Three-dimensional Momentum Distribution Research Articles

Photon energy-resolved velocity map imaging from spectral domain ghost imaging

We present an approach that combines photon spectrum correlation analysis with the reconstruction of three-dimensional momentum distribution from velocity map images in an efficient, single-step procedure. We demonstrate its efficacy with the results from the photoionization of the 2 p-shell of argon using the Free-electron LASer in Hamburg free-electron laser (FEL). Distinct spectral features due to the spin-orbit splitting of Ar are resolved, despite the large average bandwidth of the ionizing pulses from the FEL. This demonstrates a clear advantage over the conventional analysis method, and it will be broadly beneficial for velocity map imaging experiments with FEL sources. The retrieved linewidth of the binding energy spectrum approaches the resolution limitation prescribed by the spectrometers used to collect the data. Our approach presents a path to extend spectral-domain ghost imaging to the case where the photoproduct observable is high-dimensional.

Controlling Magnetic and Electric Nondipole Effects with Synthesized Two Perpendicularly Propagating Laser Fields

Nondipole effects are ubiquitous and crucial in light-matter interaction. However, they are too weak to be directly observed. In strong-field physics, motion of electrons is mainly confined in transverse plane of light fields, which suppresses the significance of nondipole effects. Here, we present a theoretical study on enhancing and controlling the nondipole effect by using the synthesized two perpendicularly propagating laser fields. We calculate the three-dimensional photoelectron momentum distributions of strong-field tunneling ionization of hydrogen atoms using the classical trajectory Monte Carlo model and show that the nondipole effects are noticeably enhanced in such laser fields due to their remarkable influences on the sub-cycle photoelectron dynamics. In particular, we reveal that the magnitudes of the magnetic and electric components of nondipole effects can be separately controlled by modulating the ellipticity and amplitude of driving laser fields. This novel scenario holds promising applications for future studies with ultrafast structured light fields.

Orbital effects on tunnel-electron momentum distributions: Ar and H[formula omitted] studied by electron–ion coincidence momentum imaging

Three-dimensional momentum distributions of tunnel-electrons produced from Ar and H2 in circularly polarized intense laser fields (1035 nm, 35 fs, 2×1014 W/cm2) have been measured by electron–ion coincidence momentum imaging. The photoelectrons recorded with a gas mixture of Ar and H2 exhibit torus-like distributions in the momentum space. Although ionization potentials are similar (15.8 eV for Ar and 15.4 eV for H2), significant differences are identified in the radius and the width of the photoelectron torus recorded in coincidence with the counterpart ions (Ar+ and H2+). The differences are confirmed by theoretical calculations based on the strong-field approximation, showing that the orbital character of ionizing electrons is encoded in the momentum distribution of tunnel electrons.

Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose-Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state.

Multichromatic Polarization-Controlled Pulse Sequences for Coherent Control of Multiphoton Ionization

In this review, we report on recent progress in the generation and application of multichromatic polarization-tailored pulse sequences for the coherent control of multiphoton ionization (MPI) dynamics and present unpublished experimental results that complement our previous findings. Specifically, we utilize single-color, bichromatic, and trichromatic polarization-controlled pulse sequences generated by spectral amplitude, phase and polarization modulation of a carrier-envelope phase (CEP)-stable white light supercontinuum for MPI. The analysis of the number of ionization pathways and the number of distinct final free electron states shows that both increase significantly, but scale differently with the number of absorbed photons and the number of pulses in the sequence. In our experiments, ultrafast polarization shaping is combined with high-resolution photoelectron tomography to generate, control, and reconstruct three-dimensional photoelectron momentum distributions from atomic and molecular MPI. We discuss the use of polarization-controlled single-color and bichromatic pulse sequences in perturbative and non-perturbative coherent control of coupled electron-nuclear dynamics in molecules, atomic spin-orbit wave packet dynamics and the directional photoemission from atoms and chiral molecules. We compare the coherent control of CEP-insensitive intraband multipath interference in the MPI with a fixed number of photons with CEP-sensitive interband multipath interference in the ionization with a different number of photons. The generation and control of free electron vortices with even-numbered rotational symmetry by MPI with single-color pulse sequences is contrasted with the bichromatic control of CEP-sensitive electron vortices with odd-numbered rotational symmetry. To illustrate the potential of multichromatic pulse sequences for coherent control, we present a trichromatic scheme for shaper-based quantum state holography.

