We derive a complete expression for the nonrecoil quantum electrodynamic ${\alpha }^{6}m$ correction to the Lamb shift, the fine and hyperfine structure of light $N$-electron atoms. The derivation is performed in the framework of nonrelativistic quantum electrodynamics. The obtained formulas generalize previous ones derived for the specific cases of the helium atom, and the fine and hyperfine structure of lithium, and pave the way for improving the theory of light atoms with three and more electrons.

We study strong-field ionization of H and selected rare-gas atoms by solving the three-dimensional time-dependent Schrödinger equation in the single-active-electron approximation with particular attention to the effect of pulse length on the total ionization yields (TIYs) produced by counter-rotating bicircular (CRBC) lasers compared to co-rotating bicircular (COBC) lasers. To this end, TIYs, photoelectron momentum distributions, and above-threshold ionization spectra are presented for various pulse durations and peak intensities. For pulses containing five or more cycles of the fundamental near-infrared laser field, the CRBC/COBC ratio of TIYs is affected due to ionization via excited states and multiphoton ionization channels. For pulses containing less than five cycles, the CRBC/COBC ratio of TIYs depends on both the frequency combination and number of optical cycles: With the $1\omega \text{−}2\omega$ frequency combination, the ratio of TIYs is enhanced (reduced) for pulses with an odd (even) number of optical cycles. The $1\omega \text{−}3\omega$ frequency combination was considered for pulses containing two or three optical cycles, and for both pulse lengths the CRBC/COBC ratio of TIYs is less than unity.

A theoretical analysis is presented for the excitation of single many-electron atoms and ions by twisted (or vortex) light. Special emphasis is put on excitations that can proceed via several electric and magnetic multipole channels. We argue that the relative strength of these multipoles is very sensitive to the topological charge and kinematic parameters of the incident light and can be strongly modified with respect to the plane-wave case. Most remarkably, the modification of multipole transitions by twisted radiation can be described by means of a geometrical factor. This factor is independent of the shell structure of a particular target atom and just reflects the properties of the light beam as well as the position of an atom with respect to the vortex axis. An analytical expression for the geometrical factor is derived for Bessel photons and for a realistic experimental situation in which the position of an atom is not well determined. To illustrate the use of the geometrical factor for the analysis of (future) measurements, detailed calculations are presented for the $3s3p{}^{3}P_1\to 3s3p{}^{1}P_1$ excitation in neutral Mg.

We show that quantum wave packets exhibit a sharp macroscopic peak as they spread in the vicinity of the critical point of the Anderson transition. The peak gives a direct access to the multifractal properties of the wave functions and specifically to the multifractal dimension $d_2$. Our analysis is based on an experimentally realizable setup: the quantum kicked rotor with quasiperiodic temporal driving, an effectively three-dimensional disordered system recently exploited to explore the physics of the Anderson transition with cold atoms.

Based on two-photon entanglement, quantum remote sensing enables the measurement and detection to be done nonlocally and remotely. However, little attention has been paid to implement a noncontact way to sense a real object's angular rotation, which is a key step towards the practical applications of precise measurements with entangled twisted photons. Here, we use photon pairs entangled in orbital angular momentum (OAM) to show that a real object's angular rotation can be measured nonlocally. Our experiment reveals that the angular sensitivity of the object encoded with idler photons is proportional to the measured OAM values of signal photons. It suggests potential applications in developing a noncontact way for angle remote sensing of an object with customized measurement resolution. Moreover, this feature may provide potential application in sensing of some light-sensitive specimens when the entangled photon pairs, which have significantly different wavelengths, are used, such as one photon is infrared but the other one is visible.

A generic photonic coupler with active and lossy parts, gain saturation, and asymmetric characteristics is examined. Saturable activity is shown to be able to enhance the overall stability of the steady states, prevent evolution to undesirable unbounded modes, and allow for bistable operation in specific regions of the parametric space. Both stability and bistability are studied in the phase space of the system, where the basins of attraction of each state are identified, providing an accurate description of the dependence of the electric fields on the initial conditions. Continuous families of exceptional points are detected via suitable regulation of the coupling and asymmetry features of the configuration. In this way, a complete description of the nonlinear dynamics landscape is provided, which should be crucial for multiple application-driven designs incorporating such a ubiquitous optical component.

Bell nonlocality and quantum contextuality are two important resources which, however, behave very differently in many tasks where the quantum correlation has an edge over its classical counterpart. In this work, we directly compare these two behaviors, which via the Cabello-Severini-Winter graph-theoretical approach, can be associated with a same exclusivity graph. In particular, we consider the exclusivity graph that leads to $I_{3322}$-type inequalities in the Bell and the contextual scenarios, respectively. We find that maximal violation of Bell inequality is around 6.251, and maximal violation of the noncontextuality inequality is around 6.588 for a five-dimensional system and 6.571 for a four-dimensional system, respectively. The results predict a gap of $\mathrm{\Delta }\approx 0.32$ between quantum contextuality and Bell nonlocality. We then present an experimental observation of the gap by employing both the maximally entangled photon pairs from the spontaneous parametric down-conversion process and the single photons encoded into qudits from an intrinsic defect in gallium nitride. Our results will further deepen the understanding of different types of quantum correlations.

