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Simulations for x-ray imaging of wave-packet dynamics
Previous work on imaging wave-packet dynamics with x-ray scattering revealed that the scattering patterns deviate substantially from the notion of instantaneous momentum density of the wave packet. Here we show that scattering patterns can provide clear insights into the electron wave-packet dynamics if the final state of the scattered electron and the scattered photon momentum are determined simultaneously. The scattering probability is shown to be proportional to the modulus square of the Fourier transform of the instantaneous electronic spatial wave function weighted by the final state of the electron. Several cases for the choice of final state of the electron are explored. First, the case where the final state can be measured up to a given principal quantum number n and orbital angular momentum l are presented. Next, the case where the final states can only be determined up to a given energy is discussed. Lastly, the case of an initial wave packet consisting of a large amount of a known stationary state and a small amount of an unknown stationary state is examined. The scattering profile is used to determine the properties of the unknown state in the wave packet.
Radiation by a laser-driven flying-focus electron wave packet
An exact solution of the Dirac equation in the presence of an arbitrary electromagnetic plane wave is found, which corresponds to a focused electron wave packet, with the focus of the wave packet moving at the speed of light in the opposite direction of the average momentum of the electron wave packet (unless the plane wave is so intense to reflect the electron). The photon spectrum emitted by such an electron wave packet in the presence of a linearly polarized plane wave is studied both analytically and numerically. The spectrum is also compared with the one emitted by a single-momentum, plane-wave electron in the case of the electron being initially counterpropagating (on average for the flying-focus case) with the plane wave and within the locally constant field approximation. It is found that if the electron flying-focus wave packet is focused beyond a Compton wavelength, the angular distribution of the emitted radiation along the magnetic field of the electromagnetic plane wave is broader than for an electron with definite momentum. Corresponding the maximum value of the photon yield on the transverse plane is smaller in the flying-focus electron case. This could represent an experimental signature of a laser-driven flying-focus electron wave packet.
Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer
Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the Z 2 and U(1) lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the Z 2 lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.
Wave packet dynamics and control in excited states of molecular nitrogen
Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N 2 . Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ~ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.
Direct observation of entangled electronic-nuclear wave packets
We present momentum resolved covariance measurements of entangled electronic-nuclear wave packets created and probed with octave spanning phaselocked ultrafast pulses. We launch vibrational wave packets on multiple electronic states via multiphoton absorption, and probe these wave packets via strong field double ionization using a second phaselocked pulse. Momentum resolved covariance mapping of the fragment ions highlights the nuclear motion, while measurements of the yield as a function of the relative phase between pump and probe pulses highlight the electronic coherence. The combined measurements allow us to directly visualize the entanglement between the electronic and nuclear degrees of freedom and follow the evolution of the complete wavefunction. Published by the American Physical Society 2024
Parametric Instability of Alfvén Waves and Wave Packets in Periodic and Open Systems
The parametric decay instability of Alfvén waves has been widely studied, but few investigations have examined wave packets of finite size and the effect of different boundary conditions on the growth rate. In this paper, we perform a linear analysis of circular and arc-polarized wave trains and wave packets in periodic and open boundary systems in a low- β plasma. We find that both types of wave are 3–5 times more stable in open boundary conditions compared to periodic. Additionally, once the wave packet width ℓ becomes smaller than the system size L , the growth rate decreases nearly with a power law γ ∝ ℓ / L . This study demonstrates that the stability of a pump wave cannot be separated from the laboratory settings, and that the growth rate of daughter waves depends on the conditions downstream and upstream of the pump wave and on the fraction of volume it fills. Our results can explain simulations and experiments of localized Alfvén waves. They also suggest that Alfvénic fluctuations in the solar wind, including sharp impulses known as switchbacks, can be more stable than traditional theory suggests depending on wind conditions.
Nondispersing Wave Packets in Lattice Floquet Systems
We show that in a one-dimensional translationally invariant tight binding chain, nondispersing wave packets can in general be realized as Floquet eigenstates—or linear combinations thereof—using a spatially inhomogeneous drive, which can be as simple as modulation on a single site. The recurrence time of these wave packets (their “round-trip” time) locks in at rational ratios sT/r of the driving period T, where s, r are coprime integers. Wave packets of different s / r can coexist under the same drive, yet travel at different speeds. They retain their spatial compactness either infinitely (s/r = 1) or over a long time (s/r ≠ 1). Discrete time translation symmetry is manifestly broken for s ≠ 1, reminiscent of integer and fractional Floquet time crystals. We further demonstrate how to reverse engineer a drive protocol to reproduce a target Floquet micromotion, such as the free propagation of a wave packet, as if coming from a strictly linear energy spectrum. The variety of control schemes open up a new avenue for Floquet engineering in quantum information sciences.
