We develop a versatile theoretical approach to the study of ultracold atom diffractive scattering from light-field gratings by combining calculations of the optical near field generated by evanescent waves close to the surface of periodic nanostructured arrays with atom wavepacket propagation techniques. Nanometric one dimensional (1D) and 2D arrays with subwavelength periodicity deposited on a transparent surface and optically coupled to an evanescent wave source exhibit intensity and polarization gradients on the length scale of the object and can produce strong near-field periodic modulation in the optical potential above the structure. As a specific and experimentally practical example we calculate the diffraction of cold Cs atoms dropped onto a periodic optical potential crafted from a 2D nanostructure array. For an “out-of-plane” configuration we calculate a wide diffraction angle $\left(\simeq 2°\right)$ and about $60\%$ of the initial atom flux in diffraction orders $\pm 1,$ an encouraging result for future experiments.

We study the collective excitations of a neutral atomic Bose-Einstein condensate with gravitylike $1/r$ interatomic attraction induced by an electromagnetic wave. Using the time-dependent variational approach, we derive an analytical spectrum for monopole and quadrupole mode frequencies of a gravitylike self-bound Bose condensed state at zero temperature. We also analyze the excitation frequencies of the Thomas-Fermi–gravity (TF-G) and gravity (G) regimes. Our result agrees excellently with that of Giovanazzi et al. [Europhysics Lett., 56, 1 (2001)], which is obtained within the sum-rule approach. We also consider the vortex state. We estimate the superfluid coherence length and the critical angular frequencies to create a vortex around the z axis. We find that the TF-G regime can exhibit the superfluid properties more prominently than the G regime. We find that the monopole mode frequency of the condensate decreases due to the presence of a vortex.

The heating rate of ions laser cooled to the vibrational ground state of an rf quadrupole trap provide sensitive limits on partition noise (shot noise) of the rf current in the trap electrodes. The millisecond lifetimes observed in recent experiments correspond to a partition noise power spectral density (Fano factor) less than ${10}^{-8}$ of the Poisson value, showing a sensitivity $>{10}^6$ greater than the solid-state measurements.

We have studied the coupling of the two polarization modes of a polymer microlaser by pumping its gain medium with two mutually delayed orthogonally polarized femtosecond pump pulses, that have a variable interpulse delay. Because the dominant anisotropy in the laser is induced by the pump and the various time scales associated with this setup are well separated, insight into the dynamics of the system is obtained by this method. Both time-resolved and time-integrated measurements of the output of the microlaser demonstrate strong cross-coupling and memory effects between the polarization modes. These can be assigned to the interplay between the optical fields in the cavity and the inversion. The most remarkable result is that the dominant output polarization switches direction when the interpulse delay is varied. Using a simple model, both for the polarization properties of the polymer and for the polymer laser, we discuss the underlying physics of the polarization cross-coupling. An attractive aspect of our gain material, i.e., a light-emitting polymer in solution, is that it has a very long memory for the polarization anisotropy induced by the pump; such a material therefore provides a transparant model system.

The nonresonant (NR) corrections are estimated for the most accurately measured two-photon transition $1s-2s$ in the hydrogen atom. These corrections depend on the measurement process and set a limit for the accuracy of atomic frequency measurements. With the measurement process adopted in modern experiments the NR contribution to the $1s-2s$ transition energy can reach ${10}^{-2}\hspace{0.5em}\mathrm{Hz},$ while the experimental inaccuracy is quoted to be $\pm 46\hspace{0.5em}\mathrm{Hz}.$

A standard quantum oracle $S_f$ for a general function $f:\hspace{0.5em}{Z}_N\to Z_N$ is defined to act on two input states and return two outputs, with inputs $|i〉$ and $|j〉\hspace{0.5em}(i,j\in Z_N)$ returning outputs $|i〉$ and $|j\oplus f\left(i\right)\mathrm{}〉.$ However, if f is known to be a one-to-one function, a simpler oracle, $M_f,$ which returns $|f\left(i\right)\mathrm{}〉$ given $|i〉,$ can also be defined. We consider the relative strengths of these oracles. We define a simple promise problem that minimal quantum oracles can solve exponentially faster than classical oracles, via an algorithm that cannot be naively adapted to standard quantum oracles. We show that $S_f$ can be constructed by invoking $M_f$ and ${(M}_f{)}^{-1}$ once each, while $\Theta \left(\sqrt{N}\right)$ invocations of $S_f$ and/or ${(S}_f{)}^{-1}$ are required to construct $M_f.$

