Optical beams bearing orbital angular momentum have been recently recognized as potential candidates for realizing $D$-dimensional quantum systems (qudits). In this paper, we propose an optical scheme to implement an orbital angular momentum beam splitter, which changes the outgoing direction with respect to the incoming direction while leaving the qudit state unchanged. Furthermore we demonstrate that such a beam splitter can be used to sort different orbital angular states of a single photon, create arbitrary superpositions of orbital angular momentum states, and implement a high-dimensional Bennett-Brassard 1984 protocol for quantum key distribution.

We present calculations of high Rydberg states for the lithium atom by two different theoretical methods. The first method is based on the $R$-matrix theory to obtain the energy levels and the quantum defects for the $1s^{2}nd{}^{2}D$ and $1s^{2}nf{}^{2}F$ states and their adjacent continuum states. Then the quantum defect functions of the two channels are obtained which vary smoothly with energy based on quantum defect theory. The second method is based on the full core plus correlation method. Our results are compared with data in the literatures; especially the results of the $R$-matrix method are in excellent agreement with microwave measurements for the lithium atom.

The dynamics of small ($⩽55$ atoms) argon clusters ionized by an intense femtosecond laser pulse is studied using a time-dependent Thomas-Fermi model. The resulting Bloch-like hydrodynamic equations are solved numerically using the smooth particle hydrodynamics method without the necessity of grid simulations. As follows from recent experiments, absorption of radiation and subsequent ionization of clusters observed in the short-wavelength laser frequency regime $\left(98\mathrm{nm}\right)$ differs considerably from that in the optical spectral range $\left(800\mathrm{nm}\right)$. Our theoretical approach provides a unified framework for treating these very different frequency regimes and allows for a deeper understanding of the underlying cluster explosion mechanisms. The results of our analysis following from extensive numerical simulations presented in this paper are compared both with experimental findings and with predictions of other theoretical models.

We outline a formalism and develop a computational procedure to treat the process of multiphoton ionization (MPI) of atomic targets in strong laser fields. We treat the MPI process nonperturbatively as a decay phenomenon by solving a coupled set of the integral Lippmann-Schwinger equations. As basic building blocks of the theory, we use a complete set of field-free atomic states, discrete and continuous. This approach should enable us to provide both the total and differential cross sections of MPI of atoms with one and two electrons. As an illustration, we apply the proposed procedure to a simple model of MPI from a square-well potential and to the hydrogen atom.

We show the possibility of producing matter-wave switching devices by using Manakov interactions between vector matter-wave solitons using two-species Bose-Einstein condensates (BECs). Our results establish the experimental parameters for three interaction regimes in two-species BECs: symmetric and asymmetric splitting, down-switching, and up-switching. We have studied the dependence upon the initial conditions and the kind of interaction between the two matter-wave solitons.

We make a systematic study of the resonant mode coupling of the collective excitations at zero temperature in a Bose-Einstein condensate (BEC). (i) Based on the Gross-Pitaevskii equation we derive a set of nonlinearly coupled envelope equations for a three-mode resonant interaction (TMRI) by means of a method of multiple scales. (ii) We calculate the coupling matrix elements for the TMRI and show that the divergence appearing in previous studies can be eliminated completely by using a Fetter-like variational approximation for the ground-state wave function of the condensate. (iii) We provide the selection rules in mode-mode interaction processes [including TMRI and second-harmonic generation (SHG)] according to the symmetry of the excitations. (iv) By solving the nonlinearly coupled envelope equations we obtain divergence-free nonlinear amplitudes for the TMRI and SHG processes and show that our theoretical results on the shape oscillations of the condensate agree well with the experimental ones. We suggest also an experiment to check the theoretical prediction of the present study on the TMRI of collective excitations in a BEC.