Parametric Decay of Alfvénic Wave Packets in Nonperiodic Low-beta Plasmas
The parametric decay of finite-size Alfvén waves in nonperiodic low-beta plasmas is investigated using one-dimensional (1D) hybrid simulations. Compared with the usual small periodic system, a wave packet in a large system under the absorption boundary condition shows different decay dynamics, including reduced energy transfer, localized density cavitation, and ion heating. The resulting Alfvén wave dynamics are influenced by several factors relating to this instability, including the growth rate, central wave frequency, and unstable bandwidth. A final steady state of the wave packet may be achieved when the instability does not have enough time to develop within the residual packet, and the packet size shows well-defined scaling dependencies on the growth rate, wave amplitude, and plasma beta. Under the proper conditions, enhanced secondary decay can also be excited in the form of a narrow, amplified wave packet. These results may help to interpret laboratory and spacecraft observations of Alfvén waves, and to refine our understanding of the associated energy transport and ion heating.
Simultaneous Observation of Ion-scale Wave Packets with Opposite Polarizations and Their Implications on the Generation Region in the Inner Heliosphere
This paper reports a dispersion analysis of two wave packets simultaneously observed near the local proton gyrofrequency by the Parker Solar Probe. The observed wave event exhibits clear two-banded wave packets both propagating along the magnetic field, characterized by left-handed (L-mode) and right-handed (R-mode) polarizations simultaneously. By incorporating the Doppler shift effect into a linear dispersion analysis, we find two possible scenarios that explain these simultaneous opposite polarizations: (1) Two inherently L-mode waves in the plasma frame, propagate parallel and antiparallel to the solar wind velocity, with similar wave frequencies and wave numbers. The polarization of the antiparallel propagating wave reverses as it moves sunward in the plasma frame while still comoving with the solar wind in the stationary frame. This reversal manifests the polarization of the wave as an R-mode in the spacecraft frame. (2) Simultaneous L-mode and R-mode waves propagate parallel to the solar wind velocity, with different wave frequencies and wave numbers. Concurrent proton observations during the wave event reveal a dominant anisotropic ($T$⟂/$T$ ∥ > 1) core distribution with a drifting beam population. Estimation of the linear growth rate for both L-mode and R-mode waves suggests that both scenarios are plausible, indicating that the observation is near the wave-generation region. We explore the potential impact of these simultaneous waves on solar wind heating and scattering effects, hypothesizing that such waves might enhance efficiency compared to waves with a single wave packet, contingent upon the statistical significance of such waves.
Enhancing high-order harmonic generation by controlling the diffusion of the electron wave packet
We experimentally study the enhancement of high-order harmonic generation (HHG) driven by synthesized ω <#comment/> − <#comment/> 3 ω <#comment/> laser fields, where we control whether the ionization rate or the electron wave packet’s diffusion is the dominant enhancement mechanism. When minimizing the electron wave packet’s diffusion, the excursion times of the corresponding electron trajectories are reduced by a factor of 2 or more. This result is important for imaging techniques that use the returning electron wave packet to probe the remaining ion. Furthermore, we achieve a 10 × <#comment/> to 3800 × <#comment/> enhancement of the harmonic yield driven by the bichromatic fields relative to that of an optimized single-color field, showing that the bichromatic fields improve HHG’s capability as a light source. We also measure that the two-color field’s harmonics have half the divergence angle compared to their single-color counterpart, suggesting that the “short” electron trajectories play a more prominent role compared to their “long” trajectory counterparts, thus improving the wavefront of the emerging harmonic beam.
Nanometer-Scale Acoustic Wave Packets Generated by Stochastic Core-Level Photoionization Events
We demonstrate that the absorption of femtosecond hard x-ray pulses excites quasispherical, high-amplitude, and high-wave-vector coherent acoustic phonon wave packets using an all hard-x-ray pump-probe scattering experiment. The time- and momentum-resolved diffuse scattering signal is consistent with an ensemble of 3D strain wave packets induced by the rapid electron cascade dynamics following photoionization at uncorrelated excitation centers. We quantify key parameters of this process, including the localization size of the stress field and the photon energy conversion efficiency into elastic energy. The parameters are determined by the photoelectron and Auger electron cascade dynamics, as well as the electron-phonon interaction. In particular, we obtain the localization size of the observed strain wave packet to be 1.5 and 2.5 nm for bulk SrTiO 3 and KTaO 3 single crystals, respectively. The results provide crucial information on the mechanism of x-ray energy deposition into matter and shed light on the shortest collective length scales accessible to coherent acoustic phonon generation using x-ray excitation. Published by the American Physical Society 2024
Wave-packet manipulation of He Rydberg states by a seeded free-electron laser
