynamics
VC mixes core-ionized states localized in different
oxygens and creates dark and bright state
IR induced
bands
Strength of vibronic coupling
IR field
Pump-probe spectroscopy of molecules driven by IR field
both in ground and excited states
Overlapping x-ray and IR pulses
Γ
Photoelectron spectra of CO (ionization of 2b MO: I=15.6 eV)
W
I L  5 10
,
2
cm
12
τ X  τ L  100 f
ωL  ωvib (excited state)
IR only in GS
hot band
ωL  ωvib (ground state)
IR only in GS
IR only in ES
IR only in ES
IR in both states
IR in both states
Without IR
Without IR
Role of interaction with IR field in core excited state
N1s  π
N2
*
NEXAFS
Ed 10  Γ  0.05 eV
 large IR intensity
IR
1
0

X-ray
IR
ω X  ωcvib  0.236 eV
τ X  τ L  100 fs
Interaction with IR field is forbidden
in the ground state due to symmetry (d=0)
Scheme of X-ray IR pump-probe measurements
Role of spatial phase of the IR field:
Leff   L  k L z
Orthogonal orientation of X-ray and IR beams which allows
to reduce the dephasing caused by the phase factor kLz
sample
XPS: Recoil effect:
Excitation of vibrations due to ejection of photoelectron
Formal origin of
the recoil effect is
generalized FC amplitude
ce
ikR
0
k-momentum of photoelectron
To increase
the recoil effect
we need large size of
nuclear wave packet
λ  ΔR
CO molecule
Enhancement of the recoil effect
When fast photoelectron is ejected the molecule experiences recoil.
The transfer of the momentum to nuclei
c, e
ipR
0, 0  e
ipR 0

*
dk

c ( k  0.5p cos  )0 0 ( k ).


The recoil becomes to be
important when the phase
factor starts to deviate from 1
e  iα p Δ R ,
p ΔR  1.
It can occur due to:
High photoelectron momentum p
(high x-ray frequency).
Broad wave packet (IR field).
Enhancement of the recoil effect experienced by molecule due to ejection
of photoelectron
Recoil energy increases internal kinetic energy of molecule in core ionized state.
But core ionization takes maximum in turning point where kinetic energy is equal to zero
This happens only if the transition is not vertical and it is shifted by:
E rec
Δr 
Fc  F0
E rec
p2
mB

cos 2θ
2(m A  m B ) m A
Recoil shifts XPS band:
E rec
Δω  Fc Δr 
1  F0 /Fc
Shift is large when gradients
approach each other
Relative difference between the gradients of the core ionized and
ground state potentials versus internuclear distance
CO molecule
Left turning point
Right turning point
Oxygen K XPS spectrum of CO driven by strong IR pulse
I L  2.3 1014 W/cm 2
IL  0
Conclusions
•We have studied X-ray pump-probe spectra with coherent and incoherent
pump radiation as well as with CW and pulsed light sources.
•Phase of coherent pump radiation is transferred to nuclear
or electronic wave packet. This makes trajectory of the wave packet and
X-ray pump-probe spectra sensitive to the phase of the pump field.
•The phase sensitivity of the IR + X-ray pump-probe spectra depends
strongly on the duration of the X-ray pulse, delay time, shape of IR pulse,
molecular orientation.
•X-ray pump-probe spectroscopy is a proper tool to study the dynamics of
proton transfer in liquids .
•Revival effect allows to study dynamics of different relaxation processes in
liquids and to measure hyperfine structure like anharmonicity.
Acknowledgments
Royal Institute of Technology:
•Freddy Fernandes Guimarães
•Viktor Kimberg
•Viviane Felicissimo
•Ivo Minkov
•Amary Cesar
•Faris Gel’mukhanov