Coherent control of strongly driven quantum dynamics using FERMI shaped pulses

The interaction of light with matter provides indispensable insight into the quantum mechanical world of atoms and molecules on their intrinsic time and length scale. Compared to the macroscopic world, these scales are extreme: about 10 fs for the motion of the nuclei, about 10 as for the motion of the electrons; 0.2 nm is the typical length of a chemical bond. A major objective in science is the control of the nanoscopic processes on their extreme scales, which remains a challenge. Based on the concepts of quantum mechanics, specially tailored light fields can be used to address this problem. Here, the electromagnetic wave-character of light is exploited. By shaping the amplitude, phase and polarization of the electromagnetic waves, fields can be sculpted that enhance certain quantum processes while suppressing others, resulting in a net control of the system. The prerequisite is the ability to shape the electromagnetic field of ultrashort laser pulses with durations of just a few femtoseconds. Such pulses enabled scientists for the first time to trigger and control the atomic and molecular processes on their natural time scale.

In the visible range of the spectrum the spectro-temporal shaping of ultrashort laser pulses is a mature technique. Potential applications can be found in physics, chemistry and material science, for instance in the control of chemical reactions, efficient qubit manipulation, the exploration of complex reaction pathways, and the emergence of new spectroscopy concepts. To date, corresponding concepts in the extreme ultraviolet (XUV) and X-ray regime are hardly explored. The short-wavelength domain provides a perspective to access shorter time and length scales. Extremely short laser pulses with attosecond duration are available in this range, and highly localized inner-shell electrons can be addressed at these photon energies. Thus, extending spectro-temporal pulse shaping to the short-wavelength regime promises the quantum control of matter on unprecedented short time scales and with chemical sensitivity.

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Image: photoelectron spectrum showing the split-up of the energy level in helium and the control of the relative population by shaping the phase of the XUV pulses. Adapted from the original paper, licensed under a Creative Commons Attribution 4.0 International License

Polarization shaping of ultrashort extreme-ultraviolet light pulses

Conventional lasers produce light with a well-defined, time-independent polarization. Two common examples are linear polarization, where the electric field oscillates in a certain direction in the plane perpendicular to the direction of light propagation, and circular polarization, where the electric field rotates clockwise (right circular) or counter-clockwise (left circular) about the propagation direction. Recently, however, the generation of pulsed laser light whose polarization is varying on a femtosecond timescale, has attracted significant attention. Such polarization-shaped pulses have been used in a number of applications ranging from manipulation of electron wave packets to improving the sensitivity of advanced spectroscopic techniques.

In the visible, a time-dependent polarization is accomplished using a pulse shaper. On the other hand, lack of efficient optical elements and greater difficulties in controlling the propagation of light at short wavelengths significantly restrain pulse shaping in the extreme ultraviolet (XUV) and x-ray spectral regions. We show here that the externally seeded free-electron laser (FEL) FERMI provides a solution to the problem of tailoring the polarization profile of short and intense XUV pulses.

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Image: Figure 1 (c & d – click link above to view full figure): The scheme for generating an XUV FEL pulse with time-dependent polarization by combining two counter-rotating FEL sub-pulses. (b) Schematic output of the setup shown in (a) for a separation between the sub-pulse envelopes equal to their FWHM durations (60 fs) and a relative phase (set by PS before R2 in (a)) equal to π/4. Top: components of the total electric field and total intensity. The FEL wavelength is exaggerated to visualize oscillations of the fields. Bottom: temporal profiles of the intensity-normalized Stokes parameters. (c) VMI images obtained from photoionization of helium atoms for a zero delay between the sub-pulse envelopes as a function of the relative phase: the polarization varies from almost pure horizontal (phase = 0, left), to diagonal (phase = π /2, middle), to almost pure vertical (phase = π, right). (d) Intensity-normalized, time-integrated Stokes parameter S1 as a function of the relative phase for zero (left) and 30 fs (right) delay between the sub-pulse envelopes.