There is a consensus today that the the main lesson of the Aharonov-Bohm effect is that a picture of electromagnetism based on the local action of the field strengths is not possible in quantum mechanics. Contrary to this statement, it is argued here that when the source of the electromagnetic potential is treated in the framework of quantum theory, the Aharonov-Bohm effect can be explained without the notion of potentials. It is explained by local action of the field of the electron on the source of the potential. The core of the Aharonov-Bohm effect is the same as the core of quantum entanglement: the quantum wave function describes all systems together.

A no-signalling channel transforming quantum systems in Alice's and Bob's local laboratories is compatible with two different causal structures: ($A⪯B$) Alice's output causally precedes Bob's input and ($B⪯A$) Bob's output causally precedes Alice's input. Here I prove that two no-signalling channels that are not perfectly distinguishable in any ordinary quantum circuit can become perfectly distinguishable through the quantum superposition of circuits with different causal structures.

We explore the propagation of light in a two-photon state in disordered optical systems that induce Anderson localization. We show that entangled-photon pairs demonstrate a surprising behavior that we call Anderson colocalization: While neither photon exhibits Anderson localization, the spatial correlations of the pair remain intact. Furthermore, we show that entangled-photon pairs colocalize faster than classical light localizes in the same system. We also explore the propagation of anticorrelated and partially entangled photon pairs in such systems. The results are developed using a linear systems theory that extends the scope of quantum imaging to incorporate disordered systems.

If the no-signaling principle was the only limit to the strength of nonlocal correlations, we would expect that any form of no-signaling correlation can indeed be realized. That is, there exists a state and measurements that remote parties can implement to obtain any such correlation. Here, we show that in any theory in which some functions cannot be computed, there must be further limits to nonlocal correlations than the no-signaling principle alone. We proceed to argue that even in a theory such as quantum mechanics in which nonlocal correlations are already weaker, the question of computability imposes such limits.

A non-Hermitian $\mathcal{PT}$-symmetric system can have a full real spectrum but does not ensure probability-preserving time evolution in contrast to that of a Hermitian system. We present a non-Hermitian two-band model, which is composed of dimerized hopping terms and staggered imaginary on-site potentials and study the dynamics in the exact $\mathcal{PT}$-symmetric phase based on the exact solution. It is shown that an initial state, which does not involve two equal-momentum-vector eigenstates in different bands, obeys perfectly probability-preserving time evolution in terms of the Dirac inner product. Beyond this constriction, the quasi-Hermitian dynamical behaviors, such as nonspreading propagation and fractional revival of a Gaussian wave packet, are also observed.

We propose a method using a quantum annealer—an analog quantum computer based on the principles of quantum adiabatic evolution—to solve the graph isomorphism problem, in which one has to determine whether two graphs are isomorphic (i.e., can be transformed into each other simply by a relabeling of the vertices). We demonstrate the capabilities of the method by analyzing several types of graph families, focusing on graphs with particularly high symmetry called strongly regular graphs. We also show that our method is applicable, within certain limitations, to currently available quantum hardware such as D-Wave One.

We consider a state discrimination problem which deals with settings of minimum-error and unambiguous discrimination systematically by introducing a margin for the probability of an incorrect guess. We analyze discrimination of three symmetric pure states of a qubit. The measurements are classified into three types, and one of the three types is optimal depending on the value of the error margin. The problem is formulated as one of semidefinite programming. Starting with the dual problem derived from the primal one, we analytically obtain the optimal success probability and the optimal measurement that attains it in each domain of the error margin. Moreover, we analyze the case of three symmetric mixed states of a qubit.

Using first-principles calculations, we identify magic wavelengths ${\lambda }_{\mathrm{magic}}$ for the $2s$-$2p$ and $2s$-$3p$ transitions in lithium. The $ns$ and $np$ atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between ${}^6$Li and ${}^7$Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the $2s$, $2p$, $3s$, $3p$, and $3d$ levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv $2s$-$3p$ transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].

The exchange effect has been previously given as a possible explanation for a significant deviation from an allowed shape observed at low energy in the ${}^{241}$Pu $\beta$ spectrum. Calculations set out here confirm that this atomic effect explains a large part of this deviation. The equations needed to calculate the exchange effect are detailed, as well as the evaluation of the confluent hypergeometric function for complex arguments of large magnitudes. After a review of the possible other effects that could explain the remaining discrepancy at low energy, the screening correction using effective nuclear charges seems to be the best explanation. For radionuclides with high $Z$, this work has demonstrated the necessity to take into account the spatial variation of the nuclear charge experienced by the ejected electron to accurately correct for the screening effect.

Large-scale relativistic configuration-interaction calculation of energy levels of core-excited states of lithium-like ions is presented. Quantum electrodynamic, nuclear recoil, and frequency-dependent Breit corrections are included in the calculation. The approach is consistently applied for calculating all $n=2$ core-excited states for all lithium-like ions starting from argon ($Z=18$) and ending with krypton ($Z=36$). The results obtained are supplemented with systematical estimations of calculation errors and omitted effects.

