Since the development of the laser researchers have been using it as a
stroboscopic tool to observe how the world works. Research and development
efforts leading towards the Linac Coherent Light Source
(LCLS) free-electron
laser have facilitated the construction of a new accelerator-based femtosecond
x-ray source, the Sub-Picosecond Pulse Source
(SPPS) which extends our ability
to capture transient phenomena at atomic-scale resolution. In order to produce
femtosecond x-ray bursts, electron bunches at SLAC are chirped and then sent
through a series of energy-dispersive magnetic chicanes, yielding 80-fs
electron pulses. These are then transported through an undulator to create
sub-100-femtosecond x-ray pulses at 8-10 keV and 107 photons/second.
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Fig. 1. (top) Time-resolved diffracted intensity for both (111) (top) and (220)
(bottom) reflections. Red curves are Gaussian fits to the data, corresponding
to 10-90 % fall times of 430 fs and 280 fs respectively. (inset) Fluence
dependence of (111) time constant.
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Two recent experiments1,2 have now used this source to elucidate the ultrafast
transition from solid to liquid, and demonstrated a method to both measure the
duration of a femtosecond electron bunch and to overcome the jitter between a
linac-based x-ray source and a femtosecond laser.
The solid-liquid transition
Intense femtosecond excitation of semiconductor materials results in the
excitation of a dense electron-hole plasma, with accompanying dramatic changes
in the interatomic potential, leading to disordering of the material on
time-scales shorter than electron-phonon coupling times. Pump-probe
measurements using an InSb sample were conducted in a cross-beam geometry with
the optical pump pulse incident at an angle with respect to the x-ray probe
pulse. In this way, a temporal sweep is created along the crystal surface,
transforming temporal information into spatial information and enabling one to
record the complete time history around t=0 in a single shot.
Figure 1 shows the measured time-dependent intensity I(Q,t) for both the (111)
and (220) reflections, averaged over 10 single shot images. We observe that the
diffracted intensity is non-exponential and well-fit by a Gaussian-like curve.
Moreover, the (220) reflection decays with a time-constant qualitatively faster
than the (111). The 10-90 time constants for the (111) and (220) reflections
are 430 fs and 280 fs respectively, with ratio t(111) / t(220) =1.5 ±0.2. This
is equal (within experimental error) to the ratio of the magnitude of the
reciprocal lattice vectors for the two reflections. This inverse- Q-dependent
scaling and Gaussian-like time-dependence strongly implies statistical atomic
motion and suggests that the data be described using a time-dependent
Debye-Waller model, relating the time-dependent decrease in scattered intensity
to a time-dependent rms displacement,
as I(Q,t).
Here <u^2(t)> is
the time-dependent mean square displacement of the photo-excited atoms, averaged spatially
over the sample. Following an impulsive softening of the interatomic
potential, for short times afterwards (to first order in t) the atoms continue
to move with velocities set by initial conditions, i.e. inertially, following
Newton's First Law. The time-resolved diffracted intensity I(Q,t) is then
expected to be Gaussian in both Q and t with a time-constant that varies
inversely with Q, exactly as observed. By inverting the time-dependent data
one may extract the time dependence of the rms displacement. We measure a
linear time-dependence which corresponds to a velocity 2.3 Å/ ps
in good agreement
with the room temperature rms velocity in InSb
(3kbT/M)1/2 = 2.5 Å/ ps. The
implication is then of a transition state in which the potential energy is
softened enough that the atoms initially move freely with large amplitude along
an effectively barrierless potential energy surface with initial conditions set
by room-temperature thermodynamic velocities. During the first few hundred fs,
although the displacements correspond to a large fraction of the interatomic
distance and the strong covalent bonds characteristic of the crystalline state
are broken or strongly modified, the average displacement <u> from the
equilibrium lattice sites is still zero, a state intermediate between that of a solid and a liquid.
