The complete second-order hyperfine-interaction correction is calculated for centroid energy levels of H, D, and ${}^3\mathrm{He}$ atoms. For ${}^3\mathrm{He}$, the corrections of $-2.075\mathrm{kHz}$ and $-0.305\mathrm{kHz}$ beyond the leading hyperfine-mixing contribution are obtained for the $2{}^{1}S$ and $2{}^{3}S$ states, respectively. These results shift the nuclear charge radii difference derived from the ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ isotope shift and largely resolve the previously reported disagreement between the muonic and electronic helium determinations [van der Werf et al., arXiv:2306.02333; Schuhmann et al., arXiv:2305.11679].

This paper and planned subsequent ones have two broad aims. First, we construct a theory for multipartite open quantum systems comprising several layers of structure with self-consistent backactions. We develop the graded influence action formalism [Behunin and Hu, Phys. Rev. A 82, 022507 (2010); Phys. Rev. A 84, 012902 (2011)] to account for the influences of successive sublayers on the dynamics of the variables of interest. Second, we apply these methods to the study of atom-field-medium interactions and highlight their merits over conventional methods. We consider a system of $N$ harmonic oscillators, modeling the internal degrees of freedom (IDFs) of $N$ neutral atoms (A), interacting with a quantum field (F), scalar here, for simplicity, altered by the presence of a dielectric medium (M). In this paper we use the coarse-grained and stochastic effective actions in the influence functional formalism to derive the stochastic equations for the reduced density matrices of the dynamical variables in the successive layers of structure. The term “graded” refers to the specific ordering of the coarse-graining procedures. Three layers of coarse graining are performed. First, integrating over the common bath of the dielectric oscillators results not only in the appearance of necessary dissipative properties of the dielectric but also in essential nuanced features such as non-Markovian spatial correlations in the dielectric. Second, integrating over the medium variables as a whole results in a dielectric-modified quantum field, the influence of the medium on the quantum field manifesting through a frequency-dependent permittivity function. Finally, integrating over this dielectric-altered quantum field which interacts with the IDFs of the atoms allows us to derive an equation of motion which describes the nonequilibrium stochastic dynamics of the IDFs of the atoms interacting with a dielectric medium-modified quantum field. In the future we plan to calculate the nonequilibrium covariant matrix elements of the correlation functions of the IDFS of $N$ atoms in a dielectric-altered quantum field, which are useful for probing many basic quantum information issues, such as the entanglement dynamics in AFM interactions.

We report on the potential of coherent Rabi-type dynamics and the formation of the Autler-Townes (AT) doublet to dramatically transform the patterns emerging in the photoelectron momentum distribution (PMD) produced in resonant two-photon ionization of the hydrogen atom by means of ab initio time-dependent Schrödinger equation calculations. When this nonlinear process is driven by a single circularly polarized (CP) laser pulse with a duration longer than the Rabi period, the AT doublet is shown to modulate the circular symmetric pattern in the PMD and yield two concentric bands. When a second CP laser pulse with opposite helicity acts in a synchronous way, the twofold quadrupolar pattern in the PMD sunders to yield two parts (slow and fast electrons), with each inheriting the ${\mathrm{C}}_2$ rotational symmetry. When the two pulses are gradually separated in time, the twofold quadrupolar asunder patterns reported for zero time delay then rotate to produce parted spirals, whose direct visualization in the PMD may be impeded by the significant intensity of the AT minimum as revealed by the azimuthal angle-integrated energy distribution as well as by distortions from detuning the laser frequency. As the superposition of two quantum states is the basis of charge migration activities in matter, these spirals-asunder, persisting among a range of pulse parameters, provide an avenue for revealing charge migration in complex systems.

We develop a realistic one-dimensional (1D) model for describing the direct (nonsequential) two-photon double ionization of an atomic system. The model is used to calculate (generalized) total cross sections for both helium and for the two-electron heliumlike ions ${\mathrm{Li}}^{+}$ and the hydrogen anion ${\mathrm{H}}^{-}$ in their respective regimes for nonsequential double ionization. A comparison with available ab initio data from the literature reveals that the agreement is at a quantitative level, merely demonstrating the usefulness of simple 1D models for describing complex ionization behavior. This framework provides alternative ways to handle various correlated multiple ionization processes in complex matter that cannot be accessed with exact methods.

