Stimulated electronic x-ray Raman scattering
at XFELs
Nina Rohringer
Max Planck Institut für Physik Komplexer Systeme, Dresden
Center for Free-Electron Laser Science, Hamburg
Acknowledgements
Colorado State University: J.J. Rocca, D. Ryan, M. Purvis
LLNL: R. London, F. Albert, J. Dunn, A. Graf, G. Brown
LCLS, SLAC: J. Bozek, C. Bostedt, LCLS accelerator / operating team
MPI PKS: V. Kimberg, C. Weninger
Simultaneous fs X-ray diffraction and photo-emission
spectroscopy
Probing the electronic structure of the Mn4CaO5 cluster in
the oxygen-evolving complex of PS II
J. Kern et al, Sciencexpress, 14 February 2013, science.1234273
Intensity [a.u.]
SASE XFELs have limited temporal coherence
Time [fs]
LCLS bandwidth at 1keV photon energy: Dw = 6-9 eV
Coherence time: 0.3 - 0.5 fs
1st measurement: I. A. Vartanyants et al. , Phys. Rev. Lett. 107, 144801 (2011)
A route to nonlinear spectroscopy with x-rays
Stimulated x-ray Raman
scattering in atoms
X-ray amplification
and wave-packet dynamics
in molecules
I(w)
Photoionization atomic
inner-shell x-ray laser
w
w
Ne
Ne+
Rohringer et al.,
Nature 481, 488 (2012)
C. Weninger et al.,
under review (2013)
Kimberg & Rohringer,
PRL 110, 043901 (2012)
Upcoming experiments:
LCLS, Feb. 2014
FLASH, Oct. 2014
1st theoretical concept of an atomic x-ray laser
Population inversion by inner-shell photoionization
1st X-ray laser proposed back in 1967:
Duguay & Rentzepis,
Appl. Phys. Lett. 10, 350 (1967).
Ultrafast ionization of
inner-shell electrons
1st realization in the optical regime (blue laser):
Silfvast et al., Opt. Lett. 8, 551 (1983).
Fast, powerful x-ray pump required to beat Auger decay !
Photo-ionization inner-shell x-ray laser, Neon
Coherent amplification of fluorescence
Focused
XFEL beam
I(z, t) = I(0, t)× e
g(z,t )×n×z
Atomic gas volume
Duguay & Rentzepis, Appl. Phys. Lett. 10, 350 (1967).
N. Rohringer & R. London, PRA 80, 013809 (2009)
Atomic x-ray laser
(amplified spontaneous emission)
Schematic experimental setup
Grating
spectrometer
LCLS
beam
Gas cell filled
with Neon
grating
focusing
chamber
AMO high-field
chamber
Hutch 1 (AMO)
grating
spectrometer
Hutch 2 (SXR)
Diagnostics:
- Inline spectrometer for monitoring transmitted XFEL and amplified scattered x rays
- Grating spectrometer for scattered/fluorescent x rays
Single shot of highest intensity: 8×109 photons in Ne K-a line
corresponding to GL 21-23
1.2e+06
run 239, shot 18
run 239, shot 32
run 239, shot 45
Integrated counts
1e+06
800000
FWHM 2 eV
(instrumental resolution)
600000
400000
FWHM
10 eV
200000
0
820
840
860
880
900
920
940
960
980
1000
Photon energy [eV]
XFEL input
output
Photon energy
940 eV
849 eV
Pulse energy
0.25 mJ
1.1 mJ
Number of photons 1.6 x 1012
8 x 109
Pulse duration
40 fs
0.5-5 fs (calculated)
Bandwidth
10 eV
0.25 eV (calculated)
Coherence time
0.3 fs
