Real-time observation of valence electron motion
(05 August 2010)
25 September 2009
24 May 2010
The superposition of quantum states drives motion on the atomic and subatomic scales, with the energy spacing of the states dictating the speed of the motion. In the case of electrons residing in the outer (valence) shells of atoms and molecules which are separated by electronvolt energies, this means that valence electron motion occurs on a subfemtosecond to few-femtosecond timescale (1
fs = 10 −15 s). In the absence of complete measurements, the motion can be characterized in terms of a complex quantity, the density matrix. Here we report an attosecond pump–probe measurement of the density matrix of valence electrons in atomic krypton ions . We generate the ions with a controlled few-cycle laser field 1 and then probe them through the spectrally resolved absorption of an attosecond extreme-ultraviolet pulse 2 , which allows us to observe in real time the subfemtosecond motion of valence electrons over a multifemtosecond time span. We are able to completely characterize the quantum mechanical electron motion and determine its degree of coherence in the specimen of the ensemble. Although the present study uses a simple, prototypical open system, attosecond transient absorption spectroscopy should be applicable to molecules and solid-state materials to reveal the elementary electron motions that control physical, chemical and biological properties and processes. 3
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Figure 1: Probing intra-atomic electron motion by attosecond absorption spectroscopy.
a, The strong electric field of a near-infrared (NIR) laser pulse (in red) with a duration of τ L < 4 fs liberates electrons from the 4 p valence subshell of krypton atoms to generate singly charged 4 p −1, doubly charged 4 p −2 or triply charged 4 p −3 ions in the 4 p −1, 4 p −2 and 4 p −3 manifolds of quantum states, respectively, by means of optical field ionization (indicated by red arrows). A subfemtosecond EUV pulse (in violet) with a carrier photon energy of ~80 eV is passed through the ions and promotes them to core-hole excited-state manifolds 3 d −1, 3 d −14 p −1 and 3 d −14 p −2 (as indicated by the violet arrows). Transient EUV absorption spectra are acquired by recording the attosecond EUV pulse spectrum transmitted through the ionized gas target as a function of pump–probe delay with an EUV spectrometer. b, c, Spectral intensity distribution of the relevant part of the broadband attosecond probe pulse ( b) and schematic of the experimental set-up ( c). The pulse is transmitted through an ensemble of krypton atoms (~10 18 cm −3; interaction length, ~1 mm) before their ionization (blue curve) and after their ionization (red curve) by the laser pulse with a peak intensity of ~7 × 10 14 W cm −2, as well as by several optical elements shown in c and discussed in detail in Methods. arb.u., arbitrary units.
Figure 2: Transient absorption spectra of krypton ions.
Absorbance is defined as
A( E, τ) = ln( I trans( E, τ)/ I 0( E)), where I 0( E) is the spectral density recorded at a negative delay of −10 fs, that is, the attosecond probe precedes the ionizing laser pulse by 10 fs in the atomic sample, and I trans( E, τ) is the spectral density recorded at a pump–probe delay τ. The delay is varied in steps of 200 as. Error bars indicate the standard error of the mean values acquired from several spectra recorded at the same delay. The EUV probe pulse shows the formation of charge states up to Kr 3+ as indicated in the spectrum shown in the background, which is recorded at τ ≈ 10 fs. Disregarding a forerunner in the main Kr + line, the origin of which is unclear, the Kr 2+ lines appear with a significant, well-resolved delay of about one-half the laser period ( T L/2 ≈ 1.25 fs) after the Kr + lines, and the Kr 3+ lines appear with approximately the same delay after the Kr 2+ lines. The decrease in the neutral krypton population in the atomic sample manifests itself as a reduction of the absorption in the range 91–93 eV, where neutral krypton atoms absorb resonantly. Relative occupations between the ionic states Kr +, Kr 2+ and Kr 3+ are estimated as = 1:0.875:0.25.
Figure 3: Build-up of electronic coherence in Kr + produced by optical field ionization (theory).
a, Temporal evolution of the diagonal elements of the reduced density matrix of Kr + in the presence of a 750-nm, 3.8-fs laser pulse with a peak intensity of ~3 × 10 14 W cm −2 and a sinusoidal waveform. The notation of the matrix elements is explained in the text. The populations have been normalized such that the trace of the reduced density matrix at τ = 10 fs equals one. The dashed line shows the electric field of the laser pulse (in atomic units (a.u.)) used in the simulations. The hole density distributions of the corresponding orbitals of the 4 p subshell are also depicted. b, The degree of coherence, g( t) (see equation (1)), averaged over time intervals of the laser half-cycle (~1.25 fs), is shown with red dots. Squares show the half-cycle-averaged degree of coherence for an ionizing laser pulse with a duration of 7.6 fs at the same peak intensity. The degree of coherence is defined such that, after the NIR pump pulse, it equals one for a perfectly coherent hole wave packet. The detailed behaviour of the degree of coherence during ion formation is not yet understood.
Figure 4: Attosecond absorption spectroscopy reveals intra-atomic electron wave-packet motion in Kr +.
Figure 5: Reconstruction of valence-shell electron wave-packet motion.