With the use of an ultra-narrow-band extreme ultraviolet laser source, tunable near 94 nm, transition wavelengths are determined for lines connecting the $1s^{2}2s^{2}2p^2$ ${}^{3}P_{0,1,2}$ ground-term levels to the $1s^{2}2s2p^3$ ${}^{3}S_1$ excited level in neutral carbon at an absolute accuracy of $4\times {10}^{-8}$. With the determination of the zero-velocity rest-frame wavelengths these lines can be included in an analysis of a possible temporal variation of the fine-structure constant $\alpha$ from a comparison with quasar data. A value for the ${\mathrm{C}}^{12}$/${\mathrm{C}}^{13}$ transition isotope shift was also obtained yielding $0.5107\left(13\right){\mathrm{cm}}^{-1}$, in average over the three fine-structure lines. The latter measurement will allow to study isotopic evolution in the universe and test models of nuclear processes in stars.

We study the properties of a phase slip in a superfluid Fermi gas near a Feshbach resonance. The phase slip can be generated by the phase imprinting method. Below the superfluid transition temperature, it appears as a dip in the density profile and becomes more pronounced when the temperature is lowered. Therefore the phase slip can provide direct evidence of the superfluid state. The condensation energy of the superfluid state can be extracted from the density profile of the phase slip, due to the unitary properties of the Fermi gas near the resonance. The width of the phase slip is inversely proportional to the square root of the difference between the transition temperature and the temperature. The signature of the phase slip in the density profile becomes more robust across the BCS-Bose-Einstein-condensate crossover.

Quantum optics experiments on “bright” beams are based on the spectral analysis of field fluctuations and typically probe correlations between radio-frequency sideband modes. However, the extra degree of freedom represented by this dual-mode picture is generally ignored. We demonstrate the experimental operation of a device which can be used to separate the quantum sidebands of an optical field. We use this device to explicitly demonstrate the quantum entanglement between the sidebands of a squeezed beam.

We discuss the semiclassical limit of the entanglement for the class of closed pure systems. By means of analytical and numerical calculations, we obtain two main results: (i) the short-time entanglement does not depend on Planck’s constant and (ii) the long-time entanglement increases as more semiclassical regimes are attained. On one hand, this result is in contrast with the idea that the entanglement should be destroyed when the macroscopic limit is reached. On the other hand, it emphasizes the role played by decoherence in the process of emergence of the classical world. We also found that, for Gaussian initial states, the entanglement dynamics may be described by an entirely classical entropy in the semiclassical limit.

We demonstrate a general scheme for manipulating atomic species by focusing ground state xenon atoms using large quasielectrostatic potentials created by high intensity $({10}^{12}\mathrm{W}∕{\mathrm{cm}}^2)$, nanosecond, pulsed optical fields. The atomic density in the focal region was mapped out with a resolution of $2\mu \mathrm{m}$ using resonantly enhanced multiphoton ionization of neutral atoms in the vicinity of the focus. Measurements of the transverse xenon velocity induced by the optical field, and the focal length of the atom-optical lens, are in good agreement with a quasielectrostatic model based on the static polarizablity of xenon.

Unimolecular rate theories and equilibrium models of cluster dissociation are reconciled through a kinetic Monte Carlo approach. Assuming that fragmentation occurs sequentially, we calculate the time-dependent boiling temperature of slowly heated, free atomic clusters. Our approach is supported by molecular dynamics simulations of clusters made of sodium atoms or ${\mathrm{C}}_{60}$ molecules, as well as simplified rate equations.

We show that the dispersion properties imposed by an external periodic potential ensure both energy and quasimomentum conservation such that correlated pairs of atoms can be generated by four wave mixing from a Bose-Einstein condensate moving in an optical lattice potential. In our numerical solution of the Gross-Pitaevskii equation, a condensate with initial quasimomentum $k_0$ is transferred almost completely $(>95\%)$ into a pair of correlated atomic components with quasimomenta $k_1$ and $k_2$, if the system is seeded with a smaller number of atoms with the appropriate quasimomentum $k_1$.

We generalize the concept of dark-state polariton in multilevel electromagnetically induced transparency systems. We show that the quantum states of light for the pulses can be mapped onto more than one collective atomic polarization states of the multilevel atomic system, which can act as a quantum state copier or divider. Such dark-state polaritons potentially have applications in quantum information processing.