Clocking femtosecond x-rays
A non-invasive technique is used to record the arrival time of femtosecond
electron bunches at SPPS with respect to a pump laser pulse. Although the time
of arrival fluctuates from pulse to pulse, this information can be used to
place repetitive measurements in sequence with femtosecond resolution. The
optical properties of an electro-optic crystal placed adjacent to the electron
beam are strongly modified as a result of the electric-field of the electron
bunch as it passes. A femtosecond laser pulse propagating through the crystal
at the same time as the transient birefringence is induced has its polarization
rotated and can thus be used as a probe of the relative arrival time of the
electron bunch. By making use of a cross-beam geometry like the melting
experiment described above, a range of times is measured, and the timing
information is imprinted on the spatial profile of the transmitted laser beam.
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Fig. 2. (a) 20 consecutive single shot electron bunch measurements. The bright
band in each column is the electro-optic signal, its location indicates the
time of arrival of the electron bunch with respect to the laser probe pulse,
and its width corresponds to the electron bunch duration. b) Normalized arrival
time histogram of 1000 consecutive single shots.
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This experiment makes possible a wide range of repetitive measurements with
time-resolution limited by the pump and probe durations instead of the
intrinsic jitter between pump and probe. Relative timing information from
spatially-resolved electro-optic measurements could be extended to a resolution
of order 5 fs, matching the projected performance of future XFELs into the
foreseeable future.
References:
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A. M. Lindenberg, J. Larsson, K. Sokolowski-Tinten, K. J. Gaffney, C.
Blome, O. Synnergren, J. Sheppard, C. Caleman, A. G. MacPhee, D. Weinstein, D.
P. Lowney, T. K. Allison, T. Matthews, R. W. Falcone, A. L. Cavalieri, D. M.
Fritz, S. H. Lee, P. H. Bucksbaum, D. A. Reis, J. Rudati, P. H. Fuoss, C. C.
Kao, D. P. Siddons, R. Pahl, J. Als-Nielsen, S. Duesterer, R. Ischebeck, H.
Schlarb, H. Schulte-Schrepping, Th. Tschentscher, J. Schneider, D. von der
Linde, O. Hignette, F. Sette, H. N. Chapman, R. W. Lee, T. N. Hansen, S.
Techert, J. S. Wark, M. Bergh, G. Huldt, D. van der Spoel, N. Timneanu, J.
Hajdu, R. A. Akre, E. Bong, P. Krejcik, J. Arthur, S. Brennan, K. Luening, and
J. B. Hastings, "Atomic-Scale Visualization of Inertial Dynamics",
Science 308, 392 (2005)
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A. L. Cavalieri, D. M. Fritz, S. H. Lee, P. H. Bucksbaum, D. A. Reis,
J. Rudati, D. M. Mills, P. H. Fuoss, G. B. Stephenson, C. C. Kao, D. P.
Siddons, D. P. Lowney, A. G. MacPhee, D. Weinstein, R. W. Falcone, R. Pahl, J.
Als-Nielsen, C. Blome, S. Düsterer, R. Ischebeck, H. Schlarb, H.
Schulte-Schrepping, Th. Tschentscher, J. Schneider, O. Hignette, F. Sette, K.
Sokolowski-Tinten, H. N. Chapman, R. W. Lee, T. N. Hansen, O. Synnergren, J.
Larsson, S. Techert, J. Sheppard, J. S. Wark, M. Bergh, C. Caleman, G. Huldt,
D. van der Spoel, N. Timneanu, J. Hajdu, R. A. Akre, E. Bong, P. Emma, P.
Krejcik, J. Arthur, S. Brennan, K. J. Gaffney, A. M. Lindenberg, K. Luening and
J. B. Hastings, "Clocking Femtosecond X Rays",
Phys. Rev. Lett.
94,
114801 (2005)
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Correspondence and requests for materials should be address to Jerome B.
Hastings
(e-mail: jbh@slac.stanford.edu).
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SSRL is supported by the Department of Energy, Office of Basic Energy Sciences.
The SSRL Structural Molecular Biology Program is supported by the Department of
Energy, Office of Biological and Environmental Research, and by the National
Institutes of Health, National Center for Research Resources, Biomedical
Technology Program, and the National Institute of General Medical Sciences.
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