Ghost imaging (GI) is an unconventional technique that combines information from two correlated patterned light fields to compute an image of the object of interest. A standard pixelated camera records the structure of one light field (that does not interact with the object), and a bucket detector (or single-pixel camera) measures the total intensity of the second light field that is transmitted or scattered by the object. GI can be performed with visible light as well as penetrating radiation such as x-rays, electrons, etc. Penetrating radiation is usually ionizing and damages biological specimens; therefore, minimizing the dose of this radiation in a medical or biological imaging context is important. GI has been proposed as a potential way to achieve this. With prior knowledge of the object of interest, such as sparsity in a specific basis (e.g., Fourier basis) or access to a large data set for neural network training, it is possible to reconstruct an image of the object with a limited number of measurements. However, low sampling does not inherently equate to low dose. Here we specifically explore the scenario where reduced sampling corresponds to low-dose conditions. In this simulation-based paper, we examine how deep learning (DL) techniques could reduce dose in classical x-ray GI. Since GI is based on illumination patterns, we start by exploring optimal sets of patterns that allow us to reconstruct the image with the fewest measurements, or lowest sampling rate, possible. We then propose a DL neural network that can directly reconstruct images from GI measurements even when the sampling rate is extremely low. We demonstrate that our deep learning-based GI (DLGI) approach has potential in image reconstruction, with results comparable to direct imaging (DI) at the same dose. However, given the same prior knowledge and detector quantum efficiency, it is very challenging for DLGI to outperform DI under low-dose conditions. We discuss how it may be achievable due to the higher sensitivity of bucket detectors over pixel detectors.

High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically nonclassical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways, short and long trajectories, during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum-optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schrödinger-cat-like states in the driving field. Additionally, using an ab initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the nonclassical characteristics of the emitted light.

We present a framework to deal with a range of large-scale compressive-sensing problems using a quantum subroutine. We apply a quantum approximate optimization algorithm (QAOA) to support detection in a sparse-signal reconstruction algorithm: matching pursuit. The constrained optimization required in this algorithm is difficult to handle when the size of the problem is large, and the constraints usually given by unstructured patterns also become an issue. Our framework utilizes specially designed structured constraints that are easy to manipulate and reduce the optimization problem to the solution of an Ising model which can be found using Ising solvers. In this study, we simulate QAOA for this purpose and evaluate the performances. We observe that our method can outperform reference classical methods in the same context. Our results explore a promising path for applying quantum computers in the compressive-sensing field.

Recent advancements in network nonlocality have led to the concept of local operations and shared randomness-based genuine multipartite nonlocality (LOSR-GMNL). In this paper, we consider two recent experimental demonstrations of LOSR-GMNL, focusing on a tripartite scenario where the goal is to exhibit correlations impossible in a network where each two-party subset shares bipartite resources and every party has access to unlimited shared randomness. Traditional statistical analyses measuring violations of witnessing inequalities by the number of experimental standard deviations do not account for subtleties such as memory effects. We demonstrate a more sound method based on the prediction-based ratio protocol to analyze finite experimental data and quantify the strength of evidence in favor of genuine tripartite nonlocality in terms of a valid $p$ value. In our paper, we propose an efficient modification of the test factor optimization using an approximating polytope approach. By justifying a further restriction to a smaller polytope we enhance practical feasibility while maintaining statistical rigor.

The relaxation processes in atomic xenon following core ionization of the $4d$ and $4p$ subshells by extreme ultraviolet (XUV) pulses from a free-electron laser (FLASH) are investigated using ion time-of-flight spectroscopy. We compare the dynamics following ionization and Auger-Meitner decays at 90-eV photon energy, i.e., near the giant resonance, with those at 160 eV, near the Cooper minimum, where cross sections for photoionization of the $4d$ and $4p$ subshells are similar. Final states with charges higher than 4 show signatures of sequential absorption of two XUV photons, followed by subsequent Auger-Meitner decay. The averaged lifetimes of some important excited states are measured in a two-color XUV-pump–near-infrared-probe experiment. A transient enhancement in the ion yield of ${\mathrm{Xe}}^{5+}$ with an average lifetime of $(49\pm 3)$ fs is obtained, attributed to transient intermediate states following the decay of $4d$ double-core-hole states.

