Single-electron wavefunctions, or orbitals, are the mathematical constructs used to describe the multi-electron wavefunction of molecules. Because the highest-lying orbitals are responsible for chemical properties, they are of particular interest. To observe these orbitals change as bonds are formed and broken is to observe the essence of chemistry. Yet single orbitals are difficult to observe experimentally, and until now, this has been impossible on the timescale of chemical reactions. Here we demonstrate that the full three-dimensional structure of a single orbital can be imaged by a seemingly unlikely technique, using high harmonics generated from intense femtosecond laser pulses focused on aligned molecules. Applying this approach to a series of molecular alignments, we accomplish a tomographic reconstruction of the highest occupied molecular orbital of N2. The method also allows us to follow the attosecond dynamics of an electron wave packet.

Tomographic imaging of molecular orbitals

Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

High harmonic emission occurs when an electron, liberated from a molecule by an incident intense laser field, gains energy from the field and recombines with the parent molecular ion. The emission provides a snapshot of the structure and dynamics of the recombining system, encoded in the amplitudes, phases and polarization of the harmonic light. Here we show with CO2 molecules that high harmonic interferometry can retrieve this structural and dynamic information: by measuring the phases and amplitudes of the harmonic emission, we reveal ‘fingerprints’ of multiple molecular orbitals participating in the process and decode the underlying attosecond multi-electron dynamics, including the dynamics of electron rearrangement upon ionization. These findings establish high harmonic interferometry as an effective approach to resolving multi-electron dynamics with sub-Angstrom spatial resolution arising from the de Broglie wavelength of the recombining electron, and attosecond temporal resolution arising from the timescale of the recombination event. The high harmonic emission that accompanies the recombination of an electron with its parent molecular ion in an intense laser field provides a snapshot of the structure and dynamics of the recombining system. Experiments with CO2 molecules now show that high harmonic interferometry can retrieve this structural and dynamic information by measuring the phases and amplitudes of the harmonic emission. The resulting 'fingerprints' of the multiple molecular orbitals participating in the process can be used to decode the underlying attosecond multi-electron dynamics, including the dynamics of electron rearrangement upon ionization. The light emitted from the system contains images of moving electrons that can be processed into a movie. These findings establish high harmonic interferometry as an effective approach to resolving multi-electron dynamics with sub-Angstrom spatial resolution arising from the de-Broglie wavelength of the recombining electron, and attosecond temporal resolution arising from the timescale of the recombination event. The high harmonic emission that accompanies the recombination of an electron with its parent molecular ion in an intense laser field provides a snapshot of the structure and dynamics of the recombining system. Experiments on CO2 molecules now show how to extract information from the properties of the emitted light about the underlying multi-electron dynamics with sub-Angstrom spatial resolution and attosecond temporal resolution

High harmonic interferometry of multi-electron dynamics in molecules

Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. Among numerous theoretical insights and technological improvements that produced the present state-of- the-art in quantum control, there have been several breakthroughs of foremost importance. On the technology side, the current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. On the theory side, the two most critical insights were (i) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (ii) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control (AFC), which is a laboratory procedure employing measurement-driven, closed-loop optimization to identify the best shapes of femtosecond laser control pulses for steering quantum dynamics towards the desired objective. Optimization in AFC experiments is guided by a learning algorithm, with stochastic methods proving to be especially effective. AFC of quantum phenomena has found numerous applications in many areas of the physical and chemical sciences, and this paper reviews the extensive experiments. Other subjects discussed include quantum optimal control theory, quantum control landscapes, the role of theoretical control

https://iopscience.iop.org/article/10.1088/1367-2630/12/7/075008/pdf

Control of quantum phenomena: past, present and future

As companies strive to develop artefacts intended for services instead of traditional sell-off, new challenges in the product development process arise to promote continuous improvement and increasing market profits. This creates a focus on product life-cycle components as companies then make life-cycle commitments, where they are responsible for the function availability during the extent of the life-cycle, i.e. functional products. One of these life-cycle components is manufacturing; therefore, companies search for new approaches of success during manufacturability evaluation already in engineering design. Efforts have been done to support early engineering design, as this phase sets constraints and opportunities for manufacturing. These efforts have turned into design for manufacturing methods and guidelines. A further step to improve the life-cycle focus during early engineering design is to reuse results and use experience from earlier projects. However, because results and experiences created during project work are often not documented for reuse, only remembered by some people, there is a need for design support. Knowledge engineering (KE) is a methodology for creating knowledge-based systems, e.g. systems that enable reuse of earlier results and make available both explicit and tacit corporate knowledge, enabling the automated generation and evaluation of new engineering design solutions during early product development. There are a variety of KE-approaches, such as knowledge-based engineering, case-based reasoning and programming, which have been used in research to develop design for manufacturing methods and applications. There are, however, opportunities for research where several approaches and their interdependencies, to create a transparent picture of how KE can be used to support engineering design, are investigated. The aim of the research presented in this thesis is to create new methods for design for manufacturing, by using several approaches of KE, and find the beneficial and less beneficial aspects of these methods in comparison to each other and earlier research. This thesis presents methods and applications for design for manufacturing using KE. KE has been employed in several ways, namely rule-based, rule-, programmingand finite element analysis (FEA)-based, and ruleand plan-based, which are tested and compared with each other. Results show that KE can be used to generate information about manufacturing in several ways. The rule-based way is suitable for supporting life-cycle commitments, as engineering design and manufacturing can be integrated with maintenance and performance predictions during early engineering design, though limited to the firing of production rules. The rule-, programmingand FEA-based way can be used to integrate computer-aided design tools and virtual manufacturing for non-linear stress and displacement analysis. This way may also bridge the gap between engineering designers and computational experts, even though this way requires a larger effort to program than the rule-based. The ruleand planbased way can enable design for manufacturing in two fashions – based on earlier manufacturing plans and based on rules. Because earlier manufacturing plans, together with programming algorithms, can handle knowledge that may be more intricate to capture as rules, as opposed to the time demanding routine work that is often automated by means of rules, several opportunities for designing for manufacturing exist.

