We present experiments with Bose-Einstein condensates on a combined atom chip. The combined structure consists of a large-scale “carrier chip” and smaller “atom-optics chips,” containing micron-sized elements. This allows us to work with condensates very close to chip surfaces without suffering from fragmentation or losses due to thermally driven spin flips. Precise three-dimensional positioning and transport with constant trap frequencies are described. Bose-Einstein condensates were manipulated with submicron accuracy above atom-optics chips. As an application of atom chips, a direction sensitive magnetic-field microscope is demonstrated.

Both unitary evolution and the effects of dissipation and decoherence for a general three-level system are of wide interest in quantum optics, molecular physics, and elsewhere. A previous paper presented a technique for solving the time-dependent operator equations involved but under certain restrictive conditions. We now extend our results to a general three-level system with arbitrary time-dependent Hamiltonians and Lindblad operators. Analytical handling of the SU(3) algebra of the eight operators involved leaves behind a set of coupled first-order differential equations for classical functions. Solution of this set gives a complete solution of the quantum problem, without having to invoke rotating-wave or other approximations. Numerical illustrations for multiphoton couplings and quantum control are given.

Partial $4d$ photoionization cross sections have been calculated for atomic barium including a polarization potential to evaluate the effects of core polarization. Results of three theoretical models are compared: (i) the relativistic random-phase approximation, (ii) the relativistic random-phase approximation modified to include relaxation, and (iii) the relativistic random-phase approximation modified to include relaxation and core polarization. Theory is also compared with photoelectron spectroscopy measurements. The inclusion of both relaxation and polarization effects in the calculations greatly improves agreement with experiment.

We investigate how superpositions of motional coherent states naturally arise in the dynamics of a two-level trapped ion coupled to the quantized field inside a cavity. We extend our considerations, including a more realistic setup where the cavity is not ideal and photons may leak through its mirrors. We found that a detection of a photon outside the cavity would leave the ion in a pure state. The statistics of the ionic state still keeps some interference effects that might be observed in the weak-coupling regime.

We present a technique to identify exact analytic expressions for the multiquantum eigenstates of a linear chain of coupled qubits. A choice of Hilbert subspaces is described that allows an exact solution of the stationary Schrödinger equation without imposing periodic boundary conditions and without neglecting end effects, fully including the dipole-dipole nearest-neighbor interaction between the atoms. The treatment is valid for an arbitrary coherent excitation in the atomic system, any number of atoms, any size of the chain relative to the resonant wavelength and arbitrary initial conditions of the atomic system. The procedure we develop is general enough to be adopted for the study of excitation in an arbitrary array of atoms including spin chains and one-dimensional Bose-Einstein condensates.

The robustness of the local adiabatic quantum search to decoherence in the instantaneous eigenbasis of the search Hamiltonian is examined. We demonstrate that the asymptotic time complexity of the ideal closed case is preserved, as long as the Hamiltonian dynamics is present. In the special case of pure decoherence where the environment monitors the search Hamiltonian, it is shown that the local adiabatic quantum search performs as the classical search.

The strong-field ionization in a number of light homonuclear diatomic molecules (${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{H}}_2$) irradiated by an intense laser field of low fundamental frequency $\omega ⪡I_p$ is considered theoretically and studied numerically compared to their “companion” atoms, having nearly identical ionization potential $I_p$. The background applied strong-field approach is based on using the $S$-matrix formalism of conventional strong-field approximation supplemented by the standard linear combination of atomic orbitals and molecular orbitals method utilized for approximate analytical reproduction of the two-centered wave function of an initial molecular bound state. Accordingly, the ionization of a diatomic molecule is described as a quantum-mechanical superposition (intramolecular interference) of contributions from ionization amplitudes corresponding to photoelectron emission from two atomic centers separated by equilibrium internuclear distance. Besides the bonding (or antibonding) symmetry of the highest occupied molecular orbitals (HOMO) corresponding to the outermost molecular valence shell, its spatial configuration and predominant orientation with respect to the internuclear axis and polarization of incident laser field also proved to be of substantial importance and, thus, are taken into equally detailed consideration. Moreover, wherever appropriate, the comparable contributions from other (inner) molecular valence shells of a larger binding energy (closest to that of HOMO, but of different bonding symmetry and spatial configuration) are additionally taken into account. The related results for calculated differential and/or integral molecular ionization rates, molecular photoelectron spectra, and angular distributions are fairly well consistent with available experimental data and, in particular, provide one with a transparent physical interpretation of the nature and origin of high suppression in ionization of the ${\mathrm{O}}_2$ molecule (as compared to its companion Xe atom) as well as no suppression in ionization of ${\mathrm{N}}_2$ molecules (as compared to its companion Ar atom).

