For decelerated bare lead ions at a low beam energy of 10 MeV/u, the x-ray emission associated with radiative recombination (RR) at threshold energies has been studied at the electron cooler of CRYRING@ESR at GSI, Darmstadt. In our experiment, we observed the full x-ray emission pattern by utilizing dedicated x-ray detection chambers installed at $0^{\circ }$ and ${180}^{\circ }$ observation geometry. Most remarkably, no line distortion effects due to delayed emission are present in the well-defined x-ray spectra, spanning a wide range of x-ray energies (from about 5 to 100 keV), which enables us to identify fine-structure resolved Lyman, Balmer, and Paschen x-ray lines along with the RR transitions into the $K, L$, and $M$ shells of the ions. For comparison with theory, an elaborate theoretical model is established taking into account the initial population distribution via RR for all atomic levels up to Rydberg states with principal quantum number $n=165$ in combination with time-dependent feeding transitions. Within the statistical accuracy, the experimental data are in very good agreement with the results of rigorous relativistic predictions. Most notably, this comparison sheds light on the contribution of prompt and delayed x-ray emission (up to 70 ns) to the observed x-ray spectra, originating in particular from yrast transitions into inner shells.

The present atomic theory provides accurate and reliable results for atoms with a small number of valence electrons. However, most current methods of calculations fail when the number of valence electrons exceeds four or five. This means that we cannot make reliable predictions for more than half of the periodic table. Here we suggest a modification of the configuration interaction plus many-body perturbation theory, which may be applicable to atoms and ions with partly filled $d$ and $f$ shells.

The electron nondipole dynamics in tunneling ionization in an elliptically polarized laser field is investigated theoretically using a relativistic Coulomb-corrected strong-field approximation (SFA) based on the eikonal approximation of the Klein-Gordon equation. We calculate attoclock angle-resolved light-front momentum distributions at different ellipticities of the laser field in quasistatic and nonadiabatic regimes and analyze them with an improved simple man's model. The nondipole correlations between longitudinal and transverse momentum components are examined. Deviations of the nondipole photoelectron momentum distribution calculated via SFA with respect to the available experimental results as well as with the improved simple man's model are discussed and interpreted in terms of nonadiabatic as well as Coulomb effects in the continuum and under the barrier. The favorable prospects of an experimental observation are discussed.

Engineering many-body systems of particles in lattices has attracted intense interest in the last few decades, thanks to their promising applications such as in quantum computation or topological matter. While lattices of different dimensions have been demonstrated with magnetic and/or optical fields, little work has been done upon three-dimensional (3D) electrostatic lattices to tame polar molecules. Here, we propose a 3D electrostatic lattice consisting of periodically distributed square-patterned electrodes in space, whose potentials reach tens of millikelvin and can be controlled easily. Detailed analysis and Monte Carlo simulations indicate that ${\mathrm{ND}}_3$ molecules in its $|J,KM\rangle =|1,-1\rangle$ state can be effectively trapped and evaporatively cooled. In addition, replacing the electrodes with different patterns enables realizing 3D electric lattices with new topological geometry (e.g., honeycomb or kagome). As a natural extension of the 3D optical and magnetic lattices, the 3D electrostatic lattice offers intriguing perspectives for cold chemistry, quantum simulation, and precision metrology.

We introduce and study a two-dimensional dissipative nonlinear Anderson pumping model that is characterized by localized or delocalized eigenmodes in a linear regime and in addition includes nonlinearity, dissipation, and pumping. We find that above a certain pumping threshold, the model has narrow spectral lasing lines generated by isolated clusters of Anderson attractors. With the increase of the pumping, the lasing spectrum is broadened even if narrow lasing peaks are still well present in the localized phase of linear modes. In the metallic phase, the presence of narrow spectral peaks is significantly suppressed. We argue that the model captures the main features observed for random lasers.

The multiphonon state plays an important role in quantum information processing and quantum metrology. Here we propose a scheme to realize dynamical emission of phonon pairs based on the technique of stimulated Raman adiabatic passage in a single-cavity optomechanical system, where the optical cavity is driven by two Gaussian pulse lasers. By exploring quantum trajectories of the state populations and the average phonon number, we find that the dynamical phonon-pair emission can be realized under the appropriate parameter conditions and is tunable by controlling the time interval between the consecutive pulses of pump lasers. In particular, the numerical results for the standard and generalized second-order correlation functions of the mechanical mode show that the system can behave as an antibunched phonon-pair emitter. Our proposal can be extended to achieve an antibunched $n$-phonon emitter, which has potential applications for on-chip quantum communication.

