Figure - available from: Journal of Physics B Atomic Molecular and Optical Physics
This content is subject to copyright. Terms and conditions apply.
Experimental TRPES spectrum for NH3 pumped at 160.9 nm and probed at 400 nm. The color scale represents the photoelectron yield in arbitrary units. The vertical solid line marks the expected photoelectron energy for ionization into the (0300) $X{}^{2}{A}_{2}^{{\prime\prime} }$ cationic state.
Source publication
Electronic coherences in molecules are ultrafast charge oscillations on the molecular frame (MF) and their direct observation and separation from electronic population dynamics is challenging. Here we present a valence shell lab frame (LF) scattering method suited to probing electronic coherences in isolated systems. MF electronic coherences lead t...
Citations
... It relies on the presence of coherence between different populated electronic states in the system and is therefore sometimes referred to as coherent mixed scattering (CMS) [37]. It is worth noting that the manner in which coherences manifest in UXS has interesting analogies in photoelectron spectroscopy [66][67][68]. ...
Nonadiabatic transitions at conical intersections and avoided crossings play a pivotal role in shaping the outcomes of photochemical reactions. Using the photodissociation of LiF as a model, this theoretical study explores the application of gas phase nonresonant ultrafast x-ray scattering to map nonadiabatic transitions at an avoided crossing, utilizing the part of the scattering signal that probes electronic coherence directly. The presented scattering signals are rotationally averaged and calculated from two- rather than one-electron (transition) densities, which inherently accounts for all possible electronic transitions driven by the x-ray photon. This approach provides quantitative predictions of the experimental signals, thereby facilitating future experimental endeavors to observe nonadiabatic effects and coherent electron dynamics with ultrafast x-ray scattering.
... Molecular Frame Quantum Tomography in NH 3 -In this proof-of-concept demonstration we used the NH 3 molecule, resonantly excited to a pair of electronic states, which are nonadiabatically coupled by molecular frame (MF) rotation [53,54]. MFQT was achieved by combining data from ultrafast time-resolved measurements [54], with that of high-resolution spectroscopy [55]. ...
... Molecular Frame Quantum Tomography in NH 3 -In this proof-of-concept demonstration we used the NH 3 molecule, resonantly excited to a pair of electronic states, which are nonadiabatically coupled by molecular frame (MF) rotation [53,54]. MFQT was achieved by combining data from ultrafast time-resolved measurements [54], with that of high-resolution spectroscopy [55]. The resulting density matrix is used to construct the time-resolved electronic probability distribution in the MF, for molecules at several orientation angles in the lab frame. ...
... where Ω = {φ, θ, χ} are the Euler angles specifying the molecular orientation, and n, n → ± are indices associated with the coherently excited electronic states. The Molecular Angular Distribution Moments (MADMs) A K QS (n, n ; t) specify the evolving excited state molecular dynamics [52] [53,54,57]. The MADMs A 0 00 (±, ±; t) track the total population in each excited state, while A 2 00 (±, ±; t) track the alignment of the z-axis for the population in each state. ...
A methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems is developed, and applied to fully characterize a non-adiabatc electronic wavepacket in ammonia molecules (NH$_3$). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences fully characterising the electronic and vibrational dynamics in the molecular frame. Beyond characterizing the system, time and orientation angle dependent expectation values of any relevant operator may be constructed using the LFDM. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on charge flow in the molecular frame, and entanglement within the system can be determined. In general MFQT provides new routes to the study of ultrafast molecular dynamics, information processing, metrology and optimal control schemes.
... determine the time-varying orientationdependent shape of the vibronic coherences in the laboratory frame, which we refer to as Electronic Angular Distribution Moments (EADMs). 55 The diagonal matrix elements A K QS (α, vα; t) determine the time varying probability distribution of molecular orientations in a particular vibronic state and are called the Axis Distribution Moments (ADMs). 54 These collectively dictate the orientationdependent shape of all the density matrix elements in the lab frame. ...
... Any experiment designed to specifically target the reduced vibronic density matrix will not be sensitive to these coherences if the experiment is initiated in an isotropic ensemble. On the other hand, as discussed in Ref. 55 and Sec. IV, experiments that measure the anisotropy in the distribution of a particle scattered off the excited molecule will potentially be directly sensitive to a number of MADMs. ...
... In particular, this approximate method fails in cases in which rotational and electronic degrees of freedom are coupled. 48,55 In Sec. III, we present a numerical calculation of only electronic dynamics within the rigid rotor and BO approximations that demonstrates the concepts presented thus far, and verifies some of the theoretical results. ...
In most cases, the ultrafast dynamics of resonantly excited molecules are considered and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here, we provide a formalism in terms of a lab frame density matrix, which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences, which are potentially experimentally accessible, are rejected by the orientation-averaged reduced vibronic density matrix. Instead, molecular angular distribution moments are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.
... 394 Momentum analysis of LFPAD anisotropies relying on ultrafast time-energy-angle resolved observables, when an electron wave-packet launched by a pump pulse is probed by valence ionization, was recently proposed as a new method to access molecular frame electronic coherences, as demonstrated for dissociation of excited states of the NH 3 molecule. 1,395 Inner-shell ionization of aligned molecules: Femtosecond photoelectron diffraction ...