full temporal coherence
Gas pressure: 500Torr
Focal radius: 1-2 mm
Interaction length: 1.6 cm
Rohringer et al., Nature 481, 488 (2012)
Pumping-power dependence of Ne K-a transition
(every point corresponds to an average over 10 LCLS shots)
Average GL = 19-21.3 @ pulse energy of 0.25 mJ
Rohringer et al., Nature 481, 488 (2012)
A route to nonlinear spectroscopy with x-rays
Stimulated x-ray Raman
scattering in atoms
X-ray amplification
and wave-packet dynamics
in molecules
I(w)
Photoionization atomic
inner-shell x-ray laser
w
w
Ne
Ne+
Rohringer et al.,
Nature 481, 488 (2012)
C. Weninger et al.,
under review (2012)
Kimberg & Rohringer,
PRL 110, 043901 (2012)
LCLS, Sept. 2010
LCLS, Aug. 2011
Upcoming experiments:
LCLS, Feb. 2014
FLASH, Oct. 2014
X-ray pumping of Neon near the K-edge
LCLS bandwidth: 7 eV
Total ion yield
[1s]3p
867.2 eV
3 eV
[1s]4p
868.8 eV
FWHM
0.27 eV
D. V. Morgan et al.,
PRA 55, 1113 (1997)
3p
2p
2s
2p
2s
1s
1s
K edge
2p
2s
1s-3p
Stimulated Electronic X-ray Raman Scattering
7 eV FWHM
K edge
3p
2p
2s
1s
Weninger et al., under review (2013)
1s-3p
Emitted line profile as a function of pump photon energy
K edge
Weninger et al., submitted (2013)
Stochastic line shift due to
“anomalous” linear dispersion of resonance scattering
1st RIXS experiments on Cu with
Synchrotron radiation (1976)
Continuum
wout
Detuning, D
win
wout
win
P. Eisenberger, P.M. Platzman, H. Winick,
PRL 36, 623 (1976).
Width of resonance: 0.25 eV
Width of SASE spike: Dw=1/t =0.1 eV
Master Equations for atomic and ionic density matrices
coupled to Maxwell’s equation
Effective sRIXS cross section as a function of propagation depth
RIXS process dominated by 5 spectral intensity spikes –
5 distinct modes in the emitted spectrum
Simulated spectral / temporal intensity profiles of sRIXS process
Simulated Single-Shot Raman Spectra
Coupled generalized Maxwell-Bloch equations
K edge
Line profile – comparison of experiment to simulation
Experiment
K edge
Weninger et al., submitted (2013)
Theory
Raman Signal Strength as a Function of Pump Energy
Number of seed photons: 103-104 (varying due to spectral sidebands of the XFEL)
Estimated number of photons of spontaneous RIXS: 100
Saturated amplification by 7-8 orders of magnitude
Weninger et al., submitted (2013)
High-resolution x-ray Raman spectroscopy
by statistical analysis (covariance mapping)
Covariance map from 5000 simulated single-shot
spectra
Weninger&Rohringer, in preparation
Self-stimulated x-ray emission processes in diatomic molecules
Valence excited
Ground
XFEL pump
XFEL pump
Ground
Core-ionized
X-ray emission
Atomic
lasing
Core-ionized
X-ray emission
XFEL pump
Core-excited,
dissociative
Valence dissociative
Ground
Kimberg & Rohringer,
PRL. 110, 043901 (2012).
Q. Miao, J.-C. Liu, H. Agren, J.-E. Rubensson
& F. Gel’mukhanov,
PRL 109, 233905 (2012).
