The Power-Zienau-Woolley Hamiltonian for the quantum electrodynamics of atoms and molecules is written in terms of purely transverse electromagnetic field variables and so-called polarization fields for the charged particles. It is well known that the attempt at finding solutions to the coupled equations that arise from the Hamiltonian is marred by the occurrence of infinite “self-energies” for both particles and the field. Because of the occurrence of the Dirac $\delta$ function in the nonzero Poisson-brackets/commutation relation for the fields, and in the definition of the polarization fields, these variables, classical and quantum, must be identified as distributions, in the mathematical sense. The Schwartz “impossibility theorem” shows that there is no general multiplication rule for distributions, so one has to find a framework that gives meaning to the Hamiltonian The energy of the electric polarization field is analyzed in the Colombeau algebra and shown to be finite; in particular Coulomb's law ($1/r,r>0$) with a finite self-energy ($r=0$) is obtained. How these ideas could be extended to the free-field Hamiltonian is discussed. A finite zero-point energy for the electromagnetic field is to be expected. Relevant mathematical results are summarized in an Appendix.

Recently, handling of contextual sets, in particular Kochen-Specker (KS) sets, in higher dimensions has been given an increasing attention, both theoretically and experimentally. However, methods of their generation are diverse, not generally applicable in every dimension, and of exponential complexity. Therefore, we design a dimensional upscaling method, whose complexity does not scale with dimension. As a proof of principle we generate manageable-sized KS master sets in up to 27 dimensional spaces and show that well over 32 dimensions can be reached. From these master sets we obtain an ample number of smaller KS sets. We discuss three kinds of applications that work with KS sets in higher dimensions. We anticipate other applications of KS sets for quantum information processing that make use of large families of nonisomorphic KS sets.

We consider two memory nodes of a quantum network connected by flying qubits. We are particularly interested in the case where a flying qubit produced by one node has to be transformed before it can interface efficiently with the next node. Such transformations can be utilized as a key part of the distribution of quantum states and hence entanglement between the nodes of a hybrid quantum network linking together different quantum technologies. We show how and why the probability of interfacing successfully is determined by the overlap of the spectral shape of the actual flying qubit and the ideal shape. This allows us to analytically and numerically analyze how the probability of success is impacted by realistic errors, and show the utility of our scheme (in consonance with known error correction methods) in connecting hybrid nodes of a quantum network. We focus here on a concrete implementation in which the memory nodes consist of three-level atoms in cavities and the flying qubits are photons.

Entanglement swapping, which establishes entanglement between two independent and distant entangled states, is a key element of a quantum repeater in an entanglement-based quantum network. In continuous-variable (CV) entanglement swapping, it is essential to enhance the entanglement of entanglement swapping because it decreases with loss and noise in the quantum channel. Here, we propose a scheme of enhancing entanglement of CV entanglement swapping by a photon subtraction (PS) operation in noisy channels. We apply both one- and two-sided PS operations in CV entanglement swapping through lossy single- and dual-channel transmission schemes, respectively. In the lossy channel, we show that the two-sided PS operation enables one to obtain higher entanglement and longer transmission distance compared to the one-sided PS operation. Furthermore, we show that the two-sided PS operation can enhance the entanglement of the entanglement swapping in the noisy single-channel CV entanglement swapping. Our results provide a feasible solution to enhance entanglement of CV entanglement swapping, and they have potential applications in building quantum repeaters.

Obtaining reliable state preparation protocols is a key step toward practical implementation of many quantum technologies, and one of the main tasks in quantum control. In this work, different reinforcement learning approaches are used to derive a feedback law for state preparation of a desired state in a target system. In particular, we focus on the robustness of the obtained strategies with respect to different types and amount of noise. Comparing the results indicates that the learned controls are more robust to unmodeled perturbations with respect to simple feedback strategy based on optimized population transfer, and that training on a simulated nominal model retains the same advantages displayed by controllers trained on real data. The possibility of effective off-line training of robust controllers promises significant advantages toward practical implementation.

