Imaging electronic quantum motion with light

Abstract

Imaging the quantum motion of electrons not only in real-time, but also in real-space is essential to understand for example bond breaking and formation in molecules, and charge migration in peptides and biological systems. Time-resolved imaging interrogates the unfolding electronic motion in such systems. We find that scattering patterns, obtained by X-ray time-resolved imaging from an electronic wavepacket, encode spatial and temporal correlations that deviate substantially from the common notion of the instantaneous electronic density as the key quantity being probed. Surprisingly, the patterns provide an unusually visual manifestation of the quantum nature of light. This quantum nature becomes central only for non-stationary electronic states and has profound consequences for time-resolved imaging.X-ray imaging | attosecond science | quantum electrodynamics T he scattering of light from matter is a fundamental phenomenon that is widely applied to gain insight about the structure of materials, biomolecules and nanostructures. The wavelength of X-rays is of the order of atomic distances in liquids and solids, which makes X-rays a very convenient probe for obtaining realspace, atomic-scale structural information of complex materials, ranging from molecules (1) to proteins (2) and viruses (3). The power of X-ray scattering relies as well on the fact that the X-rays interact very weakly with the electrons in matter. In a given macroscopic sample, generally no more than one scattering event per X-ray photon takes place, the probability for multiple scattering being extremely small. The key quantity in X-ray scattering is the differential scattering probability (DSP), which is related to the Fourier transform of the electronic density ρðxÞ as follows (4, 5)where dP e ∕dΩ is the differential scattering probability from a free electron and Q is proportional to the momentum transfer of the scattered light. Procedures exist, for both crystalline (6) and non-crystalline samples (7), to reconstruct ρðxÞ from the scattering pattern. Equation 1 can be obtained from a purely classical description of electromagnetic radiation scattered by a stationary electron density (5), yielding a result identical to that obtained from a quantum electrodynamics (QED) description of light. Eq. 1 gives us access to a static view of the electronic density. On the other hand, much progress has been made in recent years towards understanding electronic motion with time-domain table-top experiments (8-13), owing to the availability of laser pulses on the sub-fs time scale (14,15). An ultimate goal of imaging applications encompasses unraveling the motion of electrons and atoms with spatial and temporal resolutions of order 1 Å and 1 fs, respectively (16). Recent breakthroughs make it possible to generate hard X-ray pulses of a few fs (17, 18), and pulses of length 100 as can in principle be realized (19,20). Hence, a fundamental question that needs to be addressed is: How does an ultrashort light pulse interact and scatter from a non-stationary...

Imaging electron dynamics with time- and angle-resolved photoelectron spectroscopy

“…Therefore, angle-resolved photoelectron spectra do not follow the time evolution of the electron density. A similar effect that a measured signal from an electronic wave packet does not follow the time-dependent electron density has been shown for time-resolved resonant [23,24] and nonresonant [21] x-ray scattering patterns as well as time-resolved electron diffraction patterns [40].…”

“…In can be applied for a Gaussian-shaped probe pulse polarized along in with the amplitude of the electric field E(r 0 ,t) = √ (8π/c)I 0 (r 0 )e −2 ln 2( t−tp τp ) 2 , where r 0 is the position of the object, t p is the time of the measurement, τ p is the pulse duration (FWHM of the pulse intensity), and I 0 (r 0 ) = cE 2 (r 0 ,t = 0)/(8π ), that [21] 2πω in V …”

“…In these studies, the effect of the broad bandwidth of an ultrashort probe pulse has either been neglected [17,18,20] or approximated [19]. However, we have earlier demonstrated that an accurate treatment within the quantum electrodynamics (QED) approach taking into account all transitions that can be induced by a broadband probe pulse is necessary for a correct description of ultrafast x-ray scattering from a nonstationary electronic system [21][22][23][24]. Therefore, since this should also be true for time-resolved photoelectron imaging, we apply the QED treatment to describe the interaction of a nonstationary electronic system with an ultrashort isolated probe pulse inducing single-photon ionization.…”

“…We describe the interaction between the electronic system and the photoionizing ultrashort probe pulse using a similar formalism to the one applied for the study of ultrafast x-ray scattering [21][22][23][24]. Since we assume that the probe pulse does not temporally overlap with the pump pulse, the interaction of the electronic system with the probe pulse can be considered independently from the pump pulse [25].…”

Time-resolved electron(e,2e)momentum spectroscopy: Application to laser-driven electron population transfer in atoms

“…Moreover, various aspects of electronic motions can be retrieved using different probe schemes. For example, attosecond transient absorption spectroscopy tracks the frequencies, phases, and lifetimes of excited oscillating dipoles [17,18], time-resolved x-ray absorption and x-ray Raman spectroscopy provide element-specific probes of evolving electronic motion and chemical bonding [19,20], and x-ray and electron diffraction are able to directly image electronic spatial motions with (sub)angstrom resolution [21][22][23].…”