Periodic Reporting for period 1 - Orbital Cinema (Photoemission Orbital Cinematography: An ultrafast wave function lab)
Reporting period: 2023-07-01 to 2024-12-31
Directly watching in slow-motion videos how electrons move in quantum mechanical orbitals and how this motion shapes the functionalities of condensed matter has been a dream shared by all natural and life sciences. Yet, this vision comes with the daunting challenge of mapping the microscopic structure of electronic orbitals with simultaneous ultrafast time resolution. The overall project objective is turning such an “orbital cinematography” into reality. Our approach relies on the unique synergies between photoemission orbital tomography (POT), ultrafast photoemission spectroscopy, lightwave electronics and advanced theory. We will combine these methodologies to a cinematography at unprecedented time scales faster than a single oscillation period of light and systematically explore the nanocosmos on its intrinsic time scales of femto- to attoseconds. For example, we plan to take actual slow-motion movies of molecular orbitals during charge transfer processes, surface chemical reactions, and wave packet motion driven by lightwaves.
In the reporting period, our focus was placed on setting up several unique experiments that will become key enablers for orbital cinematography. Altogether, three novel ultrafast laser experiments have been designed. One is already operating, two more are in the set-up phase. We also commissioned a new instrument for developing the unique sample systems on which the project objectives can be attained. This instrument is already in full use, several samples have been shipped to the laser experiments.
In parallel, we have completed key investigations towards the goal of Orbital Cinema. An important aspect of our experimental work so far is extending the scope of POT. The motivation is simple: The broader the applicability of this key component, the greater the ultimate impact of orbital cinematography. The most important contribution in this regard, achieved in the reporting period, is the first tomographic identification of a complete set of molecular orbitals (38 orbitals over a binding energy range of 10 eV for a nanographene). This unique experimental dataset allows benchmarking density functional theory at an unprecedented level of detail. Remarkably, the results of this benchmarking suggest that, perhaps unexpectedly, the calculated Kohn-Sham orbitals approximate the experimentally measured Dyson orbitals much better than previously thought. This fundamental finding is very good news for orbital cinematography, as it provides a strong link between photoemission data and the orbitals which we want to image in time and space. We have also provided theoretical support to extend POT to new material classes. To summarize this work, we have significantly expanded the scope of POT in the material, spectral and conceptual dimensions.
A second aspect we have worked on are the foundations for observing the dynamics of molecular excitons in space and time. Excitons are formed if a molecule is optically excited by absorbing a photon. In the simplest case, this lifts an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) and leaves behind a hole in the HOMO. Since electron and hole attract each other electrically, they form a bound entity—the exciton. The precise shape and the dynamics of excitons are key to understanding important processes in optoelectronics, photochemistry and light harvesting. In our work, we have filled a gap in the investigations of excitons with POT: Recent experimental and theoretical work has concentrated on the case in which the electron and the hole are each in one state only, commonly LUMO and HOMO (as in the example above). In more complex systems, however, this simple picture breaks down, and excitons must be treated as entangled states, composed of multiple electron-hole transitions. To do justice to this, we have developed a theory that allows interpreting measured photoemission momentum maps as the Fourier-transformed coherent sum of the electronic part of the exciton wave function. This result is the sought-after extension of POT to general exciton states, establishing a universal “exciton tomography” as the basis for future investigations of exciton dynamics in Orbital Cinema. Remarkably, exciton tomography retains the intuitive orbital picture of POT, while respecting both the entangled character of the exciton wave function and the energy conservation in the photoemission process. In fact, its predictions have already been verified by experiments on C60.
A third aspect is the demonstration that time-resolved (tr) POT can also give access to fully coherent electron dynamics—a crucial aspect for Orbital Cinema. A common way to perform trPOT is the pump-probe scheme, where a first laser pulse (the pump) excites the system, while a second, delayed laser pulse (the probe) photoemits an electron from the excited system and thus probes the system’s dynamics at a fixed delay between the two pulses. In such an experiment, we have observed that the trPOT signal changes over time. For long delays, we observe the wave function of the electron excited from the HOMO collapsing into another orbital, the LUMO. At this point, the information on the initial state (the HOMO) is lost, and indeed the observed photoelectron distribution is that of the LUMO, with no traces of the wave function of the initial state left in the signal: Photoemission has proceeded via the real population of an intermediate state. Although this offers the opportunity to study properties of the intermediate state (e.g. its lifetime), it does not allow the investigation of coherent electron dynamics, because there is no uninterrupted “connection” from the electron in its initial state to the observation at the detector. However, for short delays, we observe a different momentum map: that of the initial state, the HOMO. Apparently, no collapse of the wave function has taken place on the way to the detector, and thus the photoelectron still carries the information of the initial state, which therefore becomes visible at the detector. In this case, the photoemission is driven by a coherent two-photon excitation, via a virtual intermediate state that does not induce a wave function collapse. The visualization of this coherent process in momentum space is an important result, because it is this kind of coherent dynamics, i.e. the elementary evolution of the wave function without wave function collapses, which we aim to trace in Orbital Cinema during charge transfer processes, surface chemical reactions and wave lightwave-driven packet motion.