... [447][448][449] Despite the popularity of challenging pump-probe experiments, quite few probe the dynamics beyond the simple photoelectron spectra, often leading to a limited characterization of the internal dynamics, with remaining ambiguities. The rich information embodied in angularly resolved studies from oriented molecules will be greatly beneficial to fully characterize the electronic states involved, their coupling with nuclear motion, 450 and the electron wavepacket coherences 395,451,452 and bifurcations, up to now quite elusive, both in valence excitation and ionization with broad pulses. ...
In this perspective article, main trends of angle-resolved molecular photoelectron spectroscopy in the laboratory up to the molecular frame, in different regimes of light-matter interactions, are highlighted with emphasis on foundations and most recent applications.
... Collectively, we will refer to these as the Molecular Angular Distribution Moments (MADM). The off diagonal elements A K QS (α, α , v α , v α ; t) determine the time varying orientation-dependent shape of the vibronic coherences in the laboratory frame, which we refer to as Electronic Angular Distribution Moments (EADMs) [55]. The diagonal matrix elements A K QS (α, v α ; t) determine the time varying probability distribution of molecular orientations in a particular vibronic state, and are called the Axis Distribution Moments (ADMs) [54]. ...
... Any experiment designed to specifically target the reduced vibronic density matrix will not be sensitive to these coherences, if the experiment is initiated from an isotropic ensemble. On the another hand, as discussed in [55] and section 4, experiments that measure the anisotropy in the distribution of a particle scattered off the excited molecule will potentially be directly sensitive to a number of MADMs. Thus the orientation averaged reduced vibronic density matrix does not accurately represent the information available from such experiments. ...
... While the fixed molecule approximation is useful, particularly for expensive vibronic calculations, a calculation which treats the rotational states explicitly is preferable yielding the vibronic dynamics at any orientation angle from Eq. 16, and equivalently the full lab frame molecular probability distribution. In particular, this approximate method fails in cases in which rotational and electronic degrees of freedom are coupled [48,55]. In the following section we present a numerical calculation of only electronic dynamics within the rigid rotor and BO approximations that demonstrates the concepts presented thus far, and verifies some of the theoretical results. ...
In most cases the ultrafast dynamics of resonantly excited molecules are considered, and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here we provide a formalism in terms of a lab frame density matrix which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences which are potentially experimentally accessible are rejected by the orientation-averaged reduced vibronic density matrix. Instead, Molecular Angular Distribution Moments (MADMs) are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography, and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.
... While the ionization cross-section will display a coordinate and electronic state dependence, it will not be symmetryforbidden; these symmetries will simply be reflected in the differential angular yields in an angle-resolved measurement of the photoelectron emission. Lastly, the measurement of the time-evolving photoelectron angular distributions [5][6][7] , either completely or simply in the form of the photoelectron anisotropy, 8 can yield complementary insight into the electronic states and symmetries involved in the photoionization dynamics. ...
... 83 A completely different proposal for observing electronic coher-ences in molecules employs TRPES to probe rotational wave packets. 7 In most cases the ultrafast dynamics in the excited electronic states of molecules are conceived of and simulated in the molecular frame, even though experiments are carried out in the laboratory frame (LF). Most ultrafast studies are primarily concerned with the internal degrees of freedom, in which coupled electronic-nuclear wave packet evolve on atto-and femtosecond time scales. ...
... The timeresolved photoelectron angular distributions were employed to determine the so-called electronic angular distribution moments (EADMs) and thereby completely separate the electronic population dynamics from electronic coherences. 7 That study employed VUV-TR-PES, but any ultrafast angle-resolved scattering observable could yield analogous information. In that work, by measuring the lab-frame angular distributions, the authors could experimentally measure the corresponding LF anisotropies, β LM (t, ε), analyze the time evolution of these quantities, and compare to wave packet simulations. ...
Time-resolved photoelectron spectroscopy (TRPES) has become one of the most widespread techniques for probing nonadiabatic dynamics in the excited electronic states of molecules. Furthermore, the complementary development of ab initio approaches for the simulation of TRPES signals has enabled the interpretation of these transient spectra in terms of underlying coupled electronic-nuclear dynamics. In this perspective, we discuss the current state-of-the-art approaches, including efforts to push femtosecond pulses into vacuum ultraviolet and soft X-ray regimes as well as the utilization of novel polarizations to use time-resolved optical activity as a probe of nonadiabatic dynamics. We close this perspective with a forward-looking prospectus on the new areas of application for this technique.
... These include, but are not limited to, ultrafast pump-probe spectroscopies such as transient absorption or time-resolved photoelectron spectroscopy [6][7][8][9][10][11]. The second category is comprised of (generally non-linear) spectroscopic methods which are sensitive to the coherences that may form as a result of non-adiabatic coupling of the initially excited electronic state to its complement [12][13][14][15][16][17][18][19][20][21][22]. For example, recently, timeangle-resolved scattering, making use of angular momentum coherences, was demonstrated to completely separate electronic population dynamics from electronic coherences [15]. ...
