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Publications by
Max Möller

All publications of HI Jena


D. Würzler, S. Skruszewicz, A. M. Sayler, D. Zille, M. Möller, P. Wustelt, Y. Zhang, J. Tiggesbäumker, and G. G. Paulus
Accurate retrieval of ionization times by means of the phase-of-the-phase spectroscopy, and its limits
Physical Review A 101, 033416 (2020)

Abstract: By applying recently introduced, phase-of-the-phase spectroscopy [S. Skruszewicz et al., Phys. Rev. Lett. 115, 043001 (2015)], we analyze the phase-dependent photoelectron signal from Xe ionized in intense, parallel, two-color (1800 nm and 900 nm) laser fields. With such a field configuration, tuning of the relative phase between the ionizing, ω , and the perturbative, 2ω, field results in a modulation of the ionization rate, as well as modifications of the trajectories of electrons propagating in the laser-dressed continuum. Based on a semiclassical model, we confirm that phase dependencies, due to the perturbation of the ionization rate, encode the ionization times of the electrons. Here, using the fork structure, a well-known feature originating from well-defined dynamics allows us to distinguish between electrons ionized within distinct time windows. However, due to the simultaneous perturbation of the electron trajectories, the assignment of the ionization times can be distorted by up to 80 as, i.e., a 10° phase shift, which is independent of the degree of the perturbation.

Y. Zhang, D. Zille, D. Hoff, P. Wustelt, D. Würzler, M. Möller, A. M. Sayler, and G. Paulus
Observing the Importance of the Phase-Volume Effect for Few-Cycle Light-Matter Interactions
Physical Review Letters 124, 133202 (2020)

Abstract: The spatially dependent phase distribution of focused few-cycle pulses, i.e., the focal phase, is much more complex than the well-known Gouy phase of monochromatic beams. As the focal phase is imprinted on the carrier-envelope phase (CEP), for accurate modeling and interpretation of CEP-dependent few-cycle laser-matter interactions, both the coupled spatially dependent phase and intensity distributions must be taken into account. In this Letter, we demonstrate the significance of the focal phase effect via comparison of measurements and simulations of CEP-dependent photoelectron spectra. Moreover, we demonstrate the impact of this effect on few-cycle light-matter interactions as a function of their nonlinear intensity dependence to answer the general question: if, when, and how much should one be concerned about the focal phase?


P. Wustelt, F. Oppermann, L. Yue, M. Möller, T. Stöhlker, M. Lein, S. Gräfe, G. Paulus, and A. Sayler
Heteronuclear Limit of Strong-Field Ionization: Fragmentation of HeH⁺ by Intense Ultrashort Laser Pulses
Physical Review Letters 121, 073203 (2018)

Abstract: The laser-induced fragmentation dynamics of this most fundamental polar molecule HeH+ are measured using an ion beam of helium hydride and an isotopologue at various wavelengths and intensities. In contrast to the prevailing interpretation of strong-field fragmentation, in which stretching of the molecule results primarily from laser-induced electronic excitation, experiment and theory for nonionizing dissociation, single ionization, and double ionization both show that the direct vibrational excitation plays the decisive role here. We are able to reconstruct fragmentation pathways and determine the times at which each ionization step occurs as well as the bond length evolution before the electron removal. The dynamics of this extremely asymmetric molecule contrast the well-known symmetric systems leading to a more general picture of strong-field molecular dynamics and facilitating interpolation to systems between the two extreme cases.