We report a two-dimensional pump-control-probe spectroscopic study of the dynamics of singly excited He Rydberg-state wave packets with a seeded extreme ultraviolet (XUV) free-electron laser (FEL) source. A pair of coherent XUV pulses, defined by their coarse time separation and relative phase, created and manipulated the wave packets. The He atoms were postionized by infrared (IR) pulses, and the ion yield was measured as a function of XUV phase and IR arrival time. We tagged and sorted the relative phase of the XUV pulse pair on a single-shot basis by fitting each FEL spectrum with a suitable function that accounts for nonidealities of the XUV pulse pairs, associated with the seeding process; more generally, the fit returns the time-dependent electric field of the FEL spectra. The experimental two-dimensional maps of ion yields, measured as a function of IR (probe) delay and of XUV (pump-control) phase, were compared with the solution of the first-order time-dependent Schrödinger equation for this field. Despite the fact that the experimental conditions imply strong excitation, beyond the approximations of first-order perturbation theory, the simulated map satisfactorily reproduces the experimental one for temporally well-separated pulses. We show that by selecting data at appropriate values of pump-control phase, we enhance or suppress the amplitude of chosen wave-packet components consisting of two or more Rydberg states. When the temporal overlap of the pulse pair cannot be neglected, the phase reconstruction is underdetermined, and we provide a simplified comparison between data and simulations. Published by the American Physical Society 2024
Simultaneous imaging of vibrational, rotational, and electronic wave-packet dynamics in a triatomic molecule
Light-induced molecular dynamics often involve the excitation of several electronic, vibrational, and rotational states. Since the ensuing electronic and nuclear motion determines the pathways and outcomes of photoinduced reactions, our ability to monitor and understand these dynamics is crucial for molecular physics, physical chemistry, and photobiology. However, characterizing this complex motion represents a significant challenge when different degrees of freedom are strongly coupled. In this Letter, we demonstrate how the interplay between vibrational, rotational, and electronic degrees of freedom governs the evolution of molecular wave packets in the low-lying states of strong-field-ionized sulfur dioxide. Using time-resolved Coulomb explosion imaging (CEI) and quantum mechanical wave packet simulations, we directly map the bending vibrations of the molecule, show how the vibrational wave packet is influenced by molecular alignment, and elucidate the consequences of nuclear motion for the coupling between the two lowest electronic states of the cation. Furthermore, our results demonstrate that multicoincident CEI can be an efficient experimental tool for characterizing coupled electronic and nuclear motion in polyatomic molecules.
Excitonic wave-packet evolution in a two-orbital Hubbard model chain: A real-time real-space study
Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space real-time evolution of an excitonic wave packet using a two-orbital Hubbard model in a chain. The exciton is created by exciting an electron from a lower-energy half-filled orbital to a higher-energy empty orbital. Here we carry out the real-time dynamics of the resulting excitonic wave packet using the time-dependent density matrix renormalization group. We find clear evidence of charge-spin and spin-orbit separation in real space, by tracking the time evolution of local observables. We show that the velocity of the orbiton can be tuned varying the interorbital interactions. We also present a comparative study of the dynamics of a hole in one-orbital and two-orbital Hubbard models. Moreover, we analyze the dynamics of an exciton with spin-flip excitation, where we observe fractionalized spinons induced by Hund's interaction.
An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter
Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool with which to study dynamical processes in warm dense matter beyond the Born–Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigated three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examined each of these approximations in regard to atomic and molecular hydrogen in addition to a dense hydrogen plasma. We found that the biggest improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match experimental pressures of dense hydrogen. Ultimately, we found that semi-empirical scaling parameters are necessary to correct for the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.
Interference Control of Fano Resonances and Dynamical Imaging of an Electron Wave Packet
The Fano line shape, arising from the interference of pathways for the excitation of discrete and continuum states, plays a fundamental role in many branches of physics, chemistry, and materials science. Exciting the resonance with a high harmonic provides naturally a phase delay between the pathways leading to a complex asymmetry parameter. We demonstrate that its amplitude and phase can be controlled on the femtosecond and attosecond time scales, respectively. With our high-energy-resolution (10-meV) experiment, we dynamically image a resonance-enhanced electron wave packet during its temporal evolution, extracting both the amplitude and the phase. Calculations reproduce our experimental results. Our approach constitutes a method for measuring the photoionization delays of a resonance and enables the reconstruction of the electron wave packet in the time domain. This concept of an interference-controlled Fano line shape is a step toward attosecond quantum optics with potential ramifications into nanoscience and next-generation optical materials.
Imaging ring-current wave packets in the helium atom
We study the reconstruction of a wave packet and the corresponding electron dynamics in an atom via photoelectron angular distributions (PADs) in a pump-probe scheme as a function of time delay. The method is applied to the superposition of ground and one or two excited states in helium atom representing field-free charge migrations on the attosecond timescale in form of ring currents around the core. It is based on the interference between one- and two-photon transitions from ground and excited states into the continuum. In the reconstruction predictions of first- and second-order perturbation theory are used to determine the unknown phases and amplitudes from the PADs, which we simulate via solutions of the time-dependent Schrödinger equation in single-active-electron approximation. Results of calculations show that the reconstruction technique works well for peak laser intensities less than 10 13 W/cm 2 . Knowledge of the electric field of the probe pulse is required with shot-to-shot variations of carrier-to-envelope phase and peak intensity of up to 10% and 20%, respectively. The relevance of different one- and two-photon pathways for the reconstruction as a function of peak intensity and pulse duration is analyzed—specifically their role for ultrashort probe pulses with broad bandwidths.