Coherent control mechanisms in bichromatic multiphoton ionization

Free electron vortices (FEVs) generated by multiphoton ionization (MPI) with ultrashort laser pulses have attracted significant attention due to their varied symmetries and unusual topological properties. We study two physical mechanisms of coherent control in atomic MPI with bichromatic polarization-shaped femtosecond laser pulses which give rise to the rich variety of FEVs. In the experiments, we combine pulse shaping of a carrier-envelope phase-stable supercontinuum with photoelectron tomography to generate and reconstruct three-dimensional photoelectron momentum distributions (PMDs). Simultaneous measurements of energetically separated photoelectrons from intraband and interband interference in a single PMD allow us to compare phase and polarization control of the angular distributions by both mechanisms. We investigate phase control in three scenarios: first, counterrotating circularly polarized pulses are employed to contrast the phase-insensitive angular momentum eigenstate created by intraband interference via frequency mixing with the phase-sensitive c 7 rotationally symmetric FEV from pure interband interference of two single-color ionization pathways. In the second scenario, we use orthogonal linearly polarized pulses to compare the phase control properties of a six-lobed angular momentum wave packet from intraband interference to those of a complex shaped interband PMD in the presence of phase fluctuations. Finally, we demonstrate phase control of a photoelectron hologram from mixed interband interference. In a (3 + 1) resonance enhanced MPI scheme, the red pump pulse induces a bound electron wave packet probed by the time-delayed blue pulse. The latter simultaneously creates a reference wave packet by three-photon ionization to form the photoelectron hologram. Rotation of the hologram with c 1 or c 5 rotational symmetry maps the time evolution of the bound wave packet. To analyze our results, we develop analytical expressions for the wave functions of intraband and interband interference in perturbative non-resonant MPI. The experiments are complemented with two-dimensional TDSE simulations to follow the FEV formation dynamics and to validate the physical pictures.

Three-flavor collective neutrino conversions with multi-azimuthal-angle instability in an electron-capture supernova model

We investigate the multi-azimuthal angle (MAA) effect on collective neutrino oscillation by considering the three-dimensional neutrino momentum distribution in a realistic electron-capture supernova model with an $8.8 M_{\odot}$ progenitor. We find that the MAA effect induces collective flavor conversions at epochs when it is completely suppressed under the axial-symmetric approximation. This novel activity is switched on/off by the growth of the MAA instability and imprints additional time evolution in the expected neutrino event rate. We validate our results by extending the linear stability analysis into the three-flavor scheme including mixing angles, and confirm that the onset of collective neutrino oscillation matches the steep growth of flavor instability. We discuss how the MAA effect alters neutrino detection at Super-Kamiokande and DUNE.

The effective isotropy of the hydrogen local potential in biphenyl and other hydrocarbons.