Superfluids with strong spatial modulation can be experimentally produced in the area of cold atoms under the influence of optical lattices. Here we address ${}^{87}\mathrm{Rb}$ bosons at $T=0$ K in a flat geometry under the influence of a periodic potential with the Gross-Pitaevskii theory. The statics and dynamics of vortex excitations are studied in the case of one-dimensional (1D) and of two-dimensional (2D) optical lattices, as function of the intensity of the optical lattice. We compute how the vortex energy depends on the position of its core and the energy barrier that a vortex has to surmount in order to move in the superfluid. The dynamics of a vortex dipole, a pair of vortices of opposite chirality, differ profoundly from the case of a uniform superfluid. In the 1D case, when parallel ridges of density are present, the dynamics depends on the positions of the two vortices. If they are in the same channel between two ridges, then the two vortices approach each other until they annihilate each other in a short time. If the two vortices are in distinct channels, the dipole undergoes a rigid translation but with a velocity depending on the intensity of the optical lattice and this translation velocity can even change sign with respect to the case of the uniform superfluid. Superimposed on this translation an oscillatory motion is also present. A superposition of translation along a channel and an oscillation is also found with a single vortex when the system is bounded inside a circular trap. These oscillatory motions can be both longitudinal, i.e., along the channel, as well as transverse. In all cases the transverse motions are one sided, in the sense that the vortex core never crosses the equilibrium position nearest the starting position. In the case of the 2D lattices we study (square, triangular, and honeycomb), the two vortices of a dipole move mainly by jumps between equilibrium positions and approach each other until annihilation. This behavior has some similarity with what has been found for a vortex dipole in the supersolid state of dipolar bosons. We show that a rapid ramp down of the optical potential improves the visibility of the density holes at the vortex core.

Many studies have shown that high-energy $\gamma$-photon beams can be efficiently generated via nonlinear Compton scattering driven by laser pulses with intensities greater than ${10}^{22}\mathrm{W}/{\mathrm{cm}}^2$ recently available in laboratories. Here we propose a laserless scheme to efficiently generate high-energy polarized $\gamma$-photon beams by collision of two ultrarelativistic electron beams. The self-generated field of a dense driving electron beam provides a strong deflection field for the other ultrarelativistic seeding electron beam. A QED Monte Carlo code based on the locally constant field approximation is employed to simulate the collision process, and the polarization properties of the $\gamma$ photons produced are investigated. The simulation results and theoretical analysis indicate that the photon polarization, including both linear and circular polarizations, can be tuned by changing the initial polarization of the seeding beam. If an unpolarized seeding beam is used, linearly polarized photons with an average polarization of 55% can be obtained. If the seeding beam is transversely (longitudinally) polarized, the linear (circular) polarization of photons above 3 GeV can reach 90% (67%), which is favorable for highly polarized, high-energy $\gamma$-photon sources.

There is a prevalent effort to achieve quantum-enhanced metrology using criticality. However, the extent to which estimation precision is enhanced through criticality still needs further exploration under the constraint of finite time resources. We clarify relations between quantum metrology and criticality through a unitary parametrization process with a Hamiltonian governed by $\text{su}(1,1)$ Lie algebra. We demonstrate that the determination of the generator in the parametrization can be treated as an extended brachistochrone problem. Furthermore, the dynamic quantum Fisher information about the parameter exhibits a power-law dependence on the evolution time as the system approaches its critical point. By investigating the dynamic sensing proposals of three quantum critical systems, we show that the asymptotic behavior of sensitivity is consistent with our predictions. Our theory provides a deep understanding of the interplay of quantum metrology and criticality, providing insights into the underlying connections that involve both quantum phenomena and classical problems.

We investigate keV collisions between antiprotons and the rare-gas atoms neon and argon. We use a correlated approach in which the eight electrons from the $L$ shell of neon and $M$ shell of argon are active and up to two-electron processes are included, going thus beyond the approximate theoretical approaches used so far. Our results show that the electronic correlation plays a major role in the single- and double-ionization processes. Furthermore, we show that two-electron processes contribute significantly to the electronic stopping power. These results apply to both target atoms studied in this paper and we therefore conclude that a correlated approach is in general necessary to obtain accurate antiproton electronic stopping-power cross sections. Our paper paves the way to a better understanding and knowledge of antiproton collision physics.