... The second category is comprised of (generally non-linear) spectroscopic methods which are sensitive to the coherences that may form as a result of non-adiabatic coupling of the initially excited electronic state to its complement [12][13][14][15][16][17][18][19][20][21][22]. For example, recently, timeangle-resolved scattering, making use of angular momentum coherences, was demonstrated to completely separate electronic population dynamics from electronic coherences [15]. Another prominent example is the TRUECARS (transient redistribution of ultrafast electronic coherences in attosecond Raman signals) technique [12]. ...
We consider the formation of transient electronic coherences driven by conical intersection-mediated population transfer between two electronic states. By invoking simple symmetry arguments, we identify several fundamental factors which modulate the magnitude of these electronic coherences. We consider the sub-cases where the two electronic states have either the same or different point group symmetry at the Franck-Condon geometry. For the different symmetry case, due to fundamental symmetries of the molecular Hamiltonian, significant coherences are unlikely to form. Although for states of the same symmetry, large magnitude electronic coherences can form. The magnitude of these coherences are highly dependent on the topography of the conical intersection. These results offer a guide to experimental studies of electronic coherences induced by nuclear motion in the vicinity of a conical intersection, as well as to ab initio simulations which are employed to simulate them.
... molecular wavepacket dynamics. In such cases both MFPADs and LFPADs can track the time varying electronic character of the excited state, thus allowing measurement of time-resolved electronic-vibrational dynamics, including their non-adiabatic coupling [4,11,22,23,[25][26][27]. MFPADs, as in the static case, provide a greater depth of information and potentially directly imprint the electronic character of the wavepacket onto the photoelectron observable [11,25]. ...
A theory and method for a matrix-based reconstruction of molecular frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is developed and basic applications are explored. As with prior studies of MF reconstruction, the experimental side of this protocol is based upon time-resolved LF measurements in which a rotational wavepacket is prepared and probed as a function of time via photoionization, followed by a numerical reconstruction routine. In contrast to other methodologies, the protocol presented here does not require determination of the photoionization matrix elements, and consequently takes the relatively simple numerical form of a matrix equation. Significantly, this simplicity allows the successful reconstruction of MFPADs for nonlinear polyatomic molecules with D nh point group symmetry. We numerically demonstrate this scheme for two realistic molecular photoionization cases: N2 and C2H4. This new technique is expected to be generally applicable to a broad range of MF reconstruction problems involving photoionization of polyatomic molecules.
... In particular, extending the delays to 15-20 ps would allow the detailed examination of the rotational structure and corresponding interactions, as well as of the nature of the electronic coherences. 27,29,53 Such data would allow a more detailed comparison with both highresolution absorption measurements and the multichannel quantum defect analysis of Jungen et al. 24 Characterization of both the VUV and NIR wavelength dependence of the photoelectron data would also provide a more complete picture of the energetics and dynamics, particularly with respect to the role of autoionizing resonances and their influence on the time-dependent dynamics. Such states may ultimately prove valuable in controlling interferences and ionization dynamics. ...
We have used the FERMI free-electron laser to perform time-resolved photoelectron imaging experiments on a complex group of resonances near 15.38 eV in the absorption spectrum of molecular nitrogen, N2, under jet-cooled conditions. The new data complement and extend the earlier work of Fushitani et al. [Opt. Express 27, 19702–19711 (2019)], who recorded time-resolved photoelectron spectra for this same group of resonances. Time-dependent oscillations are observed in both the photoelectron yields and the photoelectron angular distributions, providing insight into the interactions among the resonant intermediate states. In addition, for most states, we observe an exponential decay of the photoelectron yield that depends on the ionic final state. This observation can be rationalized by the different lifetimes for the intermediate states contributing to a particular ionization channel. Although there are nine resonances within the group, we show that by detecting individual photoelectron final states and their angular dependence, we can identify and differentiate quantum pathways within this complex system.
... In the meantime, several other studies have emphasized the possibilities of state of the art XUV and Xray lasers, accessing the necessary temporal and spectral windows for tracing non-adiabatic events. 34,[42][43][44][45][46] All of the aforementioned studies focus on the fundamental physics that can be potentially accessed by various novel techniques. They are either introduced on model systems to highlight their advantages over other techniques in a certain aspect, or applied to small molecules, offering a clear interpretation to verify that they are feasible. ...
The role of quantum-mechanical coherences in the elementary photophysics of functional optoelectronic molecular materials is currently under active study. Designing and controlling stable coherences arising from concerted vibronic dynamics in organic chromophores is the key for numerous applications. Here, we present fundamental insight into the energy transfer properties of a rigid synthetic heterodimer that has been experimentally engineered to study coherences. Quantum non-adiabatic excited state simulations are used to compute X-ray Raman signals, which are able to sensitively monitor the coherence evolution. Our results verify their vibronic nature, that survives multiple conical intersection passages for several hundred femtoseconds at room temperature. Despite the contributions of highly heterogeneous evolution pathways, the coherences are unambiguously visualized by the experimentally accessible X-ray signals. They offer direct information on the dynamics of electronic and structural degrees of freedom, paving the way for detailed coherence measurements in functional organic materials.