We provide an initial characterization of pairwise concurrence in quantum states which are invariant under cyclic permutations of party labeling. We prove that maximal entanglement can be entirely described by adjacent pairs, then give explicit descriptions of those states in specific subsets of four- and five-qubit states (X states). We also construct a monogamy bound on shared concurrences in the same subsets in four and five qubits, finding that above nonmaximal entanglement thresholds, no other entanglements are possible.

Doppler and sideband cooling are long-standing techniques that have been used together to prepare trapped atomic ions in their ground state of motion. In this paper we study how these techniques can be extended to cool both radial modes of motion of a single ion in a Penning trap. We numerically explore the prerequisite experimental parameters for efficient Doppler cooling in the presence of an additional oscillating electric field to resonantly couple the radial modes. The simulations are supported by experimental data for a single ${}^{40}\mathrm{Ca}^{+}$ ion Doppler cooled to $\sim 100$ phonons in both radial modes at a magnetron frequency of 52 kHz and a modified cyclotron frequency of 677 kHz. For these frequencies, we then show that mean phonon numbers of 0.35(5) for the modified cyclotron and 1.7(2) for the magnetron motions are achieved after 68 ms of sideband cooling.

The interplay of $\pi$-flux and lattice geometry can yield full localization of quantum dynamics in lattice systems, a striking interference phenomenon known as Aharonov-Bohm caging. At the single-particle level, this full-localization effect is attributed to the collapse of Bloch bands into a set of perfectly flat (dispersionless) bands. While interparticle interactions generally break the cages, not much is known regarding the fate of Aharonov-Bohm caging in the presence of classical nonlinearities, as captured by a discrete nonlinear Schrödinger equation. This scenario is relevant to recent experimental realizations of photonic Aharonov-Bohm cages, using classical light propagating in arrays of coupled waveguides. In this article, we demonstrate that caging always occurs in this nonlinear setting, as long as the nonlinearities remain local. As a central result, we identify special caged solutions that are accompanied by a breathing dynamics of the field intensity that we describe in terms of an effective two-mode model reminiscent of a bosonic Josephson junction. Also, motivated by a formal similarity with the Gross-Pitaevskii equation describing interacting bosons, we explore the quantum regime of Aharonov-Bohm caging using small ensembles of interacting particles, and reveal quasicaged collapse-revival dynamics. The results stemming from this work open an interesting route towards the characterization of nonlinear dynamics in interacting flat-band systems.

The properties of x-ray diffraction are compared for two principally different scattering mechanisms: potential and resonant. The first mechanism is well represented by elastic scattering from atomic electrons (Rayleigh scattering), while the second one is offered by recoilless resonant scattering from nuclei (Mössbauer scattering). Diffraction in Bragg geometry from a semi-infinite crystal is considered. Mainly, the spatial aspects of scattering are discussed like angular dependencies, distributions of electric and magnetic fields inside the crystal and, especially, the role of asymmetry in the diffraction geometry. The results of the model calculations are presented for a complex reflection coefficient, for total wave fields and their interaction with atoms, for path lengths in transmission of radiation through the crystal, and for an interplay between absorption and reflection of radiation by the atomic ensemble.

Controlling the interaction between the spin wave and the electromagnetic field is an important issue of optoelectronics. The effect of photon blockade is to indicate the interaction that prevents multiple photons from entering the cavity simultaneously, which is the pivotal effect to achieve the photons at the quantum level. Here in this study, we investigate an effective way of photon controlling and find the photon-blockade effect in the hybrid optomagnonic microcavity. Specifically, we show that the magnons and photons in both transverse electric and transverse magnetic modes can be converted into the supermode photons under the Kerr effect. Also the correlation function of the photons is analytically studied, which shows the asymmetry behavior for the two different supermodes. This proposed system opens up a route to control the optical mode in hybrid microresonators, which are important for advanced quantum technologies.

We investigate quantum violation of macrorealism for multilevel spin systems under the condition of coarsening of measurement times, i.e., when measurement times have experimental indeterminacy. This is studied together with the effect of coarsening of measurement outcomes for which individual outcomes cannot be unambiguously discriminated. In our treatment, along with different measurement outcomes being combined into two groups in order to model the coarsening of measurement outcomes, importantly, varying degrees of coarsening of measurement time intervals have also been considered. This then reveals that while, for a given dimension, the magnitude of quantum violation of macrorealism decreases with the increasing degree of coarsening of measurement times, interestingly, this effect of coarsening of measurement times can be annulled by increasing the dimension of the spin system so that in the limit of large spin, the quantum violation of macrorealism continues to persist. Thus, the result obtained demonstrates that classicality for large spins does not emerge from quantum mechanics in spite of the coarsening of measurement times.

