Due to the no-cloning theorem, the unknown quantum state can only be cloned approximately or exactly with some probability. There are two types of cloners: universal and state-dependent cloner. The optimal universal cloner has been found and can be viewed as a special state-dependent quantum cloner that has no information about the states. In this paper, we investigate the state-dependent cloning when the state set contains more than two states. We get some bounds of the global fidelity for these processes. This method is not dependent on the number of the states contained in the state set. It is also independent of the numbers of copying.

For a system of indistinguishable fermions with pairwise interactions, we consider renormalized, perturbative expansions for the three- and four-particle propagators (Green’s functions) in terms of exact one-particle propagators, along with a pair interaction that may be bare (as it appears in the Hamiltonian) or dressed (polarized). Care is taken to provide a rigorous foundation for the diagrammatic representations of these perturbation series; in particular, it is demonstrated how each topologically distinct diagram represents an embedding (in three-dimensional space) of numerous separate terms in the perturbation series. Within a renormalized ladder approximation for the three- and four-particle propagators, we derive diagram weights (which differ from the two-particle diagram weights) in order to limit the perturbation series to topologically distinct, permutationally independent diagrams. These results lay the foundation for perturbative approximations that decouple the propagator and density matrix equations of motion.

A nonperturbative approach to the description of spectral line shapes of Ly-α radiation produced by multicharge ion-pair collisions is proposed. A closed expression that describes the central part of the line as well as the wings with an oscillation structure due to the extremum in the difference between the potential-energy curves has been obtained. It has been found that the exchange interaction leads to the formation of two satellites in the red and blue wings of the Ly-α perpendicular transitions.

The transformation introduced by Giusti-Suzor and Fano, and extended by Lecomte and Ueda, for the study of resonance structures in the multichannel quantum-defect theory (MQDT) is used to reformulate MQDT into the forms having one-to-one correspondence with those in Fano’s configuration mixing (CM) theory of resonance for the photofragmentation processes involving one closed and many open channels. The reformulation thus allows MQDT to have the full power of the CM theory, still keeping its own strengths such as the fundamental description of resonance phenomena without an assumption of the presence of a discrete state as in CM.

The existence of Young-type interference patterns, recently measured [N. Stolterfoht et al., Phys. Rev. Lett. 87, 023201 (2001)] in double-differential cross sections for single-electron ionization of ${\mathrm{H}}_2$ molecules by ion impact, is theoretically supported by calculations obtained using a molecular distorted-wave model introduced here. The importance of adequately describing the target as a molecule is emphasized. The contributions from direct and interference terms are separated.

The excitation of a two-level dipolar $\left(d\ne 0\right)$ molecule with two Gaussian pulsed lasers is examined theoretically for the case where one laser’s frequency is tuned close to the energy level separation (pump laser) while the second laser’s frequency is extremely small (probe laser). The final excited state populations are shown to depend on the probe laser’s absolute carrier phase while remaining independent of the pump laser’s absolute carrier phase. They do not depend on the relative phase difference between the two laser fields as in many other pump-probe scenarios. The absolute carrier-phase effect is negligible for nondipolar $\mathrm{}(d=0\mathrm{})\mathrm{}$ molecules. The probe laser absolute carrier-phase effect arises through the coherent excitation of multiple optical paths from the initial to the final state containing a common number of pump photons ${(N}_{\mathrm{pump}}=1)$ and a varying number of probe photons. Excited state populations, after the interaction of the pulses with the molecule is complete, are examined as a function of the probe laser’s absolute carrier phase for varying field strengths, frequencies, and pulse durations in order to verify the source of the probe laser absolute carrier-phase effect and to determine the conditions needed to most readily detect it.

The paper studies Bloch oscillations of cold neutral atoms in the optical lattice. The effect of spontaneous emission on the dynamics of the system is analyzed both analytically and numerically. The spontaneous emission is shown to cause (i) the decay of Bloch oscillations with the decrement given by the rate of spontaneous emission and (ii) the diffusive spreading of the atoms with a diffusion coefficient depending on both the rate of spontaneous emission and the Bloch frequency.

Motivated by recent experiments on trapped ultracold bosonic atoms in an optical lattice potential, we consider the nonequilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a “π phase” imprint on a superfluid ground state (i.e., the initial phases of neighboring wells differ by π), and discuss the subsequent appearance of the density wave order and “Schrödinger cat,” i.e., macroscopic quantum interference, states.

We study the interaction of dark solitons with a localized impurity in Bose-Einstein condensates. We apply the soliton perturbation theory developed earlier in optics for describing the soliton dynamics and soliton-impurity interaction analytically, and then verify the results by direct numerical simulations of the Gross-Pitaevskii equation. We find that a dark soliton can be reflected from or transmitted through a repulsive impurity in a controllable manner, while near the critical point the soliton can be quasitrapped by the impurity. Additionally, we demonstrate that an immobile soliton may be captured and dragged by an adiabatically moving attractive impurity.

We theoretically study the focusing of atoms using strongly localized light pulses. It is shown that when inhomogenously polarized light is focused at high angular apertures, one may obtain useful potentials for atom focusing. Here we analyze the case of pulsed light potentials for red- and blue-detuned focusings of atoms. In particular, we show that the atomic beam aperture must be stopped considerably down in order to reduce the sidelobes of the atomic density, which is similar to the situation often encountered in conventional optics. It is suggested that an annular aperture in front of the atomic beam could be useful for increasing the resolution, at the cost of a lower atomic density.