D. Zille, D. Adolph, M. Möller, A. M. Sayler, and G. G. Paulus
Chirp and carrier-envelope-phase effects in the multiphoton regime: measurements and analytical modeling of strong-field ionization of sodium
New Journal of Physics 20, 063018 (2018)

Abstract: We investigate the influence of chirp on carrier-envelope-phase (CEP)-dependent strong-field few-cycle laser-induced photoelectron spectra of sodium, well within the multiphoton regime. Our measurements and analytical model of this process reveal a simple chirp-dependence, which has the potential to be utilized as an online monitor of laser chirp. Moreover, this effect could extend single-shot measurements of the CEP using above-threshold ionization to longer, chirped pulses, and significantly lower the required pulse energies. Specifically, at a wavelength of 775 nm and an intensity of 6.5 x 10^{12} W/cm^{2} the CEP- and energy-dependent left-right asymmetries of emitted electrons are measured in a time-of-flight spectrometer. In these asymmetry maps, inclined stripe-like structures emerge, where the inclination is tunable with the chirp of the pulse. We report a simple analytical model, explaining the effect as the interference of electrons with even and odd angular momenta, located at energies in between adjacent above-threshold ionization peaks. As we demonstrate, the analytical model is in good agreement with the measurement, as well as with solutions of the three-dimensional time-dependent Schrödinger equation. Further, the analytical model, which can easily be extended to other atoms, allows us to derive an equation, describing the relation between the slope of the inclined stripes and the chirp of the laser.


Y. Zhang, P. Kellner, D. Adolph, D. Zille, P. Wustelt, D. Würzler, S. Skruszewicz, M. Möller, A. M. Sayler, and G. G. Paulus
Single-shot, real-time carrier-envelope phase measurement and tagging based on stereographic above-threshold ionization at short-wave infrared wavelengths
Optics Letters 42, 5150 (2017)

Abstract: A high-precision, single-shot, and real-time carrier-envelope phase (CEP) measurement at 1.8 μm laser wavelength based on stereographic photoelectron spectroscopy is presented. A precision of the CEP measurement of 120 mrad for each and every individual laser shot for a 1 kHz pulse train with randomly varying CEP is demonstrated. Simultaneous to the CEP measurement, the pulse lengths are characterized by evaluating the spatial asymmetry of the measured above-threshold ionization (ATI) spectra of xenon and referenced to a standard pulse-duration measurement based on frequency-resolved optical gating. The validity of the CEP measurement is confirmed by implementing phase tagging for a CEP-dependent measurement of ATI in xenon with high energy resolution.

D. Würzler, N. Eicke, M. Möller, D. Seipt, A. M. Sayler, S. Fritzsche, M. Lein, and G. G. Paulus
Velocity map imaging of scattering dynamics in orthogonal two-color fields
Journal of Physics B: Atomic, Molecular and Optical Physics 51, 015001 (2017)

Abstract: In strong-field ionization processes, two-color laser fields are frequently used for controlling sub-cycle electron dynamics via the relative phase of the laser fields. Here we apply this technique to velocity map imaging spectroscopy using an unconventional orientation with the polarization of the ionizing laser field perpendicular to the detector surface and the steering field parallel to it. This geometry allows not only to image the phase-dependent photoelectron momentum distribution (PMD) of low-energy electrons that interact only weakly with the ion (direct electrons), but also to investigate the low yield of higher-energy rescattered electrons. Phase-dependent measurements of the PMD of neon and xenon demonstrate control over direct and rescattered electrons. The results are compared with semi-classical calculations in three dimensions including elastic scattering at different orders of return and with solutions of the three-dimensional time-dependent Schrödinger equation.

D. Zille, D. Seipt, M. Möller, S. Fritzsche, G. G. Paulus, and D. B. Milošević
Spin-dependent quantum theory of high-order above-threshold ionization
Physical Review A 95, 063408 (2017)

Abstract: The strong-field-approximation theory of high-order above-threshold ionization of atoms is generalized to include the electron spin. The obtained rescattering amplitude consists of a direct and exchange part. On the examples of excited He atoms as well as Li^+ and Be^2+ ions, it is shown that the interference of these two amplitudes leads to an observable difference between the photoelectron momentum distributions corresponding to different initial spin states: Pronounced minima appear for singlet states, which are absent for triplet states.