Based on the fundamental interplay between spatial wavefronts and polarization degrees of freedom, spin-orbit interactions (SOI) of light constitute a novel tool for optical control at the nanoscale. While well described in simple geometries, SOI of light in disordered environments, where only a partial knowledge of the material's microscopy is available, remain largely unexplored. Here, we show that in transversally random media the disorder correlation can be exploited to tailor a variety of trajectories for ballistic beams via SOI. In particular, we show the existence of an oscillating spin Hall effect, stemming from the deformation of the phase of the wavefront due to SOI. In combination with a weak measurement, this phenomenon can also be maximized by an optimal choice of the disorder correlation.

Many molecular, quantum-dot, and optomechanical nanocavity-QED systems demonstrate strong nonlinear interactions between electrons, photons, and phonon (vibrational) modes. We show that such systems can be described by a universal model in the vicinity of the nonlinear resonance involving all three degrees of freedom. We solve the nonperturbative quantum dynamics in the strong-coupling regime of the nonlinear resonance, taking into account quantization, dissipation, and fluctuations of all fields. We find analytic solutions for quantum states in the rotating-wave approximation which demonstrate tripartite quantum entanglement once the strong-coupling regime is reached. We show how the strong coupling at the nonlinear resonance modifies photon emission and vibrational spectra, and how the observed spectra can be used to extract information about relaxation rates and the nonlinear coupling strength in specific systems.

In their recent paper [Li et al., Phys. Rev. A 103, 012401 (2021)], the authors proposed two quantities $C_{\mathrm{F}}^D\left(\rho \right|\mathcal{K})$ in Eq. (11) and $C_{\mathrm{F}}^C\left(\rho \right|\mathcal{K})$ in Eq. (12). The authors proved that $C_{\mathrm{F}}^C\left(\rho \right|\mathcal{K})$ is a valid coherence measure in Theorem 5 and proved that $C_{\mathrm{F}}^D\left(\rho \right|\mathcal{K})=C_{\mathrm{F}}^C\left(\rho \right|\mathcal{K})$ in Proposition 4. In this Comment, we show that the proof of Proposition 4 is not justified, that is, $C_{\mathrm{F}}^D\left(\rho \right|\mathcal{K})=C_{\mathrm{F}}^C\left(\rho \right|\mathcal{K})$ is not true, in general. Consequently, whether $C_{\mathrm{F}}^D\left(\rho \right|\mathcal{K})$ is a valid coherence measure is still an open problem.

The complex temporal behavior of an ultrashort pulse of light propagating through a multiple scattering medium can be characterized experimentally through a time-gated transmission matrix. Using a spatial light modulator, we demonstrate here that injecting singular vectors of this matrix allows us to optimally control the energy deposition at any controllable delay time. Our approach provides insights into the fundamental aspects of multispectral light scattering and could find applications in imaging or coherent control.

We show that excited-state quantum phase transitions (ESQPTs) in a system in which the parity symmetry is broken can be used to engineer an energy cat state—a Schrödinger cat state involving a quantum superposition of both different positions and energies. By means of a generalization of the Rabi model, we show that adding a parity-breaking term annihilates the ground-state quantum phase transition between normal and superradiant phases, and induces the formation of three excited-state phases, all of them identified by means of an observable with two eigenvalues. In one of these phases, level crossings are observed in the thermodynamic limit. These allow us to separate a wave function into two parts: one, with lower energy, trapped within one region of the spectrum, and a second one, with higher energy, trapped within another. Finally, we show that a generalized microcanonical ensemble, including two different average energies, is required to properly describe equilibrium states in this situation. Our results illustrate yet another physical consequence of ESQPTs.

An entangled-state generation protocol for a system of two qubits driven with an ac signal and coupled through a resonator is introduced. We explain the mechanism of entanglement generation in terms of an interplay between unitary Landau-Zener-Stückelberg (LZS) transitions, induced for appropriate frequencies and strong amplitudes of the applied ac signal and dissipative processes dominated by photon loss. In this way, we find that the steady state of the system can be tuned to be arbitrarily close to a Bell state, which is stable against photon loss. Effective two-qubit Hamiltonians that reproduce the resonance patterns associated with LZS transitions are derived.

The nonlinear single and double ionization of Sr atoms as a result of their interaction with 800-nm Ti-sapphire laser pulses of 25-fs duration is experimentally investigated within the laser intensity range $I=3\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}–30\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}$. The latter range includes the over-the-barrier intensities for both Sr and ${\mathrm{Sr}}^{+}$, while the corresponding Keldysh adiabaticity parameters are larger than unity. Nevertheless, for $I\ge 24\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}$ the recorded photoelectron-energy spectra show evidence of the (partial) applicability of tunneling or over-the-barrier ionization concepts, whereas below this value they can be discussed in terms of multiphoton ionization processes. More importantly, the data additionally point towards a further division of the multiphoton regime into two subranges separated roughly at $I\sim 4\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}$. Above this value above-threshold-ionization structures and the single-active-electron picture dominate. On the contrary, at the lowest laser intensities the photoelectron spectra and angular distributions reveal single ionization pathways where the remaining ion is left into excited states. These pathways also require photon absorption in the continuum, which in the case of strontium and other alkaline-earth-metal atoms is structured by the presence of doubly excited states which are embedded in it. Hence, in this case ionization proceeds via quasiresonant ionization ladders formed by these doubly excited states which are dominated by the interaction between the two valence electrons of Sr. We discuss in detail the above rich phenomenology and relevant ionization mechanisms and propose possible directions of further work towards the elucidation of the role of configuration interaction in ionization processes.