The structure and stability of various vortices in $F=1\mathrm{}$ spinor Bose-Einstein condensates are investigated by solving the extended Gross-Pitaevskii equation under rotation. We perform an extensive search for stable vortices, considering both axisymmetric and nonaxisymmetric vortices and covering a wide range of ferromagnetic and antiferromagnetic interactions. The topological defect called the Mermin-Ho (Anderson-Toulouse) vortex is shown to be stable for the ferromagnetic case. The phase diagram is established in a plane of external rotation $\Omega$ versus total magnetization M by comparing the free energies of possible vortices. It is shown that there are qualitative differences between axisymmetric and nonaxisymmetric vortices which are manifested in the $\Omega$ and M dependences.

Ab initio theory is developed for energies of $J=1\mathrm{}$ particle-hole states of neutral neon and for oscillator strengths of transitions from such states to the $J=0\mathrm{}$ ground state. Hole energies of low-Z neonlike ions are evaluated.

We have observed the formation of ground-state ${\mathrm{Na}}_2$ molecules via the spontaneous decay of excited molecules created by the photoassociation of ultracold atoms. We measure the binding energies of molecules created in three hyperfine components of the lowest singlet and triplet potentials of ${\mathrm{Na}}_2$ by two different methods. Two of the features are purely triplet a ${}^3{\Sigma }_u^{+}$ $\mathrm{}(v=15\mathrm{})\mathrm{}$ (quasibound) states that have not been previously observed, while the third is a mixed X ${}^1{\Sigma }_g^{+}–a$ ${}^3{\Sigma }_u^{+}$ state. The molecules are detected with high-resolution cw laser ionization techniques and binding energies are measured to within 10 MHz.

The problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons is presented. The recently developed method of quasiadiabatic time evolution is used to obtain a nonperturbative analysis. When applied to the standard vector potential coupling, an exact auxiliary equation is obtained that is in the electric dipole coupling form. This is achieved through application of the Goeppert-Mayer gauge. While the analysis to this point is general and aimed at microwave irradiation of Rydberg atoms, a Floquet analysis of the auxiliary equation is presented for the special case of the periodically driven harmonic oscillator. Closed form expressions for a complete set of Floquet states are obtained. These are used to demonstrate that for the oscillator case there are no multiphoton resonances.

Magneto-optic and magnetostatic trapping is realized near a surface using current carrying coils wrapped around magnetizable cores, with up to ${10}^9$ cesium atoms. Ramping up the current while maintaining optical dissipation leads to tightly confined atom clouds with an aspect ratio of 1:1000. We study the three-dimensional character of the magnetic potential and characterize the atom number and density as functions of the applied current. The field gradient in the transverse dimension has been varied from $<10\mathrm{}\mathrm{G}/\mathrm{c}\mathrm{m}$ to $>1\mathrm{}\mathrm{k}\mathrm{G}/\mathrm{c}\mathrm{m}.$

The recently developed time-independent effective linear two-body method [J. Phys. B: At., Mol. Opt. Phys. 33, 55 (2000)] has been generalized for time-dependent traps. The method is used to describe the dynamics of trapped Bose-Einstein condensates beyond the Thomas-Fermi regime. The calculated aspect ratios after ballistic expansion are found to be in good agreement with experimental data obtained recently by Görlitz et al. [Phys. Rev. Lett. 87, 130402 (2001)].

Magnetically trapped atoms in Bose-Einstein condensates are spin polarized. Since the magnetic field is inhomogeneous, the atoms acquire Berry phases of the Aharonov-Bohm type during adiabatic motion. In the presence of an electric field, there is an additional Aharonov-Casher effect. Taking into account the limitations on the strength of the electric fields due to the polarizability of the atoms, we investigate the extent to which these effects can be used to induce rotation in a Bose-Einstein condensate.

We study the ground state of the rotating spinor condensate and show that for slow rotation the ground state of the ferromagnetic spinor condensate is a coreless vortex. While the coreless vortex is not topologically stable, we show that there is an energetic threshold for the creation of a coreless vortex. This threshold corresponds to a critical rotation frequency that vanishes as the system size increases. Also, we demonstrate the dramatically different behavior of the spinor condensate with the antiferromagnetic interactions. For antiferromagnetic spinor condensate the angular momentum as a function of rotation frequency exhibits the familiar discrete staircase behavior, but in contrast to an ordinary condensate the first step is to the state with angular momentum of $1/2$ per particle.

In this paper the behavior of matter waves in suddenly terminated potential structures is investigated numerically. It is shown that there is no difference between a fully quantum mechanical treatment and a semiclassical one with regards to energy redistribution. For the quantum case it is demonstrated that there can be substantial reflection at the termination. The neglect of backscattering by the semiclassical method brings about major differences in the case of low kinetic energies. A simple phenomenological model is shown to partially explain the observed backscattering using dynamics of reduced dimensionality.

A fast rotating Bose-Einstein condensate confined in a quadratic-plus-quartic potential is found to dynamically generate a “giant vortex” that absorbs all phase singularities into a central low density hole, thereby sustaining a quasi-one-dimensional circular superflow at a supersonic speed.