We present an experimental investigation of the hydrogen nuclear momentum distribution in biphenyl using deep inelastic neutron scattering. Our experimental results suggest that the local potential affecting hydrogen is both harmonic and isotropic within experimental uncertainties. This feature is interpreted as a consequence of the central limit theorem, whereby the three-dimensional momentum distribution is expected to become a purely Gaussian function as the number of independent vibrational modes in a system increases. We also performed ab initio phonon calculations on biphenyl and other saturated hydrocarbons, from methane to decane. From the results of the simulations, one can observe that the nuclear momentum distribution becomes more isotropic as the number of atoms and normal modes in the molecule increases. Moreover, the predicted theoretical anisotropy in biphenyl is clearly larger than in the experiment. The reason is that the total number of normal modes necessary to reproduce the experimental results is much larger than the number of normal modes encompassed by a single unit cell due to the presence of structural disorder and intermolecular interactions in the real crystal, as well as coupling of different normal modes. Finally, experimental data were collected, over a subset of detectors on the VESUVIO spectrometer at ISIS, with a novel setup to increase the count rate and signal-to-background ratio. We envision that such an optimized experimental setup can provide faster measurements and more stringent constraints for phonon calculations.

Probing time delay of strong-field resonant above-threshold ionization* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11574101, 11674116, 11774111, and 11934006), the Open Fund of Hubei Provincial Key Laboratory of Optical Information and Pattern Recognition (Grant No. 201902), and the International Cooperation Program of Hubei Innovation Fund (Grant No. 2019AHB052).

The high-resolution three-dimensional photoelectron momentum distributions via above-threshold ionization (ATI) of Xe atoms are measured in an intense near circularly polarized laser field using velocity map imaging and tomography reconstruction. Compared to the linearly polarized laser field, the employed near circularly polarized laser field imposes a more strict selection rule for the transition via resonant excitation, and therefore we can selectively enhance the resonant ATI through certain atomic Rydberg states. Our results show the self-reference ionization delay, which is determined from the difference between the measured streaking angles for nonadiabatic ATI via the 4f and 5f Rydberg states, is 45.6 as. Our method provides an accessible route to highlight the role of resonant transition between selected states, which will pave the way for fully understanding the ionization dynamics toward manipulating electron motion as well as reaction in an ultrafast time scale.

Coulomb focusing in retrapped ionization with near-circularly polarized laser field.

The full three-dimensional photoelectron momentum distributions of argon are measured in intense near-circularly polarized laser fields. We observed that the transverse momentum distribution of ejected electrons by 410-nm near-circularly polarized field is unexpectedly narrowed with increasing laser intensity, which is contrary to the conventional rules predicted by adiabatic theory. By analyzing the momentum-resolved angular momentum distribution measured experimentally and the corresponding trajectories of ejected electrons semiclassically, the narrowing can be attributed to a temporary trapping and thereby focusing of a photoelectron by the atomic potential in a quasibound state. With the near-circularly polarized laser field, the strong Coulomb interaction with the rescattering electrons is avoided, thus the Coulomb focusing in the retrapped process is highlighted. We believe that these findings will facilitate understanding and steering electron dynamics in the Coulomb coupled system.

Time-resolved 3D imaging of ultrafast spin–orbit wave packet dynamics

We combine bichromatic polarization pulse shaping with photoelectron imaging tomography for time-resolved spatial imaging of ultrafast spin–orbit wave packet (SOWP) dynamics in atoms. Polarization-shaped two-color pump-probe sequences are generated by spectral amplitude and phase modulation of a femtosecond input pulse and used to excite SOWPs in the potassium fine-structure doublet. By selecting different spectral bands for pump and probe pulse, we achieve interference-free detection of the spatiotemporal SOWP dynamics. Using tomographic techniques, we reconstruct the three-dimensional photoelectron momentum distribution (3D-ED) created by the probe pulse. Time-resolved measurement of the 3D-ED reveals the orbital realignment dynamics induced by spin–orbit interaction in the neutral atom.