In this paper, exact analytical solutions are derived for the second-order moment and the mean-square displacement based on the transport theory fluence that is caused by an arbitrary anisotropic point source, which is located at the origin of a three-dimensional coordinate system. In particular, the derivations are carried out as a function of the number of scattering events. The resulting formulas in the steady-state and time domain depend, apart from the scattering coefficient and partly the absorption coefficient, only on the anisotropy factor of the considered rotationally invariant scattering phase function. We additionally present the second-order moment and the mean-square displacement for the fluence of fluorescence light in the steady-state domain.

Incompatibility of quantum devices is a useful resource in various quantum information theoretical tasks, and it is at the heart of some fundamental features of quantum theory. While the incompatibility of measurements and quantum channels is well studied, the incompatibility of quantum instruments has not been explored in much detail. In this work, we revise a notion of instrument compatibility introduced in the literature that we call traditional compatibility. Then, we introduce the notion of parallel compatibility and show that these two notions are inequivalent. We then argue that the notion of traditional compatibility is conceptually incomplete and prove that, while parallel compatibility captures measurement and channel compatibility, traditional compatibility does not capture channel compatibility. Hence, we propose parallel compatibility as the conceptually complete definition of the compatibility of quantum instruments.

We present a kicked harmonic oscillator where the impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom and not by the canonical quantization of a time-dependent Hamiltonian. The ancilla is dynamically entangled with the oscillator position, while the background Hamiltonian remains static. The dynamics of this system is determined in closed analytical form, allowing for the evaluation of a properly defined Loschmidt echo, ensemble averages, and phase-space portraits. As in the case of standard Floquet systems, we observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidence of chaotic behavior, however, not originating from any classically chaotic system.

Work is an observable quantity associated with a process; however, there is no Hermitian operator associated with its measurement. We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian via two von Neumann measurements of the system's energy carried out by a measuring apparatus modeled as a free particle of finite localization and interaction time with the system. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation. This measurement model allows us to quantify the effect that measuring has on the estimated work distribution and associated average work done on the system and average heat exchanged with the measuring apparatus.

Intense ultrafast pulses cause dissociative ionization and shaping the pulses may allow control of both electronic and nuclear dynamics that determine ion yields. We report on a combined experimental and theoretical effort to determine how shaped laser pulses affect tunnel ionization, the process that precedes many strong-field phenomena. We carried out experiments on Ar, ${\mathrm{N}}_2$, ${\mathrm{H}}_2\mathrm{O}$, and ${\mathrm{O}}_2$ using a phase-step function of amplitude $\frac{3}{4}\pi$ that is scanned across the spectrum of the pulse. In addition, we changed the amount of chirp in the pulses. Semiclassical as well as fully quantum mechanical time-dependent Schrödinger equation calculations are found to be in excellent agreement with experimental results. We find that precise knowledge of the field parameters in the time and frequency domains is essential to afford reproducible results and quantitative theory and experiment comparisons.

In this work, we investigate the non-Markovian (NM) dynamical evolution of a three-level atom coupled to a semi-infinite one-dimensional photonic waveguide and driven by a classical driving field. The single-end of waveguide behaves as a perfect mirror while light can pass through the opposite end with no backreflection. We derive the exact analytical expressions for the wave function of the driven three-level atom by solving a set of delay differential equations and give the conditions of atom-photon bound state formation that can inhibit the dissipation, which appears in the atom-mirror interspace in order to trap a considerable amount of initial atomic excitation. We show that when the evolution time of the system is shorter than the time delay taken by a photon to perform a round trip between the atom and mirror, the atomic dynamics exhibits Markovian properties, which depend on the driving strength and rescaled parameters. If the evolution time of the system exceeds the time delay, the photon can be reabsorbed by the atom with the photon emitted by the atom having completed the round trip, which exhibits NM memory effects, where the population eventually convergences to the finite-steady values. We also study the influence of the loss and dephasing on the formation of a bound state. Finally, the above results are extended to a more general quantum system involving single-end photonic waveguide coupled to an arbitrary number of noninteracting three-level atoms driven by the driving fields. The presented formalism might open a way to better understand exactly the NM dynamics of driven multilevel atoms coupled to a semi-infinite waveguide.