Victor
Kimberg
Photo-ionization X-ray lasing scheme in molecular Nitrogen
Fluorescence spectrum
2S +
u
3sg-1
3sg-1
1S +
g
[1] B. Kempgens, et al. J. Phys. B 29, 5389 (1996)
[2] P. Glans, et al. J. El. Spec. Rel. Phen. 82, 193 (1996)
Alignment of the molecule matters
Impulsive (field-free) laser alignment of the molecular ensemble
aligned ensemble
<cos2q>=0.8
isotropic ensemble
Contours of the 3sg
orbital
(final state)
E
q
Number of emitted x-ray photons as a function of
the incoming XFEL photon number
(50 fs pulse duration, 1.5 mm focus)
Impulsive laser alignment
Degree of alignment for various laser parameters and temperatures
Aligned ensemble
800 nm, 110 fs, 6x1013 W/cm2 :
1 – 100 K : <cos2q>=0.62; 0.164
2 – 300 K : <cos2q>=0.5; 0.22
800 nm, 100 fs, 1x1014 W/cm2 :
3 – 100 K : <cos2q>=0.70
4 – 50 K : < cos2q>=0.77
Anti-Aligned ensemble
Emission spectra for two different electronic final states
3sg-1
1pu-1
fluorescence
spectrum
<cos2q>= 0.5
<cos2q>=0.77
<cos2q>=0.22
Stimulated X-ray Raman scattering
to study charge transfer
Dt
w1
Start valence/vibrational wavepacket
at atomic site A
w2
Dt
w3
ws
“charge transfer”
Probe at
atomic site B
S. Mukamel et al. ( PRL 89, 043001 (2002), PRB 72, 235110 (2005); PRA 76, 012504 (2007); PRB
79, 085108 (2009)
Evolution of emitted spectrum
FEL input: transform limited 5 fs pulse, 2.5 x 1012 photons (LCLS II)
Emission shift to w=2w00-w22
Propagation depth [mm]
Shift of emission frequency
due to 4-wave mixing
Saturation broadening
Onset of saturation
Energy [eV]
Kimberg & Rohringer,
PRL. 110, 043901 (2012).
Stimulated x-ray Raman scattering creates
Vibrational and electronic wave-packet
normalized
0.01
Internuclear distance [a.u.]
Final state
Internuclear distance [a.u.]
normalized
Internuclear distance [a.u.]
Time [fs]
0.1
1
Time [fs]
Intermediate state
Internuclear distance [a.u.]
Different ways to for stimulated X-Ray Raman scattering
1. Two-color Raman scattering with seeded source
Pick 2 distinct frequencies within 10 eV SASE bandwidth
allows selection of intermediate and final state
2. Impulsive Raman scattering with seeded source
“attosecond pulses”,
broad bandwidth transform limited pulse
(10 eV bandwidth, 0.25 fs pulse duration)
3. Impulsive Raman with broadband SASE
temporal resolution limited to coherence time of source
for non-linear processes depending on higher-order
field correlation functions
N. Morita and T. Yajima, PRA 30, 2525 (1984).
Y. H. Jiang et al., PRA 81, 051402(R) (2010).
M. Belsley et al. PRA 64, 063806 (2001).
K. Meyer et al., PRL 108 098302 (2012),
Two-color SASE XFEL operation
Relative separation of the pulses: ≈ 2% of central photon energy
SASE bandwidth of each indiviual pulse: ≈ 0.5% of central photon energy
Two pulses can be delayed within electron bunch length
Lutman et al., Phys. Rev. Lett. 110, 134801 (2013).