One of the major concerns of Schrödinger, Lorentz, Einstein, and many others about the wave function is that it is defined on the $3\mathbf{N}$-dimensional configuration space, rather than on the three-dimensional (3D) physical space. This gives the impression that quantum mechanics cannot have a $3\mathrm{D}$ space or space-time ontology, even in the absence of quantum measurements. In particular, this seems to affect interpretations which take the wave function as a physical entity, in particular, the many-worlds and the spontaneous collapse interpretations, and some versions of the pilot wave theory. Here, a representation of the many-particle states is given, as multilayered fields defined on the three-dimensional physical space. This representation is equivalent to the usual representation on the configuration space, but it makes it explicit that it is possible to interpret the wave functions as defined on the physical space. As long as only unitary evolution is involved, the interactions are local. I intended this representation to capture and formalize the nonexplicit and informal intuition of many working quantum physicists, who, by considering the wave function sometimes to be defined on the configuration space and sometimes on the physical space, may seem to researchers in the foundations of quantum theory as adopting an inconsistent view about its ontology. This representation does not aim to solve the measurement problem, and it allows for Schrödinger cats just like the usual one. But, it may help various interpretations to solve these problems, through inclusion of the wave function as (part of) their primitive ontology. In appendices, it is shown how the multilayered field representation can be extended to quantum field theory.

Weak values are quantities accessed through quantum experiments involving weak measurements and postselection. It has been shown that “anomalous” weak values (those lying beyond the eigenvalue range of the corresponding operator) defy classical explanation in the sense of requiring contextuality [M. F. Pusey, Phys. Rev. Lett. 113, 200401 (2014)]. Here we elaborate on and extend that result in several directions. First, the original theorem requires certain perfect correlations that can never be realized in any actual experiment. Hence, we provide theorems that allow for a noise-robust experimental verification of contextuality from anomalous weak values, and compare with a recent experiment. Second, the original theorem connects the anomaly to contextuality only in the presence of a whole set of extra operational constraints. Here we clarify the debate surrounding anomalous weak values by showing that these conditions are tight: if any one of them is dropped, the anomaly can be reproduced classically. Third, whereas the original result required the real part of the weak value to be anomalous, we also give a version for any weak value with nonzero imaginary part. Finally, we show that similar results hold if the weak measurement is performed through qubit pointers, rather than the traditional continuous system. In summary, we provide inequalities for witnessing nonclassicality using experimentally realistic measurements of any anomalous weak value, and clarify what ingredients of the quantum experiment must be missing in any classical model that can reproduce the anomaly.

In quantum error correction, the description of the noise channel cannot be completely accurate and fluctuation always appears in the noise channel. It is found that when fluctuation of the physical noise channel is considered, the average effective channel is dependent only on the average of the physical noise channel, and the average of the physical noise channel here plays the role of the independent error model in previous works. Now one may conclude that in the independent error model, the results in previous works are also valid for the average channel where fluctuation exists. In some typical cases, our numerical simulations in the concatenated quantum error-correction protocol with a five-qubit code, seven-qubit Steane code, and nine-qubit Shor confirm this conjecture. For a five-qubit code, the effective channels approximate to the depolarizing channel as the concatenated level increases. For the Steane code, the effective channels approximate to one Pauli channel as the concatenated level increases. For the Shor code, the effective channels approximate to either a Pauli-$X$ or Pauli-$Z$ channel in each level, and in the next concatenated level, the effective channels approximate to the other. The numerical results for these codes indicate that the degree of approximation increases as the concatenated level increases, and the fluctuation of the noise channel decays exponentially as concatenated quantum error correction is performed. On the error-correction threshold, the attenuation ratio of the standard deviation of channel fidelity has a roughly stable value. In contrast, standard deviations of off-diagonal elements of the quantum process matrix (Pauli form) decay more quickly than standard deviations of diagonal elements.

We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of the whole parameter space reveals a wide range of different regimes, ranging from strongly non-Markovian to Markovian dynamics. In contrast to analytical models, all non-Markovianity measures and criteria have to be applied to data with fluctuations and statistical uncertainties. We discuss the practical usefulness of the different approaches.

The resource theory of quantum coherence is an important topic in quantum information science. Standard coherence distillation and dilution problems have been thoroughly studied. In this paper, we introduce and study the problem of one-shot coherence distillation with catalysts. In order to distill more coherence from a state of interest, a catalytic system can be involved and a jointly free operation is applied to both systems. The joint output state should be a maximally coherent state in tensor product with the unchanged catalysts, with some allowable fidelity error. We consider several different definitions of this problem. First, with a small fidelity error in both systems, we show that, even via the smallest free operation class (physically implementable incoherent operations), the distillable coherence of any state with no restriction on the catalysts is infinite, which is a “coherence embezzling phenomenon.” We then define and calculate a lower bound for the distillable coherence when the dimension of catalysts is restricted. Finally, in consideration of physical relevance, we define the “perfect catalysts” scenario where the catalysts are required to be pure and precisely unchanged. Interestingly, we show that in this setting catalysts basically provide no advantages in pure state distillation via incoherent operations and strictly incoherent operations under certain smoothing restriction. Our work enhances the understanding of catalytic effect in quantum resource theory.