We experimentally demonstrate coherent control of a laser. A resonant 100-fs optical pulse is injected into a vertical cavity surface emitting laser to introduce a field component with well-defined phase and thereby excite beating oscillations between the transverse lasing modes. By changing the relative phase between two injected pulses, we can enhance or destroy the beating oscillations and select which lasing modes are excited. We discuss resonant pulse injection into lasers and show how mode competition improves controllability by suppressing the phase-sensitive effects of the carriers.

We propose a simple and fast scheme for producing maximally entangled states for many trapped ions. The scheme only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the regime, where the Rabi frequency is of the order of the vibrational frequency. Our scheme operates in a fast way and is insensitive to heating of vibrational motion, which is important in view of decoherence. Thus, our scheme opens promising prospects for entanglement engineering in a scalable way.

In this paper a method is developed further that makes it possible to tailor the position dependence of the coupling strength between a system and a bath in a very flexible way. To do so, generalized raising/lowering operators from supersymmetric quantum mechanics are used, together with the Lindblad approach to dissipation. A one-dimensional numerical example illustrates the application of the method to a problem with polynomial position dependence, and the extension to problems of higher dimension is discussed.

We have previously proposed a conjecture stating that quantum-mechanical transition amplitudes can be parametrized in terms of a quantum action. Here we give a proof of the conjecture and establish the existence of a local quantum action in the case of imaginary time in the Feynman-Kac limit (when temperature goes to zero). Moreover we discuss some symmetry properties of the quantum action.

The problem investigated in this paper is einselection, i.e., the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection method in the quantum theory of irreversible processes, which is general enough for giving reliable predictions. This approach leads to a definition (or redefinition) of the coupling with the environment involving only fluctuations. The range of application of perturbation calculus is then wide, resulting in a rather general master equation. Two distinct cases of decoherence are then found: (i) a “degenerate” case (already encountered with solvable models) where decoherence amounts essentially to approximate diagonalization; (ii) a general case where the einselected states are essentially classical. They are mixed states. Their density operators are proportional to microlocal projection operators (or “quasiprojectors”) that were previously introduced in the quantum expression of classical properties. It is found at various places that the main limitation in our understanding of decoherence is the lack of a systematic method for constructing collective observables.

For a quantum system coupled to a heat bath environment the nonlinear dissipation is studied starting from imaginary-time path-integral formulation. An effective classical potential (ECP) is obtained in which not only the frequency of the potential but also the slope of the coupling form factor are treated as trial functions, they are determined by minimizing the effective classical potential. Further, terms of higher order are also added in an improved Gaussian measure in order to regularize integrals of fluctuation modes at low temperatures. Various approximations to thermodynamic functions of a double-well potential are compared with the dissipative path-integral Monte Carlo method. In particular, it occurs for single- or double-well potentials, where nonlinear dissipation can induce the appearance of multistable states and barrier drift. Nonmonotonic varying of the barrier height of the ECP with temperature is found in a bistable system.

Generalizing Khinchin’s classical axiomatic foundation, a basis is developed for nonadditive information theory with the Tsallis entropy indexed by q. The classical nonadditive conditional entropy is introduced and then translated into quantum theory. To examine if this theory has points superior to the ordinary additive information theory with the von Neumann entropy corresponding to the limit $\overrightarrow{q}1,$ separability of a one-parameter family of the Werner-Popescu states of the $N^n$ system (i.e., the n-partite N-level system) is discussed. The nonadditive information theory with $q>\mathrm{}1\mathrm{}$ is shown to yield a limitation on separability that is stronger than the one derived from the additive theory. How the strongest limitation can be obtained in the limit $\overrightarrow{q}\infty$ is also shown.