Probing time delays and coherent imaging of multiphoton resonant ionization

We measure the laser-intensity-dependent photoelectron momentum and energy spectra and identify the emerged resonant $(4s,3d$, and $4f)$ states of multiphoton ionization of Ne at 400 nm. We employ parallelly polarized two-color fields involving a strong ionizing 400-nm field and a weak 800-nm field to probe the relative time delay of resonant states. By analyzing phase-resolved three-dimensional photoelectron momentum distributions, we find the time delay of resonant states has an anisotropic angle dependence. Using an intuitive model, we show that the angle-dependent time delay carries the information of subcycle evolution of quantum states and reflects the temporal coherent properties of multiphoton resonant states during absorption and emission of photons. We find that the relative time delays among the resonant ionization via $4s,3d$, and $4f$ states along the polarization depend on the number of photons absorbed. This study has implications for coherent imaging of electron wave packets in the multiphoton ionization regime.

Interplay between Coulomb-focusing and non-dipole effects in strong-field ionization with elliptical polarization

We study strong-field ionization and rescattering beyond the long-wavelength limit of the dipole approximation with elliptically polarized mid-IR laser pulses. Full three-dimensional photoelectron momentum distributions (PMDs) measured with velocity map imaging and tomographic reconstruction revealed an unexpected sharp ridge structure in the polarization plane (2018 Phys. Rev. A 97 013404). This thin line-shaped ridge structure for low-energy photoelectrons is correlated with the ellipticity-dependent asymmetry of the PMD along the beam propagation direction. The peak of the projection of the PMD onto the beam propagation axis is shifted from negative to positive values when the sharp ridge fades away with increasing ellipticity. With classical trajectory Monte Carlo simulations and analytical analysis, we study the underlying physics of this feature. The underlying physics is based on the interplay between the lateral drift of the ionized electron, the laser magnetic field induced drift in the laser propagation direction, and Coulomb focusing. To apply our observations to emerging techniques relying on strong-field ionization processes, including time-resolved holography and molecular imaging, we present a detailed classical trajectory-based analysis of our observations. The analysis leads to the explanation of the fine structure of the ridge and its non-dipole behavior upon rescattering while introducing restrictions on the ellipticity. These restrictions as well as the ionization and recollision phases provide additional observables to gain information on the timing of the ionization and recollision process and non-dipole properties of the ionization process.

Probing the ionization wave packet and recollision dynamics with an elliptically polarized strong laser field in the nondipole regime

We explore ionization and rescattering in strong mid-infrared laser fields in the nondipole regime over the full range of polarization ellipticity. In three-dimensional photoelectron momentum distributions (3D PMDs) measured with velocity map imaging spectroscopy, we observe the appearance of a sharp ridge structure along the major polarization axis. Within a certain range of ellipticity, the electrons in this ridge are clearly separated from the two lobes that commonly appear in the PMD with elliptically polarized laser fields. In contrast to the well-known lobes of direct electrons, the sharp ridge is created by Coulomb focusing of the softly recolliding electrons. These ridge electrons are directly related to a counterintuitive shift of the PMD peak opposite to the laser beam propagation direction when the dipole approximation breaks down. The ellipticity-dependent 3D PMDs give access to different ionization and recollision dynamics with appropriate filters in the momentum space. For example, we can extract information about the spread of the initial wave packet and the Coulomb momentum transfer of the rescattering electrons.

Control of photoelectron momentum distributions by bichromatic polarization-shaped laser fields

Bichromatic polarization-shaped femtosecond laser pulses are used to control three-dimensional photoelectron momentum distributions (3D-EDs) from resonance enhanced multi-photon ionization of potassium atoms. The light fields consisting of two spectral bands with different ellipticity are produced using an ultrafast polarization pulse shaper equipped with a custom polarizer in the Fourier plane. The tomographically reconstructed 3D-EDs from ionization with counterrotating circularly or orthogonal linearly polarized bichromatic laser pulses show different angular momentum superposition states at four distinct photoelectron energies. The analysis of the measured 3D-EDs reveals that the underlying physical mechanism is based on the interplay of ionization pathway selection via quantum mechanical selection rules for optical transitions and intrapulse frequency mixing of the spectral bands with different ellipticity.