We prove that any multiple-copy entanglement transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A 65, 052315 (2002)] can be implemented by a suitable entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)]. Furthermore, we show that the combination of multiple-copy entanglement transformation and the entanglement-assisted one is still equivalent to the pure entanglement-assisted one. The mathematical structure of multiple-copy entanglement transformations then is carefully investigated. Many interesting properties of multiple-copy entanglement transformations are presented, which exactly coincide with those satisfied by the entanglement-assisted ones. Most interestingly, we show that an arbitrarily large number of copies of state should be considered in multiple-copy entanglement transformations.

An algebraic analysis of Grover’s quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state $\mid \psi ⟩$ of $n$ qubits. This approach reveals the geometrical structure of the quantum search process, which turns out to be confined to a four-dimensional subspace of the Hilbert space. It unifies and generalizes earlier results on the time evolution of the amplitudes during the search, the optimal number of iterations, and the success probability. Furthermore, it enables a direct generalization to the case in which the initial state is a mixed state, providing an exact formula for the success probability.

Collisions between 98-keV ${\mathrm{N}}^{7+}$ ions and a HCl target have been investigated experimentally. The kinetic-energy distribution of fragment ${\mathrm{H}}^{+}$ ions originating from multiple electron capture was detected at angles in the range 20°–160° with respect to the incident beam direction. Proton energies as large as 100 eV were observed, and calculations made in the simple Coulomb explosion model suggest that up to seven target electrons may be involved during the collision. Using the Landau-Zener model, we show that the ${\mathrm{N}}^{7+}$ projectile mainly captures outer-shell electrons from HCl. From the experimental data we derived multiple-capture cross sections which we compared with results from a model calculation made using the classical over-barrier model and also with a semiempirical scaling law. For the specific case of double capture, several structures appeared, which were assigned using ab initio calculations to states of ${\mathrm{HCl}}^{2+}$.

The fluctuations of a number of particles in the Bose-Einstein condensate are studied in the grand canonical ensemble with an effective single-mode Hamiltonian, which is derived from an assumption that the mode corresponding to the Bose-Einstein condensate does not asymptotically correlate with other modes. The fluctuations are evaluated in the dilute limit with a proposed simple method, which is beyond the mean-field approximation. The accuracy of the latter is estimated; it is shown that the mean-field scheme does not work for the single-mode Hamiltonian, while for the Hartree Hamiltonian it allows us to estimate the condensate fluctuations up to a numerical factor. As a hypothesis, a formula is proposed that relates the fluctuations in the canonical ensemble with that of the grand canonical one.

We propose a scheme for the lithography of arbitrary, two-dimensional nanostructures via matter-wave interference. The required quantum control is provided by a $\pi ∕2\text{−}\pi \text{−}\pi ∕2$ atom interferometer with an integrated atom lens system. The lens system is developed such that it allows simultaneous control over the atomic wave-packet spatial extent, trajectory, and phase signature. We demonstrate arbitrary pattern formations with two-dimensional ${}^{87}\mathrm{Rb}$ wave packets through numerical simulations of the scheme in a practical parameter space. Prospects for experimental realizations of the lithography scheme are also discussed.

Motivated by a recent experiment [Chikkatur et al., Science, 296, 2193 (2002)] on the merging of atomic condensates, we investigate how two independent condensates with random initial phases can develop a unique relative phase when we move them together. In the adiabatic limit, the uniting of independent condensates can be understood from the eigenstate evolution of the governing Hamiltonian, which maps degenerate states (corresponding to fragmented condensates) to a single state (corresponding to a united condensate). In the nonadiabatic limit corresponding to the practical experimental configurations, we give an explanation on why we can still obtain a large condensate fraction with a unique relative phase. Detailed numerical simulations are then performed for the nonadiabatic merging of the condensates, which confirm our explanation and qualitative estimation. The results may have interesting implications for realizing a continuous atom laser based on the merging of condensates.