We present possible ground-state structures of two-component atomic Fermi gases with repulsive interactions in a thin spherical shell geometry by implementing a self-consistent Hartree-Fock approximation. The system exhibits a miscible-immiscible transition from a homogeneous mixture to two-chunk phase separation as the interaction strength crosses a critical value. While the critical value is relatively insensitive to population imbalance for equal-mass mixtures, it decreases with the mass ratio when mass imbalance is present. The interaction may be tuned by the two-body scattering length or the radius of the sphere, thereby allowing the system to cross the transition by varying different parameters. When the atoms on the sphere are rotating, three-chunk sandwich structures emerge in mass-imbalanced mixtures as a consequence of maximal angular momentum along the rotation axis. Some indications of geometric effects and possible experimental implications are also discussed.

Directional optical sources can give rise to the directional excitation and propagation of light. The directionality of the conventional directional dipole (CDD) sources is attributed to the interference of the electric and/or magnetic dipoles, while the effect of the toroidal dipole on optical directionality remains unexplored. Here, we numerically and analytically investigate the directional properties of the toroidal dipole. We show that the toroidal dipole can replace the electric dipole in the CDD sources to form the pseudo-directional dipoles (PDDs), which can be applied to achieve analogous near-field directional coupling with a silicon waveguide. Moreover, the directionality of the PDDs can be flexibly controlled by changing the geometric parameters of the toroidal dipole, leading to tunable asymmetric coupling between the sources and the waveguide. These alternative types of directional sources provide more degrees of freedom for tailoring the optical directionality compared to the conventional sources. The results may open new possibilities for directional light manipulation and can find applications in on-chip optical routing, waveguiding, and nanophotonic communications.

First-principle simulations of photoionization processes in solids can quickly become a numerically very demanding task. In some cases, simple analytical expressions for the photoionization rates can help. However, choosing the most appropriate analytical model can be difficult, with no standard solution. We show how the best formalism can be determined based on the wave form of the pulse reflected from a sample due to photoionized, nearly free electrons in the conduction band. For the typical case of diamond, we compare three analytical models and benchmark them against highly accurate first-principles, time-dependent density functional theory (TDDFT) simulations by analyzing the match between the reflected pulses calculated with the different methods in the time and frequency domains. We also show that for very short sub-10-fs pulses, due to interband contributions, a semiclassical description based on analytical photoionization models does not provide an adequate description. The software package piglet developed for the finite-difference time domain simulations of photoionization-governed propagation is made available to the scientific community.

Vacuum Rabi splitting relies on symmetrical splitting of the common resonance frequency of atoms and the cavity in which the atoms reside. In this work, we argue that vacuum Rabi splitting is a manifestation of virtual light-matter two-mode squeezing. We establish a connection between squeezing parameters of virtual excitations and frequency shifts of the physical modes, which allows to nondestructively extract the squeezing parameters without measuring correlations. To this end, we use the mapping between the Dicke model and two interacting harmonic oscillators, which we analyze in the framework of bare and physical modes.

We show that all nonrelativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combinations of unitary evolutions. This means that, for open quantum systems, their continuous dynamics can always be described by the Lindblad master equation with all jump operators being unitary. We call this formalism the probabilistic unitary formulation of open quantum system dynamics. This formalism is shown to be exact under all cases, and does not rely on any assumptions other than the continuity and differentiability of the density matrix. Moreover, it requires as few as $d-1$ jump operators, instead of $d^2-1$, to describe the open dynamics in the most general case, where $d$ is the dimension of Hilbert space of the system. Importantly, different from the conventional Lindblad master equation, this formalism is state dependent, meaning that the Hamiltonian, jump operators, and rates in general all depend on the current state of the density matrix. Hence one needs to know the explicit expression of the density matrix in order to write down the probabilistic unitary master equation explicitly. Experimentally, the formalism provides a scheme to control a quantum state to evolve along designed nonunitary quantum trajectories, and can be potentially useful in quantum computing and quantum control scenes since only unitary resources are needed for implementation.