Full jet evolution in quark–gluon plasma and nuclear modification of jet structure in Pb+Pb collisions at 2.76A TeV

We study the evolution of full jet shower in quark-gluon plasma via solving a set of coupled differential transport equations for the three-dimensional momentum distributions of quarks and gluons contained in the full jets. The evolution equations include all partonic splitting processes as well as the collisional energy loss and transverse momentum broadening for both the leading and radiated partons of the full jets. Combining with realistic hydrodynamic simulation for the space-time evolution of the fireball created in Pb+Pb collisions at 2.76A TeV, we calculate the nuclear modification of single inclusive full jet spectra, the momentum imbalance of photon-jet and dijet pairs, and jet shape function (at partonic level). The roles of various jet-medium interaction mechanisms on the modification of full jet energy and internal structure are studied.

Full jet evolution in quark-gluon plasma and nuclear modification of jet production and jet shape inPb+Pbcollisions at2.76ATeVat the CERN Large Hadron Collider

We study the evolution of full jet shower in quark-gluon plasma via solving a set of coupled differential transport equations for the three-dimensional momentum distributions of quarks and gluons contained in the full jets. In our jet evolution equations, we include all partonic splitting processes as well as the collisional energy loss and transverse momentum broadening for both the leading and radiated partons of the full jets. Combining with a realistic (2+1)-dimensional viscous hydrodynamic simulation for the space-time profiles of the hot and dense nuclear medium produced in heavy-ion collisions, we apply our formalism to calculate the nuclear modification of single inclusive full jet spectra, the momentum imbalance of photon-jet and dijet pairs, and jet shape function (at partonic level) in Pb+Pb collisions at 2.76 ATeV. The roles of various jet-medium interaction mechanisms on the full jet modification are studied. We find that the nuclear modification of jet shape is sensitive to the interplay of different interaction mechanisms as well as the energies of the full jets.

The gamma-ray spectra of 5-carbon alkane isomers in the positron annihilation process

The gamma-ray spectra of pentane (C5H12) and its two isomers, i.e., 2-Methylbutane (CH3C(CH3)HC2H5) and 2,2-Dimethylpropane (C(CH3)4) have been studied theoretically in the present work. The recent experimental gamma-ray spectra of these three molecules show that they have the same Doppler shifts, although their molecular structures are dramatically different. In order to reveal why the gamma-ray spectra of these molecules are less sensitive to the molecular structures, the one-dimensional gamma-ray spectra and spherically averaged momentum (SAM) distributions, the two-dimensional angular correlation of annihilation radiation (ACAR), and the three-dimensional momentum distributions of the positron–electron pair are studied. The one-centered momentum distributions of the electrons are found to play more important role than the multi-centered coordinate distributions. The present theoretical predictions have confirmed the experimental findings for the first time. The dominance of the inner valence electrons in the positron–electron annihilation process has also been suggested in the present work.

Channel-resolved subcycle interferences of electron wave packets emitted from in two-color laser fields

We report on the observation of subcycle interferences of electron wave packets released during strong field ionization of $\text{H}_{2}$ with cycle-shaped two-color laser fields. With a reaction microscope we measure three-dimensional momentum distributions of photoelectrons correlated with either $\text{H}_{2}^{+}$ or protons within different energy ranges generated by dissociation of $\text{H}_{2}^{+}$ . We refer to these different types of photoelectrons as channels. Our results show that the subcycle interference structures of electron wave packets are very sensitive to the cycle shape of the two-color laser field. We explain this behavior by the dependence of the ionization time within an optical cycle on the shape of the laser field cycle. The subcycle interference structures can be further used to obtain insight into the subcycle dynamics of molecules during strong field interaction.

Control of strong-field ionization with two-color laser pulses

SynopsisExperimental results and theoretical analysis of the ionization process of argon atoms interacting with linearly polarized two-color fields (λ1 = 800 nm, λ2 = 400 nm) are presented. We observe complex asymmetry patterns in the measured three-dimensional momentum distributions.