Simulated sRIXS spectra on p* resonance in CO
using two-color SASE mode
Intensity [arb. units]
preliminary
stimulated emission
Photon energy [eV]
stimulated emission
on „elastic“ peak
Challenge: Find regime of best signal contrast ( to at least 10% change)
Summary and Outlook
New Results
Stimulated x-ray emission processes are accessible at XFELS
1st atomic inner-shell x-ray laser based on photoionization
1st demonstration of stimulated (impulsive) electronic x-ray Raman scattering
Directions
Transfer of stimulated emission processes to molecules (gas phase)
2 upcoming experiments in 2014
Feasibility studies of stimulated x-ray Raman scattering in liquids and solids
Opportunities
Use XFELs to pump electronic/vibrational wave packets
Development of new all x-ray (and x-ray / optical) pump probe techniques
Nonlinear x-ray spectroscopy
Postdoctoral position in experimental AMO physics
available in our group at CFEL in Hamburg
nina@pks.mpg.de
Project: demonstrate a molecular x-ray lasing and
stimulated RIXS in CO and N2
at 2 upcoming beam-times at the LCLS and FLASH XFEL
Outlook for stimulated X-ray Raman scattering
in molecules at SASE XFELs
sRIXS in forward direction:
- in principle high energy resolution, limited by spectral coherenc of SASE pulses
- only limited access to transitions of different symmetry
- strong pre-edge resonance
- seeding with tails of FEL pulses not possible
- two-color SASE scheme necessary
- covariance mapping: probably not sufficient to measure the transmitted spectrum
- need to measure the incoming SASE spectrum – cross correlation
- good control of relative intensities of the two SASE modes
- Rydberg states: currently being investigated
- we suspect higher gains despite smaller pump dipole transition strength
Polarization of emitted radiation control by pre-aligned sample
Example: transition dipole parralel to molecular axis
optical alignment laser
s XFEL
a
XFEL
s 800nm
s XFEL
a
s molXRL
k
Pumping power requirements for x-ray lasers
I(z) = I(0)× eg×z
Population inversion:
Gain coefficeint:
Dn
Einstein A coefficient:
Naturally broadened transition (rad. decay):
E2,N2,g2
l,n, A21
E1,N1,g2
E0
Required pump power density to compensate for level depletion:
Pumping power to maintain a specific gain:
J. J. Rocca, Rev. Scient. Instr. 70, 3799 (1999).
Small-signal gain cross section
Single shot – versus ensemble average
FWHM 20 fs
Gain at gas density of 1.6e19 atoms/cm3:
G=rs =64 cm-1
Slow-down of group velocity on resonance
Gain-guiding, due to absorption of pump
occupation of upper state
No pump absorption
occupation of upper state
normalized
normalized
(see also Casperson & Yariv, PRL 26, 293 1971)
normalized
Population
Evolution of bond-length in excited and final state
for a pump pulse of 50 fs
z=2 mm
z=3 mm
z=5 mm
0.2
0.1
x 20
<ri> (Å)
0
1.09
(a)
Population of
Intermediate (core-excited) state
(b)
Bond-length of intermediate
state
1.08
1.07
(c)
<rf> (Å)
1.14
Bond-length of final state
1.12
1.1
-40
Incoherent superposition
Of final vibrational states
-20
0
20
40
60
Retarded time (fs)
Kimberg & Rohringer,
PRL. 110, 043901 (2012).
Fine Tuning of the emission
Emission energy (eV)
v=2
V=1
v=0
Interaction length (mm)
Evolution of XFEL pump pulse and emitted XRL pulse through the gain medium
SASE Pulse 1
SASE Pulse 2
XFEL
distance [mm]
distance [mm]
XFEL
normalized
XRL
distance [mm]
distance [mm]
XRL
normalized
Beam profiles of LCLS and XRL in the far field
1
atomic XRL
transmitted XFEL
Intensity [arb. units.]
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Position [mm]
FEL and XRL have the same angular divergence, ~ 1 mrad
Rohringer et al., Nature 481, 488 (2012)
The build-up of transform-limited pulses
Number of photons
Gaussian pulse, 40 fs, 2 x 1012 photons; Length: 16 mm, Density: 1.6 x 1019 cm-3
1.e12
Saturated
gain region
1.e08
1.e04
1.e00
Linear
gain region
no spectral
gain narrowing
transform
limited
pulses
Weninger & Rohringer,
in preparation
see also: Hopf et al., PRL 35, 511 (1975); Hopf & Meystre, PRA 12, 2534 (1975)
Vibrational and electronic wave-packet dynamics
Internuclear distance [a.u.]
normalized
Time [fs]
Time [fs]
Intermediate state
normalized
Time [fs]
Time [fs]
Internuclear distance [a.u.]
final state
Internuclear distance [a.u.]
Internuclear distance [a.u.]
z= 3 mm
(exp. gain
regime)
X-ray absorption cross
section N2