We carefully rederive the Schiff theorem and prove that the usual expression of the Schiff moment operator is correct and should be applied for calculations of atomic electric dipole moments. The recently discussed corrections to the definition of the Schiff moment are absent.

We propose schemes for the generation of $d$-level quantum states (qudits) and quantum entangled states of $N$ qudits by adopting the polarization degree of freedom of photons. Arbitrary qudits can be prepared by putting $d-1$ identical and independent photons (each with a given polarization) into a single spatial and temporal mode. Then, by using $N$ such qudits, linear optics, and proper projection measurements, quantum entangled states of $N$ qudits can be produced. The frequencies of the $N$ qudits can be identical or different according to the corresponding linear optics and projection measurements.

We analyze focusing of atomic beams by the atom near-field microlenses produced by the laser fields diffracted on the apertures in the metallic screens. Analysis of the focusing properties of the atom microlenses is given in a model describing dipole interaction of atoms with a far-off-resonance laser light. Two types of the atom microlenses are considered: The Bethe-type microlens with aperture less than the light wavelength and the Fresnel-type microlens with aperture about the wavelength. It is shown that both types of the atom microlenses are able to produce strong dipole gradient forces which can focus the atomic beams. However, while the Bethe-atom microlens is able to produce sharp focusing of the beams the Fresnel-atom microlens possesses weak focusing property due to high anharmonicity of the gradient force. We conclude that the Bethe-atom microlens can be considered as a promising tool of the atom optics potentially able to focus atomic beams into spot sizes about nanometers.

In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.

Full, three-dimensional time-dependent simulations are presented demonstrating the quantized transfer of angular momentum to a Bose-Einstein condensate from a laser carrying orbital angular momentum in a Laguerre-Gaussian mode. The process is described in terms of coherent Bragg scattering of atoms from a chiral optical lattice. The transfer efficiency and the angular momentum content of the output coupled vortex state are analyzed and compared with a recent experiment.

In this paper we focus on the state equation of absorptive optical bistable system with cross-correlated multiplicative noise $\xi \left(t\right)$ and additive noise $\eta \left(t\right)$. We find that the area of optical bistability with positive cross-correlation expands in comparison with the deterministic case. Furthermore, a very peculiar phenomenon is shown, namely when the cooperativity parameter $C<4$, noise still can induce optical bistability. The phenomenon of noise-induced optical bistability in this paper is just the example of noise-induced phase transition.

We demonstrate confinement of ${}^{85}\mathrm{Rb}$ atoms in a dark, toroidal optical trap. We use a spatial light modulator to convert a single blue-detuned Gaussian laser beam to a superposition of Laguerre-Gaussian modes that forms a ring-shaped intensity null bounded harmonically in all directions. We measure a $1∕e$ spin-relaxation lifetime of $\approx 1.5\mathrm{s}$ for a trap detuning of $4.0\mathrm{nm}$. For smaller detunings, a time-dependent relaxation rate is observed. We use these relaxation rate measurements and imaging diagnostics to optimize trap alignment in a programmable manner with the modulator. The results are compared with numerical simulations.

In this work, decoherence of a system from an entangled state is studied theoretically by computing the time-dependent probability amplitude with which the system remains in that state. The system is composed of, in addition to vacuum, identical two-level atoms that interact indirectly with each other through photons and have a uniform distribution in the vacuum. Under the assumption that in the initial entangled state only one atom is allowed to be in the excited state, a general expression for the probability amplitude is obtained and applied to two specific entangled states, one symmetric and one antisymmetric, to demonstrate that the system decoheres from these two states at the same rate under certain conditions.

We investigate the Casimir-Polder interaction energy between a uniformly accelerated two-level system and an infinite plate with Dirichlet boundary conditions. Our model is a two-level atom interacting with a massless scalar field, with a uniform acceleration in a direction parallel to the plate. We consider the contributions of vacuum fluctuations and of the radiation reaction field to the atom-wall Casimir-Polder interaction, and we discuss their dependence on the acceleration of the atom. We show that, as a consequence of the noninertial motion of the two-level atom, a thermal term is present in the vacuum fluctuation contribution to the Casimir-Polder interaction. Finally we discuss the relevance of this result for the Unruh effect.

We report cross sections for ionization of He coincident with electron loss from He, Li, C, O, and Ne projectiles. For He, Li, C, and O projectiles, the cross sections were measured directly, while the Ne cross sections were obtained by transforming results for He projectiles colliding with Ne. We find that, at energies of about 100–500 keV/u, neutral projectiles can ionize a He target almost as effectively as a charged projectile. The contribution to ionization due to electron-electron interactions is found to scale with the number of available projectile electrons. Comparing ionization by the bound electrons on projectiles to ionization by free electrons, we find that the cross sections for ionization by bound electrons are systematically smaller than those for free electrons.