M. Wünsche, S. Fuchs, S. Aull, J. Nathanael, M. Möller, C. Rödel, and G. G. Paulus
Quasi-supercontinuum source in the extreme ultraviolet using multiple frequency combs from high-harmonic generation
Optics Express 25, 6936 (2017)

Abstract: A quasi-supercontinuum source in the extreme ultraviolet (XUV) is demonstrated using a table-top femtosecond laser and a tunable optical parametric amplifier (OPA) as a driver for high-harmonic generation (HHG). The harmonic radiation, which is usually a comb of odd multiples of the fundamental frequency, is generated by near-infrared (NIR) laser pulses from the OPA. A quasi-continuous XUV spectrum in the range of 30 to 100 eV is realized by averaging over multiple harmonic comb spectra with slightly different fundamental frequencies and thus different spectral spacing between the individual harmonics. The driving laser wavelength is swept automatically during an averaging time period. With a total photon flux of 4×10^9 photons/s in the range of 30 eV to 100 eV and 1×10^7photons/s in the range of 100 eV to 200 eV, the resulting quasi-supercontinuum XUV source is suited for applications such as XUV coherence tomography (XCT) or near-edge absorption fine structure spectroscopy (NEXAFS).

D. Adolph, M. Möller, J. Bierbach, M. Schwab, A. Sävert, M. Yeung, A. M. Sayler, M. Zepf, M. C. Kaluza, and G. G. Paulus
Real-time, single-shot, carrier-envelope-phase measurement of a multi-terawatt laser
Applied Physics Letters 110, 081105 (2017)

Abstract: We present the single-shot carrier-envelope phase (CEP) determination of a 1 Hz, multi-terawatt (TW) laser system with a setup based on spectral broadening in a hollow-core fiber and a stereographic measurement of the energy-dependent above-threshold ionization plateau. The latter is extremely sensitive to variations in CEP. As compared to the f-2f interferometers, this technique reduces the uncertainties due to the shot-to-shot intensity fluctuations, which are prevalent in the TW laser systems. The experimental results pave the way towards the investigation and control over CEP-sensitive processes at ultra-high intensities.

D. Zille, D. Seipt, M. Möller, S. Fritzsche, S. Gräfe, C. Müller, and G. G. Paulus
Spin-dependent rescattering in strong-field ionization of helium
Journal of Physics B: Atomic, Molecular and Optical Physics 50, 065001 (2017)

Abstract: We investigate the influence of singlet and triplet spin states on rescattered photoelectrons in strong-field ionization of excited helium. Choosing either a symmetric or antisymmetric spatial wave function as the initial state results in different scattering cross sections for the 1s2s¹S and ³S states. These cross sections are used in the semi-classical model of strong-field ionization. Our investigations show that the photoelectron momentum distributions of rescattered electrons exhibit a significant dependence on the relative spin state of the projectile and the bound electron which should be observable in experiments. The proposed experimental approach can be understood as a testbed for probing the spin dynamics of electrons during strong-field ionization and the presented results as a baseline for their identification.

P. Wustelt, M. Möller, M. Schöffler, X. Xie, V. Hanus, A. Sayler, A. Baltuska, G. Paulus, and M. Kitzler
Numerical investigation of the sequential-double-ionization dynamics of helium in different few-cycle-laser-field shapes
Physical Review A 95, 023411 (2017)

Abstract: We investigate sequential double ionization of helium by intense near-circularly polarized few-cycle laser pulses using a semiclassical ionization model with two independent electrons. Simulated He^2+ ion momentum distributions are compared to those obtained in recent benchmark experiments. We study the influence of a number of pulse parameters such as peak intensity, carrier-envelope phase, pulse duration, and second- and third-order spectral phase on the shape of the ion momentum distributions. Good agreement is found in the main features of these distributions and of their dependence on the laser pulse duration, peak intensity, and carrier-envelope phase. Furthermore, we find that for explaining certain fine-scale features observed in the experiments, it becomes important to consider subtle timing variations in the two-electron emissions introduced by small values of chirp. This result highlights the possibility of measuring and controlling multielectron dynamics on the attosecond time scale by fine tuning the field evolution of intense close-to-single-cycle laser pulses.