We present a scheme for the implementation of the discrete quantum Fourier transform using cavity quantum electrodynamics. In the proposed scheme a series of atoms whose atomic coherence carries the input state passes through a series of cavities and classical field, and the resulting state in the cavities is the quantum Fourier transform of the input state.

Recently a new Bell inequality has been introduced by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)], which is strongly resistant to noise for maximally entangled states of two d-dimensional quantum systems. We prove that a larger violation, or equivalently a stronger resistance to noise, is found for a nonmaximally entangled state. It is shown that the resistance to noise is not a good measure of nonlocality and we introduce some other possible measures. The nonmaximally entangled state turns out to be more robust also for these alternative measures. From these results it follows that two von Neumann measurements per party may be not optimal for detecting nonlocality. For $d=3,4,$ we point out some connections between this inequality and distillability. Indeed, we demonstrate that any state violating it, with the optimal von Neumann settings, is distillable.

We need secure identification schemes because many situations exist in which a person must be identified. In this paper, we propose three quantum identification schemes with entanglements. First, we propose a quantum one-time pad password scheme. In this scheme, entanglements play the role of a one-time pad password. Next, we propose a quantum identification scheme that requires a trusted authority. Finally, we propose a quantum message authentication scheme that is constructed by combining a different quantum cryptosystem with an ordinary authentication tag.

We calculate nuclear-polarization energy shifts for the hydrogenlike ${}_{82}^{208}{\mathrm{Pb}}^{81+}.$ The retarded transverse part as well as the longitudinal part is taken into account as the electromagnetic interaction between an electron and the nucleus. With a finite charge distribution for the nuclear ground state and the random-phase approximation to describe the nuclear excitations, we obtain nuclear-polarization energy of the ${1s}_{1/2}$ state as $-38.2$ $(-37.0)\hspace{0.5em}\mathrm{meV}$ in the Feynman (Coulomb) gauge. For the ${2s}_{1/2},$ ${2p}_{1/2},$ and ${2p}_{3/2}$ states, they are $-6.7$ $(-6.4),$ $-0.2$ $(-0.2),$ and $+0.0\mathrm{}$ $\mathrm{}(+0.0\mathrm{})\mathrm{}\hspace{0.5em}\mathrm{meV},$ respectively. The transverse contribution is small in comparison with the longitudinal nuclear-polarization correction. It is about $12\%$ both for the ${1s}_{1/2}$ and ${2s}_{1/2}$ states. The seagull term in the two-photon exchange diagrams is also shown to be quite important to obtain the gauge-invariant nuclear-polarization energies.

A curious effect is uncovered by calculating the time evolving probability of reflection of a Gaussian wave packet from a rectangular potential barrier while it is perturbed by reducing its height. A time interval is found during which this probability of reflection is larger (superarrivals) than in the unperturbed case. This nonclassical effect can be explained by requiring a wave function to act as a “field” through which an action, induced by the perturbation of the boundary condition, propagates at a speed depending on the rate of reducing the barrier height.

We report measurements of cold photoassociative ionization (PAI) spectra obtained from collisions within a slow, bright Na atomic beam. A high-brightness atom flux, obtained by optical cooling and focusing of the atom beam, permits a high degree of alignment and orientation of binary collisions with respect to the laboratory atom-beam axis. The results reveal features of PAI spectra not accessible in conventional magneto-optical trap studies. We take advantage of this high degree of alignment to selectively excite autoionizing doubly excited states of specific symmetry.

We perform an extension of the continuum-distorted-wave (CDW) approximation for single electron capture by introducing model potentials to describe the interaction of the active electron with the residual-target and projectile ions. The cross sections for electron transfer in collisions of bare and dressed projectile ions with H and He atoms are calculated and compared with experimental data and previous CDW calculations that make use of approximate analytical wave functions to represent the active electron initial and final states. For electron capture in proton-He collisions into definite final states the present calculations are in better agreement with experiments. We trace the differences in the results from both models to a different behavior at projectile scattering angles close to the Thomas peak. In the case of dressed projectiles with different charge states impinging on H and He the present version of CDW gives a better representation of the filling of the unoccupied orbitals of the dressed ion and, therefore, of the cross section as a function of the impinging ion charge state.