We discuss the problem of finding the most favorable conditions for closing the detection loophole in a test of local realism with a Bell inequality. For a generic nonmaximally entangled two-qubit state and two incompatible bases to be adopted for alternative measurements of two observables $\mathrm{â}$ and $\mathrm{b̂}$ on each party, we apply Hardy’s proof of nonlocality without inequality and derive an Eberhard-like inequality. For an infinity of nonmaximally entangled states we find that it is possible to refute local realism by requiring perfect detection efficiency for only one of the two observables, say $\mathrm{b̂}$, to be measured on each party: The test is free from the detection loophole for any value of the detection efficiency corresponding to the other observable $\mathrm{â}$. The maximum tolerable noise in such a loophole-free observable-asymmetric test is also evaluated.

Reciprocity in wave propagation usually refers to the symmetry of the Green’s function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of $e$ and the flux is produced by a condensate of particles with charge $2e$.

We consider a two-level system coupled to a highly non-Markovian environment when the coupling axis rotates with time. The environment may be quantum (for example a bosonic bath or a spin bath) or classical (such as classical noise). We show that an Anderson orthogonality catastrophe suppresses transitions, so that the system’s instantaneous eigenstates (parallel and antiparallel to the coupling axis) can adiabatically follow the rotation. These states thereby acquire Berry phases; geometric phases given by the area enclosed by the coupling axis. Unlike in earlier proposals for environment-induced Berry phases, here there is little decoherence, so one does not need a decoherence-free subspace. Indeed we show that this Berry phase should be much easier to observe than a conventional one because it is not masked by either the dynamic phase or the leading nonadiabatic phase. The effects that we discuss should be observable in any qubit device where one can drive three parameters in the Hamiltonian with strong man-made noise.

Motivated by the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grover’s search algorithm, which displays a first-order quantum phase transition. For site-independent and site-dependent coupling strengths as well as different operator couplings, the results show (in contrast to first-order transitions) that the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins or qubits). This might limit the scalability of the corresponding adiabatic quantum algorithm.

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the $W$ states is a new monotone.

We have considered an effect of atomic electrons on the nuclear ${}^{229m}\mathrm{Th}$-${}^{229g}\mathrm{Th}$ transition in ${}^{229}\mathrm{Th}{}^{3+}$ due to the electronic bridge process. Based on a recent experimental result we assumed the energy difference between the isomeric and the ground nuclear states to be equal to $7.6$ eV. We have calculated the ratios of the electronic bridge process probability (${\Gamma }_{\mathrm{EB}}$) to the probability of the nuclear radiative transition (${\Gamma }_N$) for the electronic $5f_{5/2}\to 6d_{3/2},6d_{5/2},7s$ and the $7s\to 7p_{1/2},7p_{3/2}$ transitions and found ${\Gamma }_{\mathrm{EB}}/{\Gamma }_N~0.01-0.1$ for the former and ${\Gamma }_{\mathrm{EB}}/{\Gamma }_N~20$ for the latter.

In order to interpret precise measurements of molecular properties, finite nuclear mass corrections to the Born-Oppenheimer approximation have to be accounted for. It is demonstrated that they can be obtained systematically using nonadiabatic perturbation theory. The formulas for the leading corrections to the relativistic contribution to energy, the transition electric dipole moment, the electric polarizability, and the magnetic shielding constant are derived. They can be conveniently calculated for a fixed position of nuclei, as in the Born-Oppenheimer approximation, and then averaged over the rovibrational function.

We present a unified multichannel approach to calculate electron spin-exchange and spin-flipping transition cross sections for collisions of H with H, H with T, and T with T. We use the theory to calculate the hyperfine quenching cross sections for collision energies that range from $1$ mK to thermal temperatures. We show that spin-flipping transitions are induced by the splitting of the $b\hspace{0.5em}{}^3{\Sigma }_u$ Born-Oppenheimer potential via the long-range magnetic interactions among electrons. We find that the spin-flipping cross sections in the tritium dimer are about a magnitude larger than that predicted by mass scaling the H-H cross sections. For the former, we show that the spin-exchange cross sections are several magnitudes larger, at cold temperatures, than that of the hydrogen system. We compare the results of the multichannel approach with those obtained using approximate methods such as the degenerate internal-state, the elastic, and Born approximations and discuss their respective range of validity.

