Time-periodic driving in the form of coherent radiation provides a powerful tool for the manipulation of topological materials or synthetic quantum matter. In this paper we propose a scheme to realize non-Hermitian semimetals exhibiting exceptional rings in the spectra through Floquet engineering. A transition from a concentric pair of the rings to a dipolar pair is observed. The concentric pair carries only a quantized Berry phase while the dipolar pair possesses opposite Chern numbers in addition, signaling a topological Lifshitz transition of the Fermi surface. The transport properties of the system are addressed, and we find that this transition process is accompanied by the emergence of a nontrivial Hall conductivity. Furthermore, we explore the quantum simulation of non-Hermitian semimetals with a quantum spin system and the characterization of the topology via the long-time dynamics.

We study topological phases in one-dimensional open Floquet systems driven by chiral symmetric nonunitary time evolution. We derive a procedure to calculate topological numbers from nonunitary time-evolution operators with chiral symmetry. While the procedure has been applied to open Floquet systems described by nonunitary time-evolution operators, we give the microscopic foundation and clarify its validity. We construct a model of chiral symmetric nonunitary quantum walks classified into class ${\mathrm{BDI}}^{†}$ or AIII, which is one of the enlarged symmetry classes for topological phases in open systems based on experiments of discrete-time quantum walks. Then we confirm that the topological numbers obtained from the derived procedure give correct predictions of the emergent edge states. We also show that the model retains $\mathcal{PT}$ symmetry in certain cases, and its dynamics is crucially affected by the presence or absence of $\mathcal{PT}$ symmetry.

We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a complex are described by the Künneth theorem. We give an explicit expression for the distances when one of the complexes is a linear map between two spaces. The codes in the construction, subsystem product codes and their gauge-fixed variants, generalize several known families of quantum error-correcting codes.

Domain adaptation (DA) is used for adaptively obtaining labels of an unprocessed data set with a given related, but different labeled data set. Subspace alignment (SA), a representative DA algorithm, attempts to find a linear transformation to align the subspaces of the two different data sets. The classifier trained on the aligned labeled data set can be transferred to the unlabeled data set to predict the target labels. In this paper, two quantum versions of the SA are proposed to implement the DA procedure on quantum devices. One method, the quantum subspace alignment algorithm (QSA), can achieve quadratic speedup in the number and dimension of given samples. The other method, the variational quantum subspace alignment algorithm (VQSA), can be implemented on near-term quantum devices through a variational hybrid quantum-classical procedure. The results of the numerical experiments on different types of data sets demonstrate that the VQSA can achieve high accuracy in dealing with DA tasks.

We calculate and measure the magic wavelengths for the $6s^2{}^{1}S_0-6s6p{}^{3}P_1$ intercombination transition of the neutral ytterbium atom. The calculation is performed with the ab initio configuration interaction $+$ all-order method. The measurement is done with laser spectroscopy on cold atoms in an optical dipole trap. The magic wavelengths are determined to be 1035.68(4) nm for the $\pi$ transition $(\mathrm{\Delta }m=0)$ and 1036.12(3) nm for the $\sigma$ transitions $\left(\right|\mathrm{\Delta }m|=1)$ in agreement with the calculated values. Laser cooling on the narrow intercombination transition could achieve better results for atoms in an optical dipole trap when the trap wavelength is tuned to near the magic wavelength.

We demonstrate quantum signatures of deterministic nonlinear dynamics in the transition to superradiance of a generalized open Dicke model with different coupling strengths for the co- and counterrotating light-matter interaction terms. A first-order phase transition to coexisting normal and superradiant phases is observed, corresponding with the emergence of switching dynamics between these two phases, driven by quantum fluctuations. We show that this phase coexistence gives rise to a hysteresis loop also for the quantum mechanical system. Additionally, a transition to a superradiant oscillatory phase is observed clearly in quantum simulations.

We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various applications of our framework. We show that any relative entropy (i.e., an additive function on pairs of quantum states that satisfies the data processing inequality) must be bounded by the min and max relative entropies. We prove that the generalized trace distance, the generalized fidelity, and the purified distance are optimal extensions. And in entanglement theory we introduce a technique to extend pure-state entanglement measures to mixed bipartite states.