We load ${10}^5$ magnesium atoms in a dipole trap from a millikelvin-hot magneto-optical trap (MOT) using a continuous-loading scheme. Light-assisted two-body processes limit the maximum achievable density in a MOT, resulting in a reduced transfer efficiency into a dipole trap when using the conventional sequential scheme. It is overcome in a continuous-loading scheme where a loss channel is opened in the MOT. This allows the accumulation of atoms in the dipole trap over the trap lifetime, determined by collisions with the background gas. This results in a significantly higher number of trapped atoms even at a lower steady-state peak density in the MOT.

Using the multipole expansion, we analyze photoinduced reactions in an ultracold atomic gas composed of identical neutral bosons. While the Franck-Condon factor dominates the photoinduced spin-flip reactions, we have found that for a frozen-spin process in which the atomic spins are conserved, the reaction rate is governed by the monopole $r^2$ and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number $k$ acquires an extra $k^4$ factor in comparison to the spin-flip process. Comparing the relative strength of the $r^2$ and quadrupole modes in dimer photoassociation, we predict that the mutual importance of these two modes changes with temperature and scattering length.

We study the two-dimensional Bose-Hubbard model with anisotropic hopping. Focusing on the effects of anisotropy on superfluid properties such as the helicity modulus and the normal-to-superfluid [Berezinskii-Kosterlitz-Thouless (BKT)] transition temperature, two different approaches are compared: large-scale quantum Monte Carlo simulations and the self-consistent harmonic approximation (SCHA). For the latter, two different formulations are considered, one applying near the isotropic limit and the other applying in the extremely anisotropic limit. Thus we find that the SCHA provides a reasonable description of superfluid properties of this system provided the appropriate type of formulation is employed. The accuracy of the SCHA in the extremely anisotropic limit, where the BKT transition temperature is tuned to zero (i.e., at a quantum critical point) and therefore quantum fluctuations play a dominant role, is particularly striking.

We experimentally verify the quantum non-Gaussian character of a conditionally generated noisy squeezed single-photon state with a positive Wigner function. Employing an optimized witness based on probabilities of squeezed vacuum and squeezed single-photon states, we prove that the state cannot be expressed as a mixture of Gaussian states. In our experiment, the non-Gaussian state is generated by conditional subtraction of a single photon from a squeezed vacuum state. The state is probed with a homodyne detector and the witness is determined by averaging a suitable pattern function over the measured homodyne data. Our experimental results are in good agreement with a theoretical fit obtained from a simple yet realistic model of the experimental setup.

Angular momentum in electromagnetic wave systems is an important yet difficult subject to deal with, both classically and quantum mechanically. We investigate the angular momentum of partially coherent electromagnetic wave fields and establish the general formalism for angular momentum conservation, based on the Maxwell stress tensor for partially coherent sources and fields in the space-frequency domain. This formalism is applied to study the angular momentum properties of several classes of partially coherent electromagnetic beams possessing circulation.

Laws of refraction and reflection of light are governed by the classic Fresnel formulas. These formulas are not applicable to partially coherent light. We develop a general theory of refraction and reflection of electromagnetic beams of any state of coherence. We find that coherence properties of such beams change, in general, on refraction and on reflection at a planar interface.

We demonstrate that the theoretical description of current experiments of quasi-two-dimensional (quasi-2D) Fermi gases requires going beyond the usual 2D theories. We provide such a theory for the highly spin-imbalanced quasi-2D Fermi gas. For typical experimental conditions, we find that the location of the recently predicted polaron-molecule transition is shifted to lower values of the vacuum binding energy due to the interplay between transverse confinement and many-body physics. The energy of the attractive polaron is calculated in the two-dimensional to three-dimensional (2D-3D) crossover and displays a series of cusps before converging towards the 3D limit. The repulsive polaron is shown to be accurately described by a 2D theory with a single interaction parameter.

Electrostatic calibration is important in Casimir force measurements. It is necessary for the estimation of the unknown system parameters such as the absolute separation distance and the identification of the electrostatic force model. Correct estimates of the unknown parameters and the electrostatic force model are crucial for interpreting the Casimir force data. In this paper, we present an electrostatic calibration method with higher sensitivity and robustness. It is based on large-amplitude dynamic force measurements. It is proven in theory that the unknown system parameters can be obtained accurately and the electrostatic force model can be identified by our method. The effectiveness and robustness of our method are tested on synthetic data with added noise when the Casimir force measurement is conducted between a sphere and a flat surface.

We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare accurate solutions of them with those obtained in a Born-Oppenheimer projection approximation. We illustrate how geometric magnetism manifests in them, and explore the relationship between solutions obtained in the diabatic and adiabatic pictures. We provide an example, involving a neutral atom dressed by an external field, in which the system mimics the behavior of a charged particle that interacts with, and is scattered by, a ferromagnetic material. We also introduce a similar system that exhibits Aharonov-Bohm scattering. We propose possible practical applications. We provide a theoretical approach that underscores universality in the appearance of geometric gauge forces. We do not insist on degeneracies in the adiabatic Hamiltonian, and we posit that the emergence of geometric gauge forces is a consequence of symmetry breaking in the latter.