A series expansion of the interaction between a nucleus and its surrounding electron distribution provides terms that are well-known in the study of hyperfine interactions: the familiar quadrupole interaction and the less familiar hexadecapole interaction. If the penetration of electrons into the nucleus is taken into account, various corrections to these multipole interactions appear. The best known correction is a scalar term related to the isotope shift and the isomer shift. This paper discusses a related tensor correction, which modifies the quadrupole interaction if electrons penetrate the nucleus: the quadrupole shift. We describe the mathematical formalism and provide first-principles calculations of the quadrupole shift for a large set of solids. Fully relativistic calculations that explicitly take a finite nucleus into account turn out to be mandatory. Our analysis shows that the quadrupole shift becomes appreciably large for heavy elements. Implications for experimental high-precision studies of quadrupole interactions and quadrupole moment ratios are discussed. A literature review of other small quadrupole-like effects is presented as well (pseudoquadrupole effect, isotopologue anomaly, etc.).

We study the numerical solution of the nonrelativistic Schrödinger equation for two-electron atoms in ground and excited $S$ states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the energy, Cauchy error in the wave function, and variance in local energy that are exponentially fast for all practical purposes. The method requires three separate subdomains to handle the wave function’s cusplike behavior near the two-particle coalescences. The use of three subdomains is essential to maintaining exponential convergence and is more computationally efficient than a single subdomain. A comparison of several different treatments of the cusps suggests that the simplest prescription is sufficient. We investigate two alternate methods for handling the semi-infinite domain, one which involves a sequence of truncated versions of the domain and the other which employs an algebraic mapping of the semi-infinite domain to a finite one and imposes no explicit cutoffs on the wave function. The latter prescription proves superior. For many purposes it proves unnecessary to handle the three-particle coalescence in a special way. The presence of logarithmic terms in the exact solution is expected to limit the convergence to being nonexponential but the only clear evidence of that is the rate of convergence of derivatives near the three-particle coalescence point. Higher resolution than achieved in this work will ultimately be needed to see its limiting effect on other measures of error. As developed and applied here the PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wave function near cusps or at large distances, the local energy ($\mathcal{H}\psi /\psi$) is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to other bound states. As the number of collocation points grows, the method achieves exponential convergence up to the resolution tested. This study serves as a proof-of-principle of the method for more general two- and possibly three-electron applications.

We calculate the radio-frequency spectrum of a trapped cloud of cold bosonic atoms in an optical lattice. By using random phase and local-density approximations we produce both trap-averaged and spatially resolved spectra, identifying simple features in the spectra that reveal information about both superfluidity and correlations. Our approach is exact in the deep Mott limit and in the dilute superfluid when the hopping rates for the two internal spin states are equal. It contains final state interactions, obeys the Ward identities (and the associated conservation laws), and satisfies the $f$-sum rule. Motivated by earlier work by Sun, Lannert, and Vishveshwara [Phys. Rev. A 79, 043422 (2009)], we also discuss the features that arise in a spin-dependent optical lattice.

The photoionizaton processes of lithium isoelectronic sequence ($\mathrm{Be}{}^{+}$, ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, ${\mathrm{N}}^{4+}$, ${\mathrm{O}}^{5+}$, and ${\mathrm{F}}^{6+}$) under the influence of plasma environments are explored using the method of complex coordinate rotation in combination with the model potential approximation. The photoionization cross sections compared to existing theoretical predictions and varied with Debye screening lengths are reported. Under the perturbation of plasmas with certain Debye screening lengths, Cooper minima are uncovered in photoionization cross-section curves of the ground-state Li-like ions, in which the Cooper minima are absent in the respective free ion cases. The relations between the appearance of Cooper minima and the instability of the ground states due to plasma environments are discussed.

Photoassociation (PA) of ultracold metastable helium to the $2s2p$ manifold is theoretically investigated using a nonperturbative close-coupled treatment in which the laser coupling is evaluated without assuming the dipole approximation. The results are compared with our previous study [D. G. Cocks and I. B. Whittingham, Phys. Rev. A 80, 023417 (2009)], which makes use of the dipole approximation. The approximation is found to strongly affect the PA spectra because the photoassociated levels are weakly bound, and a similar impact is predicted to occur in other systems of a weakly bound nature. The inclusion of the approximation does not affect the resonance positions or widths; however, significant differences are observed in the background of the spectra and the maximum laser intensity at which resonances are discernible. Couplings not satisfying the dipole selection rule $|J-1|⩽J^{\prime }⩽|J+1|$ do not lead to observable resonances.