Methods and Applications

High-order harmonic generation (HHG) from atoms and molecules offers potential application as a coherent ultrashort radiation source in the extreme ultraviolet and soft X-ray regions1,2,3. In the three-step model4,5,6 of HHG, an electron tunnels out from the atom and may recombine with the parent ion (emitting a high-energy photon) after undergoing laser-driven motion in the continuum. Aligned molecules7,8,9,10,11 can be used to study quantum phenomena in HHG associated with molecular symmetries; in particular, simultaneous observations of both ion yields and harmonic signals under the same conditions serve to disentangle the contributions from the ionization and recombination processes. Here we report evidence for quantum interference of electron de Broglie waves12,13,14 in the recombination process of HHG from aligned CO2 molecules. The interference takes place within a single molecule and within one optical cycle. Characteristic modulation patterns of the harmonic signals measured as a function of the pump–probe delay are explained with simple formulae determined by the valence orbital of the molecules. We propose that simultaneous observations of both ion yields and harmonic signals can serve as a new route to probe the instantaneous structure of molecular systems.

Quantum interference during high-order harmonic generation from aligned molecules

We demonstrate that molecules with a moderate permanent dipole moment can be oriented with combined electrostatic and pulsed, nonresonant laser fields. We use OCS molecules as a sample. The degree of orientation can be increased by increasing the magnitude of electrostatic field and the peak intensity of the laser field or by decreasing the rotational temperature of the molecules.

Controlling the orientation of polar molecules with combined electrostatic and pulsed, nonresonant laser fields.

In this paper we describe the branching control of different ionization and fragmentation channels of coherently excited Na 2 K by means of feedback optimization of shaped femtosecond laser pulses. For this purpose the system was first excited with one photon into a pair of intersecting electronic states, from where it was ionized in a two-photonic process, so the resulting ions could size selectively be detected. By employing an evolutionary algorithm for optimizing phase and amplitude of the applied laser field, the relative signal intensities of the resulting mother and fragment ions could significantly be influenced. The peak intensities in the obtained pulse shapes correspond very well to the cross sections of the irradiated transitions; their temporal structure reflects perfectly the wavepacket dynamics of the resulting particles. Hence it was possible to extract with the self-learning algorithm – as postulated by Judson and Rabitz [Phys. Rev. Lett. 68 (1992) 1500] – intrinsic properties from the reactive system in real time.

Feedback optimization of shaped femtosecond laser pulses for controlling the wavepacket dynamics and reactivity of mixed alkaline clusters

Multiphoton ionization processes in aligned I2 molecules are actively controlled by the homemade pulse shaping system, with which a time-dependent polarization pulse can be generated and controlled. We find a correlation between a femtosecond time-dependent polarization pulse and the production efficiency of evenly or oddly charged molecular ions. We achieve much better controllability of the correlation with a time-dependent polarization pulse than with a pulse having a fixed ellipticity. The results suggest the existence of an unknown tunnel ionization mechanism which is characteristic of a time-dependent polarization pulse. Our experiments point to new directions in optimal control studies with molecular systems, as discussed in the text.

Optimal control of multiphoton ionization processes in aligned I2 molecules with time-dependent polarization pulses.

We report clear evidence of all-optical orientation of carbonyl sulfide molecules with an intense nonresonant two-color laser field in the adiabatic regime. The technique relies on the combined effects of anisotropic hyperpolarizability interaction and anisotropic polarizability interaction and does not rely on the permanent dipole interaction with an electrostatic field. It is demonstrated that the molecular orientation can be controlled simply by changing the relative phase between the two wavelength fields. The present technique brings researchers a new steering tool of gaseous molecules and will be quite useful in various fields such as electronic stereodynamics in molecules and ultrafast molecular imaging.

Shinichirou Minemoto

Papers

Quantum interference during high-order harmonic generation from aligned molecules

Controlling the orientation of polar molecules with combined electrostatic and pulsed, nonresonant laser fields.

Feedback optimization of shaped femtosecond laser pulses for controlling the wavepacket dynamics and reactivity of mixed alkaline clusters

Optimal control of multiphoton ionization processes in aligned I2 molecules with time-dependent polarization pulses.

All-Optical Molecular Orientation