The pump-probe experiments enabled by x-ray free-electron lasers (XFEL) will allow us to directly observe correlated electronic motion with attosecond time resolution by detecting photoelectron pairs in coincidence. In helium, the transition between the nonsequential and sequential regime in two-photon double ionization (TPDI) is well explained by a virtual-sequential model. Much less is known, however, about the TPDI process in more complex atoms. Recently, we extended the virtual-sequential model to arbitrary light pulses [Chattopadhyay et al. Phys. Rev. A 108, 013114 (2023)]. This extension employs multichannel scattering states for the single ionization of both the neutral and the ionized target, which we initially applied to helium. In the present study, we show that our extended virtual-sequential model reproduces the qualitative features of the angularly integrated observables with available experimental results for neon, a considerably more complex target. We observe an intriguing feature of inverted two-particle interference in the joint-energy distribution of $\mathrm{Ne}$ compared to $\mathrm{He}$. This phenomenon, attributable to the presence of a final doubly ionized state with triplet symmetry coupled to the two photoelectrons, should be observable with current experimental technologies.

We consider Bose-Einstein condensation of noninteracting homogeneous three-dimensional gas in canonical ensemble when both particle number $N$ and total momentum $\mathbf{P}$ of all particles are fixed. Using the saddle-point method, we derive the large-$N$ analytical approximations for partition function, free energy, and statistical distributions of occupation numbers of different single-particle energy levels. At temperatures below the critical point of phase transition, we predict, in some ranges of $\mathbf{P}$, fragmentation of the condensate, when more than one single-particle level is macroscopically occupied. The occupation number distributions have approximately Gaussian shapes for the levels hosting the condensate, and exponential shapes for other, noncondensate levels. Our analysis demonstrates breaking of Galilean invariance of moving finite-temperature many-particle system in the presence of Bose-Einstein condensation and extends the theory of moving and rotating quantum systems to the finite-temperature large-$N$ limit.

Over the past few decades, the study of bound states in the continuum (BICs), their formation, and properties has attracted a lot of attention, especially in optics and photonics. It is particularly noticeable that most of these investigations are based on symmetric systems. In this article, we study the formation of bound states in the continuum in electronic and photonic transport systems consisting of crossbar junctions formed by one-dimensional waveguides, considering asymmetric junctions with commensurable lengths for the upper and lower arms. These BICs in an asymmetric system go beyond the symmetry-protected paradigm. We also study how BICs form in linear junction arrays as a function of the distance between consecutive junctions and their commensurability with the upper and lower arms. New commensurability conditions in the array's central section also give rise to Fabry-Pérot-type BICs. We solve the Helmholtz equation for the crossbar junctions and calculate the transmission probability, local density of states in the intersections, and quality factor. The presence of quasi-BICs is reflected in the transmission probability as a sharp resonance in the middle of a symmetric Fano resonance, along with Dirac $\delta$-functions in the probability density and divergence in the quality factors.

We investigate the magnetic properties of photons propagating through Dirac materials in a magnetic field, considering both vacuum and medium contributions. Photon propagation properties are obtained through a second-order expansion of nonlinear Euler-Heisenberg electrodynamics at finite density and temperature considering Dirac material parameters (Dirac fine structure constant, band gap, and Fermi velocity). Total magnetization (including electron and photon contributions) and photon-effective magnetic moment are computed. Observables such as photon energy density, radiation pressure, and Poynting vector are obtained by an average of components of the energy-momentum tensor. All quantities are expressed in terms of Lagrangian derivatives. Those related to the vacuum are valid for any value of the external magnetic field, and both the weak- and strong-field limits are recovered. We discuss some ideas of experiments that may contribute to testing in Dirac materials the phenomenology of the strong magnetic field in the quantum electrodynamic (QED) vacuum and how nonlinear corrections on the magnetization, radiation pressure, and birefringence are amplified up to ${10}^3$ times QED corrections.

Characterizing high-dimensional entangled states holds pivotal significance in quantum information science and technology. Recent theoretical progress has been made to extend the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality into a general scenario with multisetting and multidimensional systems. Here, by employing two-photon orbital angular momentum entanglement, we conduct an experiment to demonstrate the CGLMP inequality across multiple settings and outcomes. Our experimental results violate the CGLMP inequality by more than 12 standard deviations, demonstrating that the maximum violation increases with both dimension and setting. Furthermore, we reveal, both theoretically and experimentally, the logical connection between the CGLMP inequality and the general Hardy's paradox. Intriguingly, our analysis establishes that, even in high-dimensional systems, Hardy's paradox can be regarded as a special instance of Bell inequality, with their respective bounds aligning under the no-signaling principle and the information causality principle. Our work may advance the foundational understanding of quantum correlations in high-dimensional quantum systems.