A fundamental feature of quantum mechanics is the incompatibility between quantum measurements, which leads to the Heisenberg uncertainty relations and is intrinsically related to detection of many other quantum features such as nonlocality and steering. Given the significance and ubiquity of incompatibility, it is desirable to quantify the degree of incompatibility between two quantum measurements which are mathematically described by positive operator valued measures. The commutator (Lie product) between operators has widely been used in quantifying incompatibility (noncommutativity) and plays a crucial role in quantum mechanics. In contrast, the anticommutator (Jordan product) between operators has been relatively less employed in the study of quantum mechanics. In this work, we explore the role of the Jordan product in characterizing measurement incompatibility. The key observation lies in that while the product of two non-negative classical observables is automatically non-negative, this is not the case for quantum observables. Indeed the Jordan product of two non-negative observables is not necessarily non-negative. This negativity of the Jordan product is a purely quantum phenomenon and is here exploited to quantify a kind of measurement incompatibility, which interpolates between noncommutativity and joint measurability. We reveal basic features of this approach, make some comparisons with existing quantifiers of incompatibility and suggest the issue of investigating its applications and implications in quantum information tasks.

Ionization of an atomic system is analyzed for intense IR and attosecond extreme ultraviolet (XUV) pulses. The analysis is based on the perturbation theory in an XUV field developed on the basis of IR-modified wave function obtained within the adiabatic approach. Detailed analytical and numerical analysis is presented for the streaking channel of ionization, which shows new interference phenomena in the momentum distribution of the ionized electrons. By utilizing the interference fringes, an alternative method for retrieving the attosecond pulse wave form and its parameters is suggested and discussed.

We investigate the behavior of a finite-momentum impurity immersed in a weakly interacting three-dimensional Bose-Einstein condensate of ultracold atoms, giving a detailed account of the dynamical quantum Cherenkov transition discussed by K. Seetharam et al. [Phys. Rev. Lett. 127, 185302 (2021)]. Using a time-dependent variational approach, we identify a transition in the far-from-equilibrium dynamics of the system after the attractive short-range impurity-boson interaction is quenched on. The transition occurs as the impurity's velocity crosses an interaction-dependent critical value and manifests in the long-time behavior of the Loschmidt echo and average impurity velocity. This behavior is also reflected in the finite-momentum ground state of the system, where the group velocity of the interaction-dressed impurity loses its dependence on the total momentum of the system as the critical point is crossed. The transition we discuss should be experimentally observable via a variety of common protocols in ultracold atomic systems such as time-of-flight imaging, rf spectroscopy, Ramsey interferometry, and absorption imaging.

We study the dynamics of phonon-mediated qubit-qubit interactions between trapped ions in the presence of an ultracold atomic gas. By deriving and solving a master equation to describe the combined system, we show that the presence of the atoms causes the quantum gate quality to reduce because of motional decoherence. On the other hand, we calculate that the gas may be used to keep the ion crystal cold in the presence of external heating due to electric-field noise. We show that tuning the atom-ion scattering length allows one to tune the cooling rate of the ions and would make it possible to temporarily reduce the effects of the gas during a quantum gate while keeping the ions cold over long timescales. In this way, the trapped ion quantum computer may be buffer gas cooled. The system may also be used for quantum-enhanced measurements of the atom-ion interactions or properties of the atomic bath.

Cavity optomechanics, which focuses on the radiation-pressure interaction between electromagnetic fields and mechanical resonators, provides a suitable platform for exploring macroscopic quantum effects. Here, we propose an approach for coupler-free resonance excitation of surface plasmon polaritons (SPPs), which comprises a top vacuum or air layer, a metal film, and graphene placed on a dielectric slab. Unlike typical systems that employ an atomic or other solid medium, our setup takes advantage of the unique features of the graphene optomechanical (GOM) medium to investigate the direct resonance excitation of SPPs via optomechanical interactions. By employing two laser beams (a control beam and a probe beam) directed through air or vacuum to the top surface, we reveal that optomechanically induced transparency (OMIT) results from destructive interference between probe field and pump field-driven mechanical oscillations. We observe that this OMIT phenomenon possess the low-loss (high transmission) criterion in the region of slightly negative probe detuning, i.e., Re $\left[{\varepsilon }_c\right]\ll 1$ and Im $[{\varepsilon }_c]<1$, which is the basis for observing the coupler-free resonance excitation of SPPs. We utilize the transfer matrix approach to compute the reflectance and transmittance spectra, and we observe small dips in the reflectance and high sharp peaks in the transmittance spectra, revealing coupler-free resonance excitation of SPPs. The amplitudes of these sharp peaks in transmittance spectra showing resonance excitation of SPPs that can be enhanced by properly adjusting the control parameters, including, the control laser beam power, angle of incidence, and the thickness of the metal film. This approach has the potential to provide advantages such as tunable coupling and dynamic control of SPPs, paving the way for plasmonic devices with enhanced functionality and performance.