We study two-dimensional (2D) matter-wave gap solitons trapped in an elliptically deformed concentric lattice potential, within the framework of the Gross-Pitaevskii equation (GPE) with self-attraction or self-repulsion. For a fixed eccentricity of the lattice, soliton families are found in both the repulsive and attractive models. In the former case, the analysis reveals two kinds of gap solitons trapped in the first oval trough (the ring-shaped potential minimum closest to the center): elliptic annular solitons (EASs), and double solitons (DSs), which are formed by two tightly localized density peaks located at diametrically opposite points of the trough, with zero phase difference between them. With the decrease of the norm, the density distribution in the EAS along the azimuthal direction changes from nearly uniform to double-peaked and, eventually, to the DS. In the attractive model, there exist only DSs in the oval trough, while EASs are not found. All such solitons without the angular momentum ($l=0$) are fully stable. For $l\ne 0$, vortical solitons—both EASs with a sufficiently large norm (in the repulsive model) and DSs (in models with both signs of the nonlinearity)—are quasistable, exhibiting rocking motion in the elliptic trough (we consider the cases of $l=1\hspace{0.5em}\mathrm{and}\hspace{0.5em}l=2$). At smaller values of the norm, the vortical annular solitons (in the repulsive model) are unstable. Stable fundamental solitons trapped in the central potential well are investigated, too, in both the attractive and repulsive models, by means of the variational approximation and numerical methods.

A rigorous quantum theory for the generation of multiphoton entangled states based on two consecutive three-frequency interactions of waves in a one-dimensional nonlinear photonic crystal is developed using the field expansion and differentiation methods. The three-photon correlation coefficient and the average photon numbers generated in the structure are calculated. All order expansion terms are included in the calculation. The generation conditions for multiphoton entangled states in such a structure are also analyzed. It is shown that the created photons in the present structures obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state. This means the nonlinear photonic crystal can be applied as a highly efficient source of an entangled multiphoton for highly integrated all-optical circuits.

Spontaneous four-wave mixing can generate highly correlated photon pairs from atomic vapors. We show that multiphoton pumping of dipole-forbidden transitions in a recoil-free geometry can result in ultrabright pair emission in the full $4\pi$ solid angle, while strongly suppressing background Rayleigh scattering and associated atomic heating, Such a system can produce photon pairs at rates of $~10$${}^{12}$ per second, given only moderate optical depths of $10-100$, or alternatively, the system can generate paired photons with subnatural bandwidths at lower production rates. We derive a rate-equation based theory of the collective atomic population and coherence dynamics and present numerical simulations for a toy model, as well as realistic model systems based on ${}^{133}\mathrm{Cs}$ and ${}^{171}\mathrm{Yb}$ level structures. Last, we demonstrate that dark-state adiabatic following electromagnetically induced transparency and/or time-scale hierarchy protects the paired photons from reabsorption as they propagate through the optically thick sample.

We investigate the spatiotemporal structure of the biphoton entangled state produced by parametric down-conversion (PDC) at the output face of the nonlinear crystal. We analyze the geometry of biphoton correlation for different gain regimes (from ultralow to high), different crystal lengths, and different tuning angles of the crystal. While for collinear or quasicollinear phase matching a X-shaped geometry, nonfactorizable in space and time, dominates, in the highly noncollinear conditions we observe a remarkable transition to a factorizable geometry. We show that the geometry of spatiotemporal correlation is a consequence of the angle-frequency relationship imposed by phase matching and that the fully spatiotemporal analysis provides a key to control the spatiotemporal properties of the PDC entangled state and in particular to access a biphoton localization in time and space in the femtosecond and micrometer range, respectively.

We propose a scheme for two-dimensional (2D) atom localization in a four-level tripod system under an influence of two orthogonal standing-wave fields. Position information of the atom is retained in the atomic internal states by an additional probe field either of a standing or of a running wave. It is shown that the localization factors depend crucially on the atom-field coupling that results in such spatial structures of populations as spikes, craters, and waves. We demonstrate a high-precision localization due to measurement of population in the upper state or in any ground state.

In dispersion-managed fibers, soliton-like solutions with periodically recurring shapes exist. These so called dispersion-managed solitons are relevant for fiber-optic telecommunication. In this article we address their behavior when there is deviation from the stationary solution, which is accompanied by the excitation of a long-lived periodic oscillation. We give a possible interpretation by applying soliton radiation beat analysis, a method capable of analyzing the soliton content.

It is shown how the interference of two circularly polarized laser beams endowed with orbital angular momentum can give rise to spatial and temporal polarization gradients, displaying axial as well as angular symmetry properties. Illustrations are given with reference to circularly polarized Laguerre-Gaussian beams as typical light beams carrying orbital angular momentum.