M. Möller
Probing Strong-field Photoionization of Atoms and Diatomic Molecules with Short-wave Infrared Radiation
Doctoral thesis
Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät (2017)

Abstract: The availability of pico- and femtosecond laser pulses, which can be focused to peak intensities in the range between 10^12 and 10^16 W/cm2, allows the investigation of the interaction between atoms or diatomic molecules with strong laser fields. It has revealed fascinating phenomena such as above-threshold ionization (ATI), high energy above-threshold ionization (HATI), non-sequential ionization (NSDI), high-harmonic generation (HHG) and, most recently, frustrated tunnel ionization (FTI). Today, these characteristic strong-field phenomena are the backbone of the burgeoning field of attosecond science. Derived applications presently mature to standard techniques in the field of ultrafast atomic and molecular dynamics. Examples are HHG as table-top source of coherent extreme ultraviolet radiation with attosecond duration or the application of HATI for the characterization of few-cycle laser pulses. Although experimental and theoretical considerations have shown that using longer laser wavelength is interesting for applications as well as for fundamental aspects, primary due to technological limitations, the vast majority of measurements has been performed at laser wavelengths below 1.0 μm.
In this thesis, an optic parametric amplification laser source of intense femtosecond laser pulses with short-wave infrared (SWIR) and infrared (IR) wavelength is put to operation, characterized and compressed to intense few-cycle pulses. Further, it is applied to investigate strong-field photoionization (SFI) of atoms and diatomic molecules using two different experimental techniques for momentum spectroscopy of laser-induced fragmentation processes.
For SFI of atoms, the velocity map imaging technique is used to measure three-dimensional momentum distributions from strong-field photoionization of Xenon by strong SWIR fields with different pulse duration. Besides observation of the pulse duration dependence of characteristic features, like the low-energy structures, which are particularly pronounced in the SWIR, an eye-catching off-axis low-energy feature, called the “fork”, which appears close to right angle to the polarization axis of the laser, is investigated in detail. The corresponding modeling with an improved version of the semi-classical model, demonstrates that on- and off-axis low-energy features can be traced to rescattering between the laser-driven photoelectron and the remaining ion. They can, thus, be understood on the same footing as HATI, where the electron scatters into high energy states.
SFI of diatomic molecules is investigated using an apparatus for Ion Target Recoil Ion Momentum Spectroscopy (ITRIMS). Besides measuring intensity dependent vector momentum distributions of the protons from SFI of the hydrogen molecular ion, it is shown that momentum conservation can be used to extract the correlated electron momentum from the measured data, although the electron is not detected. The capability of having experimental access to the momenta of all fragments, i.e. two protons and one electron, enables the analysis of correlated electron-nuclear momentum distributions. Together, with a one-dimensional two-level model, this sheds light on correlated electron-nuclear ionization dynamics during SFI of diatomic molecules by SWIR fields.


M. Schöffler, X. Xie, P. Wustelt, M. Möller, S. Roither, D. Kartashov, A. Sayler, A. Baltuska, G. G. Paulus, and M. Kitzler
Laser-subcycle control of sequential double-ionization dynamics of helium
Physical Review A 93, 063421 (2016)

Abstract: We present measured momentum distributions on the double ionization of helium with intense, near-circularly-polarized few-cycle laser pulses with a known carrier-envelope offset phase (CEP). The capability of obtaining CEP-resolved momentum distributions enables us to observe signatures of the various combinations of laser-half-cycle two-electron emissions. By comparison to semiclassical trajectory simulations, we succeed in assigning the corresponding structures in the measured distributions to certain two-electron emission dynamics. Based on this possibility, we demonstrate that the sequential double-ionization dynamics can be sensitively controlled with the pulse duration and the laser peak intensity. For the shortest pulse durations and not too high intensities we find that the two electrons are dominantly emitted with a delay of roughly a laser half cycle. For a just slightly increased intensity we find evidence that at least one of the two electrons is surprisingly likely emitted in between the peaks of the laser field oscillations rather than at the field maxima. The simulations reproduce the signatures of these kinds of two-electron emissions overall relatively well.