In parallel, we have completed key investigations towards the goal of Orbital Cinema. An important aspect of our experimental work so far is extending the scope of POT. The motivation is simple: The broader the applicability of this key component, the greater the ultimate impact of orbital cinematography. The most important contribution in this regard, achieved in the reporting period, is the first tomographic identification of a complete set of molecular orbitals (38 orbitals over a binding energy range of 10 eV for a nanographene). This unique experimental dataset allows benchmarking density functional theory at an unprecedented level of detail. Remarkably, the results of this benchmarking suggest that, perhaps unexpectedly, the calculated Kohn-Sham orbitals approximate the experimentally measured Dyson orbitals much better than previously thought. This fundamental finding is very good news for orbital cinematography, as it provides a strong link between photoemission data and the orbitals which we want to image in time and space. We have also provided theoretical support to extend POT to new material classes. To summarize this work, we have significantly expanded the scope of POT in the material, spectral and conceptual dimensions.
A second aspect we have worked on are the foundations for observing the dynamics of molecular excitons in space and time. Excitons are formed if a molecule is optically excited by absorbing a photon. In the simplest case, this lifts an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) and leaves behind a hole in the HOMO. Since electron and hole attract each other electrically, they form a bound entity—the exciton. The precise shape and the dynamics of excitons are key to understanding important processes in optoelectronics, photochemistry and light harvesting. In our work, we have filled a gap in the investigations of excitons with POT: Recent experimental and theoretical work has concentrated on the case in which the electron and the hole are each in one state only, commonly LUMO and HOMO (as in the example above). In more complex systems, however, this simple picture breaks down, and excitons must be treated as entangled states, composed of multiple electron-hole transitions. To do justice to this, we have developed a theory that allows interpreting measured photoemission momentum maps as the Fourier-transformed coherent sum of the electronic part of the exciton wave function. This result is the sought-after extension of POT to general exciton states, establishing a universal “exciton tomography” as the basis for future investigations of exciton dynamics in Orbital Cinema. Remarkably, exciton tomography retains the intuitive orbital picture of POT, while respecting both the entangled character of the exciton wave function and the energy conservation in the photoemission process. In fact, its predictions have already been verified by experiments on C60.
A third aspect is the demonstration that time-resolved (tr) POT can also give access to fully coherent electron dynamics—a crucial aspect for Orbital Cinema. A common way to perform trPOT is the pump-probe scheme, where a first laser pulse (the pump) excites the system, while a second, delayed laser pulse (the probe) photoemits an electron from the excited system and thus probes the system’s dynamics at a fixed delay between the two pulses. In such an experiment, we have observed that the trPOT signal changes over time. For long delays, we observe the wave function of the electron excited from the HOMO collapsing into another orbital, the LUMO. At this point, the information on the initial state (the HOMO) is lost, and indeed the observed photoelectron distribution is that of the LUMO, with no traces of the wave function of the initial state left in the signal: Photoemission has proceeded via the real population of an intermediate state. Although this offers the opportunity to study properties of the intermediate state (e.g. its lifetime), it does not allow the investigation of coherent electron dynamics, because there is no uninterrupted “connection” from the electron in its initial state to the observation at the detector. However, for short delays, we observe a different momentum map: that of the initial state, the HOMO. Apparently, no collapse of the wave function has taken place on the way to the detector, and thus the photoelectron still carries the information of the initial state, which therefore becomes visible at the detector. In this case, the photoemission is driven by a coherent two-photon excitation, via a virtual intermediate state that does not induce a wave function collapse. The visualization of this coherent process in momentum space is an important result, because it is this kind of coherent dynamics, i.e. the elementary evolution of the wave function without wave function collapses, which we aim to trace in Orbital Cinema during charge transfer processes, surface chemical reactions and wave lightwave-driven packet motion.
Orbital Cinema will resolve key questions related to a wide range of applications, from next-generation optoelectronics, energy conversion, photochemistry and catalysis to prospective electronics at optical clock rates. We expect it to revolutionize our understanding of the nanocosmos by elucidating – on elementary spatio-temporal scales – the inner structure of quantum leaps, strong-field control of electrons, charge transfer processes, and chemical reactions as well as their control by electric fields and light. Since the dawn of quantum mechanics, the temporal evolution of electronic orbitals has been among the most sought-after yet elusive quantum processes. Our model-free observation of orbital motion establishes an unprecedented ultrafast wave function lab that will carry us to the very foundations of quantum science.