The RaF molecule is considered to be a potential candidate to search for the electron electric dipole moment and other effects of the time-reversal $\left(T\right)$ and spatial parity $\left(P\right)$ symmetries violation of fundamental interactions as well as $T$-even, $P$-odd effects. Recently, the existence of a suitable laser-cooling scheme for this molecule was proven experimentally, R. F. Garcia Ruiz et al. [Nature (London) 581, 396 (2020)]. In the present paper, we study energy levels, $g$-factors, and sensitivities to the electron electric dipole moment as functions of the external electric field for the lowest rotational levels of ${}^{224,226,228}\mathrm{RaF}$ molecules. The state with zero sensitivity to the electron electric dipole moment suitable to test systematic effects is found. Also energy levels of ${}^{223,225}\mathrm{RaF}$ as functions of the external magnetic field are calculated for the lowest rotational levels. The values of magnetic fields corresponding to the crossing of the levels of opposite parity are found. For these values of the magnetic field, the off-diagonal matrix element of the nuclear spin-dependent parity violation interaction is calculated. The obtained data can be used to design experiments to search for the $T,P$- and $P$-violating effects using the RaF molecule.

The adiabatic potential energy curves of ${\mathrm{Rb}}_2$ in the long-range Rydberg electronic states are calculated using the two-electron $R$-matrix method [M. Tarana and R. Čurík, Phys. Rev. A 95, 042515 (2017)] for the intermediate internuclear separations between 37 and 200 a.u. The results are compared with the zero-range models to find a region of the internuclear distances where Fermi's pseudopotential approach provides accurate energies. A finite-range potential model of the atomic perturber is used to calculate the wave functions of the Rydberg electron and their features specific for the studied range of internuclear distances are identified.

We present experiments demonstrating trajectory-dependent electronic excitations at low ion velocities, for which ions are expected to primarily interact with delocalized valence electrons. The energy loss of ${\mathrm{H}}^{+},$ ${{\mathrm{H}}_2}^{+},$ ${\mathrm{He}}^{+},$ ${\mathrm{B}}^{+},$ ${\mathrm{N}}^{+},$ ${\mathrm{Ne}}^{+},$ ${}^{28,29}\mathrm{Si}^{+},$ and ${\mathrm{Ar}}^{+}$ in self-supporting silicon membranes was analyzed along channeled and random trajectories in a transmission approach. For all ions, we observe a difference in electronic stopping dependent on crystal orientation. For heavier ions, the energy-loss difference between channeling and random geometry is generally found more pronounced, and, in contrast to protons, increases for decreasing ion energy. Due to the inefficiency of core-electron excitations at employed ion velocities, we explain these results by reionization events occurring in close collisions of ions with target atoms, which are heavily suppressed for channeled trajectories. These processes result in trajectory-dependent mean charge states, which strongly affect the energy loss. The strength of the effect seems to exhibit a $Z_1$ oscillation with an observed minimum for Ne. We, furthermore, demonstrate that the simplicity of our experimental geometry leads to results that can serve as excellent benchmark systems for dynamic calculations of the electronic systems of solids using time-dependent density functional theory.

Processes of $K$-shell ionization and accompanying characteristic x-ray radiation (CXR) by high-energy electrons moving through a multifoil copper target are considered. Expressions describing the main characteristics of these processes are derived. It is shown that the average $K$-shell ionization cross section in the target is not defined just by the target material and the electron energy, but also depends on the number of foils in the target, their thickness, and separation between them. The corresponding CXR yield is therefore not unambiguously defined by the aggregated target thickness, but depends on the above parameters as well. It is demonstrated that the average $K$-shell ionization cross section in a multifoil target can be several times larger than the conventional cross section of this process without the density effect impact. This results in a considerable enhancement of CXR yield from the multifoil target compared to the case of electron incidence upon a single foil of the same aggregated thickness. A comparison of the CXR yield in the considered case with the yields of some other types of x-ray emission in multifoil targets is made.

Making use of the equivalence between the paraxial wave equation and two-dimensional Schrödinger equation, Gaussian beams of monochromatic light, possessing knotted nodal structures, are obtained in an analytical way. These beams belong to the wide class of paraxial beams called the hypergeometric-Gaussian beams [E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, Opt. Lett. 32, 3053 (2007)]. Four topologies are dealt with: the unknot, the Hopf link, the $(3,3)$-torus knot, and the trefoil. It is shown in a numerical way that neutral polarizable particles placed in such light fields, upon precise tuning of the initial conditions, can be forced to follow identical knotted trajectories. A similar outcome is also valid for charged particles that are subject to a ponderomotive potential. This effect can serve to precisely steer particles along chosen complicated pathways exhibiting nontrivial topological character, guide them around obstacles, and, depending on the knot size, seems to provide help in engineering more complex nanoparticles.