A. M. Sayler, M. Arbeiter, S. Fasold, D. Adolph, M. Möller, D. Hoff, T. Rathje, B. Fetić, D. B. Milošević, T. Fennel, and G. G. Paulus
Accurate determination of absolute carrier-envelope phase dependence using photo-ionization
Optics Letters 40, 3137 (2015)

Abstract: The carrier-envelope phase (CEP) dependence of few-cycle above-threshold ionization (ATI) of Xe is calibrated for use as a reference measurement for determining and controlling the absolute CEP in other interactions. This is achieved by referencing the CEP-dependent ATI measurements of Xe to measurements of atomic H, which are in turn referenced to ab initio calculations for atomic H. This allows for the accurate determination of the absolute CEP dependence of Xe ATI, which enables relatively easy determination of the offset between the relative CEP measured and/or controlled by typical devices and the absolute CEP in the interaction.

A. Sävert, S. P. D. Mangles, M. Schnell, E. Siminos, J. M. Cole, M. Leier, M. Reuter, M. B. Schwab, M. Möller, K. Poder, O. Jäckel, G. G. Paulus, C. Spielmann, S. Skupin, Z. Najmudin, and M. C. Kaluza
Direct Observation of the Injection Dynamics of a Laser Wakefield Accelerator Using Few-Femtosecond Shadowgraphy
Physical Review Letters 115, 055002 (2015)

Abstract: We present few-femtosecond shadowgraphic snapshots taken during the nonlinear evolution of the plasma wave in a laser wakefield accelerator with transverse synchronized few-cycle probe pulses. These snapshots can be directly associated with the electron density distribution within the plasma wave and give quantitative information about its size and shape. Our results show that self-injection of electrons into the first plasma-wave period is induced by a lengthening of the first plasma period. Three-dimensional particle-in-cell simulations support our observations.

P. Wustelt, M. Möller, T. Rathje, A. M. Sayler, T. Stöhlker, and G. G. Paulus
Momentum-resolved study of the saturation intensity in multiple ionization
Physical Review A 91, 031401 (2015)

Abstract: We present a momentum-resolved study of strong field multiple ionization of ionic targets. Using a deconvolution method we are able to reconstruct the electron momenta from the ion momentum distributions after multiple ionization up to four sequential ionization steps. This technique allows an accurate determination of the saturation intensity as well as of the electron release times during the laser pulse. The measured results are discussed in comparison to typically used models of over-the-barrier ionization and tunnel ionization.


M. Möller, F. Meyer, A. M. Sayler, G. G. Paulus, M. F. Kling, B. E. Schmidt, W. Becker, and D. B. Milošević
Off-axis low-energy structures in above-threshold ionization
Physical Review A 90, 023412 (2014)

Abstract: The velocity map of the above-threshold ionization electron spectrum at long laser wavelength exhibits a characteristic structure normal to the laser polarization, which has the appearance of a trident or a three-pronged fork. The forklike structure vanishes for few-cycle laser pulses. It is explained in terms of the classical-electron-trajectories model of strong-field ionization augmented so as to allow for rescattering. The analysis reveals its relation to the so-called low-energy structure, which was recently observed for very small transverse momenta.