We develop a semiclassical theory of the stopping of ions in matter, aiming at a wide validity range in terms of ion energies and mass number. The excitation of a target electron is described as a binary ion-electron interaction governed by a screened-Coulomb potential. The energy loss is expressed in terms of the transport cross section for electron-ion scattering which is calculated in a semiclassical approximation to the scattering phase shifts. Exact numerical integrations of the Schrödinger equation are used for quantitative tests of the derived results. This approach provides a nonperturbative representation of the energy loss which bridges the gap between classical and quantal descriptions. It applies to nonrelativistic velocities for light and heavy ions with arbitrary charge states, and it reproduces typical quantum phenomena such as the oscillatory atomic-number dependence of stopping cross sections at low energies. Calculated results have been compared with predictions from linear and nonlinear stopping theory, in particular for stopping in the electron gas and by a quantum harmonic oscillator. Moreover, attention has been paid to the Bloch correction which, in the present scheme, approaches Bloch’s well-known expression but does not blow up at low projectile speed. We have also determined a generalized Bloch correction which depends on the ion charge. Particular attention has been given to the description of static and dynamic screening of a dressed ion.

Potential roughness has been reported to severely impair experiments in magnetic microtraps. We show that these obstacles can be overcome as we measure disorder potentials that are reduced by two orders of magnitude near lithographically patterned high-quality gold layers on semiconductor atom chip substrates. The spectrum of the remaining field variations exhibits a favorable scaling. A detailed analysis of the magnetic field roughness of a $100\text{−}\mu \mathrm{m}$-wide wire shows that these potentials stem from minute variations of the current flow caused by local properties of the wire rather than merely from rough edges. A technique for further reduction of potential roughness by several orders of magnitude based on time-orbiting magnetic fields is outlined.

In this paper, we propose an interference technique that can provide a quantitative and ultrafine-resolution spectral analysis because the optical heterodyning is performed at nonzero frequency and interfering waves propagate in optical fiber. The spectrum of a laser consists of a large number of wave trains. Our study is focused on the features of wave trains. We demonstrate that wave trains emitting simultaneously have random frequency spacings, and the probability of occurrence of two or more joint wave trains with the same frequency is high. The estimated linewidth of the wave train is narrower than $1\mathrm{mHz}$, corresponding to a wavelength range of ${10}^{-23}\mathrm{m}$.

We consider the evolution of fiber-optic solitons in the presence of dissipation. Even very low loss ultimately leads to their decay. We derive an explicit expression for the limit of adiabaticity, and discuss the evolution beyond this limit. In determining the soliton content of the optical pulse, we contrast earlier approaches using inverse scattering with a soliton-radiation beat method. It turns out that the evolution beyond adiabaticity is governed by uncertainty, which earlier published studies had missed. Somewhat in analogy to the uncertainty principle of quantum mechanics, we derive a soliton uncertainty relation. We also give simple relations for the evolution of the pulse width which reproduce numerical studies very well.

The phase-matching condition of high-order harmonic generation driven by intense few-cycle pulses could be controlled by adding second-harmonic pulses to change the ionization fraction of the gaseous medium. The harmonic generation efficiency could be improved by moving the phase-matching point with an all-optical control of the ionization fraction or a proper change of the confocal parameter. A specific order of harmonics could be easily controlled to reach phase matching at a fixed higher gas pressure by adding second-harmonic pulses with a suitable intensity. Such an all-optical phase-matching control was demonstrated to be dependent upon the temporal delay between the fundamental-wave and second harmonic pulses.

The quantum states of cold ensemble of two-level atoms were rotated around axis 2 on the Bloch sphere geometrically using a laser-controlled resonant pulse sequence with pulse areas of $\pi ∕2$, $\pi$, and $\pi ∕2$, whose central pulse has a relative phase difference of $\pi +\delta ∕2$. It was ascertained that the population probability of the excited state varies according to a sinusoidal function of $\delta$ within an uncertainty of 1%. Hybrid operations of two-level atoms were realized combining the geometrical operation with the Rabi excitation around axis 2 or the time evolution around axis 3.

We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that, for two observers undergoing finite acceleration, the entanglement vanishes between the lowest-frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and inaccessible modes from a noninertial perspective. We show that classical correlations are also lost from the perspective of two accelerated observers but conserved if one of the observers remains inertial.

The participant attack is the most serious threat for quantum secret-sharing protocols. We present a method to analyze the security of quantum secret-sharing protocols against this kind of attack taking the scheme of Hillery, Bužek, and Berthiaume (HBB) [Phys. Rev. A 59, 1829 (1999)] as an example. By distinguishing between two mixed states, we derive the necessary and sufficient conditions under which a dishonest participant can attain all the information without introducing any error, which shows that the HBB protocol is insecure against dishonest participants. It is easy to verify that the attack scheme of Karlsson, Koashi, and Imoto [Phys. Rev. A 59, 162 (1999)] is a special example of our results. To demonstrate our results further, we construct an explicit attack scheme according to the necessary and sufficient conditions. Our work completes the security analysis of the HBB protocol, and the method presented may be useful for the analysis of other similar protocols.