Motivated by the experiment [St-Jean et al., Nat. Photonics 11, 651 (2017)] on topological phases with collective photon modes in a zigzag chain of polariton micropillars, we study spinless $p$-orbital fermions with local interorbital hoppings and repulsive interactions between $p_x$ and $p_y$ bands in zigzag optical lattices. We show that spinless $p$-band fermions in zigzag optical lattices can mimic the interacting Su-Schrieffer-Heeger model and the effective transverse field Ising model in the presence of local hoppings. We analytically and numerically discuss the ground-state phases and quantum phase transitions of the model. This work provides a simple scheme to simulate topological phases and the quench dynamics of many-body systems in optical lattices.

We theoretically investigate the generation of steady-state entanglement in a levitated optomechanical system with a cascade three-level atomic medium and a dielectric nanosphere. There are two cavity modes, driven by two external laser beams with different frequencies, which are responsible for trapping and cooling the nanosphere. Atoms prepared in coherent superposition are injected into the cavity to manipulate the optical fields and the effective optomechanical coupling. We show that the entanglement between the nanosphere and the cavity modes can be enhanced by selecting properly the initial population of the lower atomic level. In particular, when the atoms are prepared at that level, the corresponding optomechanical entanglement increases with the increase of the atom-field coupling strength. We also investigate in detail the influence of the effective cavity field detunings, the atomic detunings, the driving power, and the nanosphere's radius and found that there exist optimal values of the effective cavity field detuning and the driving power that maximize the optomechanical entanglement. By selecting the system's parameters properly, we further demonstrate the generation of genuine tripartite entanglement between three degrees of freedom in the system. The findings here may help flexible control of the steady-state entanglement in hybrid optomechanical systems.

We report the existence of persistently rotating azimuthons in media with self-focusing Kerr and absorption nonlinearities. The nonlinear loss is balanced by power influx from the peripheral reservoir stored in a slowly decaying tail of the field. The azimuthon modes are excited by a superposition of two Bessel beams with opposite vorticities, $\pm s$, and slightly different conicities. The excited mode exhibits vorticity in its center opposite to that of the input Bessel-beam superposition, due to spontaneous inversion of the topological charge in the course of the azimuthon formation. Unlike azimuthons in loss-free media, number $N$ of rotating intensity maxima and $s$ are not mutually independent, being related by $N=2s$. The robustness of the rotating azimuthons is enhanced in comparison to similar static dissipative patterns. They can be excited in almost any transparent material, in the range of intensities for which the nonlinear absorption, induced by multiphoton absorption, is relevant. Close to the ionization threshold, the rotating azimuthons are similar to recently observed helical filaments of light in air and ${\mathrm{CS}}_2$.

Using a polaron master equation approach, we investigate the cooperative two-photon resonance behavior between two modes of a field inside a semiconductor microcavity containing two quantum dots. The cooperative two-mode two-photon resonance occurs when two off-resonant quantum dots, initially prepared in exciton states, emit one photon in each cavity mode and deexcite simultaneously. Using this two-photon two-mode interaction, we demonstrate how to generate an entangled state of two qutrits (tripartite unit of quantum information). The bases for the qutrits are formed by the states of the cavity modes containing zero, one, and two photons. We also study the effect of exciton-phonon coupling on the entanglement and the probability of generating two-qutrit states, and explore the role of the phonon bath temperature.

Some authors have claimed that there exists a minimum size (on the order of the Compton radius) for electron states composed entirely of positive-frequency solutions to the free Dirac equation. Other authors have put forward counterexamples to such claims. This article asks how the counterexamples of A. J. Bracken and G. F. Melloy [J. Phys. A. 32, 6127 (1999)] bypass two arguments against their possibility. The first is an old argument that, because of the prohibition on faster-than-light motion, the electron must be larger than a certain minimum size if it is to have the correct angular momentum and magnetic moment. This challenge can be addressed by analyzing the flow of energy and charge for the counterexample states. The second argument is an explicit proof (presented in C.-P. Chuu et al. [Solid State Commun. 150, 533 (2010)]) that there is a minimum size for purely positive-frequency electron states. This proof hinges on the assumption of a small spread in momentum space, which is violated by the counterexamples that have been put forward.

Contextuality is regarded as a nonclassical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over classical analogs. In our work, we adapt the $N$-cycle scenarios with odd $N$ to multiple independent observers which measure the system sequentially. We analyze the possibility of violating the inequalities as a function of the number of observers and under different measurement protocols. We then reinterpret the results as an open quantum system where the environment is divided into fragments. In this context, the results show the emergence of noncontextuality in such a setting, bringing together the quantum behavior to our classical experience. We then compare such emergence of noncontextuality with that of objectivity under the “environment as a witness” paradigm.