M. B. Schwab, A. Sävert, O. Jäckel, J. Polz, M. Schnell, T. Rinck, L. Veisz, M. Möller, P. Hansinger, G. G. Paulus, and M. C. Kaluza
Few-cycle optical probe-pulse for investigation of relativistic laser-plasma interactions
Applied Physics Letters 103, 191118 (2013)

Abstract: The development of a few-cycle optical probe-pulse for the investigation of laser-plasma interactions driven by a Ti:sapphire, 30 Terawatt (TW) laser system is described. The probe is seeded by a fraction of the driving laser's energy and is spectrally broadened via self-phase modulation in a hollow core fiber filled with a rare gas, then temporally compressed to a few optical cycles via chirped mirrors. Shadowgrams of the laser-driven plasma wave created in relativistic electron acceleration experiments are presented with few-fs temporal resolution, which is shown to be independent of post-interaction spectral filtering of the probe-beam.


M. Möller, Y. Cheng, S. Khan, B. Zhao, K. Zhao, M. Chini, G. G. Paulus, and Z. Chang
Dependence of high-order-harmonic-generation yield on driving-laser ellipticity
Physical Review A 86, 011401 (2012)

Abstract: High-order-harmonic-generation yield is remarkably sensitive to driving laser ellipticity, which is interesting from a fundamental point of view as well as for applications. The most well-known example is the generation of isolated attosecond pulses via polarization gating. We develop an intuitive semiclassical model that makes use of the recently measured initial transverse momentum of tunneling ionization. The model is able to predict the dependence of the high-order-harmonic yield on driving laser ellipticity and is in good agreement with experimental results and predictions from a numerically solved time-dependent Schrödinger equation.

T. Rathje, N. Johnson, M. Möller, F. Süssmann, D. Adolph, M. Kübel, R. Kienberger, M. F. Kling, G. G. Paulus, and A. M. Sayler
Review of attosecond resolved measurement and control via carrier-envelope phase tagging with above-threshold ionization
Journal of Physics B 45, 074003 (2012)

Abstract: A precise, real-time, single-shot carrier–envelope phase (CEP) tagging technique for few-cycle pulses was developed and combined with cold-target recoil-ion momentum spectroscopy and velocity-map imaging to investigate and control CEP-dependent processes with attosecond resolution. The stability and precision of these new techniques have allowed for the study of intense, few-cycle, laser-matter dynamics with unprecedented detail. Moreover, the same stereo above-threshold ionization (ATI) measurement was expanded to multi-cycle pulses and allows for CEP locking and pulse-length determination. Here we review these techniques and their first applications to waveform characterization and control, non-sequential double ionization of argon, ATI of xenon and electron emission from SiO_2 nanospheres.


S. Khan, Y. Cheng, M. Möller, K. Zhao, B. Zhao, M. Chini, G. Paulus, and Z. Chang
Ellipticity dependence of 400 nm-driven high harmonic generation
Applied Physics Letters 99, 161106 (2011)

Abstract: We studied the dependence of high harmonic generation efficiency on the ellipticity of 400 nm driving laser pulses at 7.7 × 10^14 W/cm2 and compared it with the 800 nm driving laser under the same conditions. The measured decrease of high harmonic yield with the ellipticity of the 400 nm laser is ∼1.5 times slower that of the 800 nm, which agrees well with theoretical predictions based on a semi-classical model. The results indicate that it is feasible to use the generalized double optical gating with 400 nm lasers for extracting single attosecond pulses with high efficiency.

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus
Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime
Applied Physics Letters 99, 121108 (2011)

Abstract: Polarization gating is used to extend a real-time, single-shot, carrier-envelope phase (CEP) measurement, based on high-energy above-threshold ionization in xenon, to the multi-cycle regime. The single-shot CEP precisions achieved are better than 175 and 350 mrad for pulse durations up to 10 fs and 12.5 fs, respectively, while only 130 μJ of pulse energy are required. This opens the door to study and control of CEP-dependent phenomena in ultra-intense laser-matter interaction using optical parametric chirped pulse amplifier based tera- and petawatt class lasers.