The Jaynes-Cummings model (JCM) is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight [Ann. Phys. 186, 381 (1988)] of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e., where the rate of change of the two are anticorrelated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anticorrelation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix.

We show that it is impossible to create a two-dimensional static electric field $\vec{E}$ with a local minimum in $E^2$ at a point in space for which $\vec{E}\ne 0$. This fact may have consequences in the design of state selectors and guides of slow-moving molecules.

We present an experimental method to engineer arbitrary pure states of qudits with $d=3,4$ using linear optics and a single nonlinear crystal.

It is demonstrated that in a one-dimensional Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field, a stimulated wave of flipped spins can be triggered by a flip of a single spin. This analytically solvable model illustrates mechanisms of quantum amplification and quantum measurement.

The question whether the velocity of the projectile and that of the electrons at the maximum of the ECC (electron capture to the continuum) cusp are equal is analyzed by means of classical mechanical calculations. The analysis is made for collisions of 20 keV protons with He atoms. Our theoretical results as well as experimental data do not support the large energy shift of the ECC cusp observed recently by Shah et al. [Phys. Rev. A 67, 010704(R) (2003)].

First-principles calculations on stoichiometric ${\mathrm{Mo}}_n{\mathrm{S}}_{2n}$ and ${\mathrm{W}}_n{\mathrm{S}}_{2n}(n=1\text{–}8)$ clusters show that their lowest energy atomic structures are dominated by a central core of metal atoms while the S atoms cap this core. We discuss in detail terminal, edge, and face capping of tetrahedral and octahedral Mo clusters by sulfur atoms for off-stoichiometric compositions also. Capping on the terminal sites is found to be least favorable. Edge capped ${\mathrm{Mo}}_4{\mathrm{S}}_6$ and face capped ${\mathrm{Mo}}_6{\mathrm{S}}_8$ clusters have high symmetries and high stability among all the clusters we have studied. We find that magnetic isomers are lowest in energy for some clusters though bulk $M{\mathrm{S}}_2$ ($M=\mathrm{Mo}$ and W) is nonmagnetic. Our results on ${\mathrm{Mo}}_6{\mathrm{S}}_{8+p}(p=0\text{–}6)$ clusters further show that ${\mathrm{Mo}}_6{\mathrm{S}}_{12}$ is magic with $4{\mu }_B$ magnetic moment. The origin of magnetism and bonding nature in these clusters is discussed. Our finding could lead to the possibility of magnetic clusters of a variety of nonmagnetic transition-metal compounds and their interesting assemblies.

Severe deviations from uniform Coulomb explosion can be manifested for extremely ionized molecular heteroclusters, due to kinematic effects. We established unique features of the spatial distribution, energetics, and time-resolved dynamics in Coulomb explosion of multicharged light-heavy heteroclusters, consisting of light, low-charge and heavy, high-charge, ions, e.g., hydroiodic acid ${\left(H^{+}{I}^{q_I+}\right)}_n$ and its isotopic substituents ${\left(D^{+}{I}^{q_I+}\right)}_n$ and ${\left(T^{+}{I}^{q_I+}\right)}_n$, where extreme multielectron ionization in ultraintense laser fields (peak intensity $I={10}^{17}–{10}^{20}\mathrm{W}{\mathrm{cm}}^{-2}$) results in $q_I=25$ at $I={10}^{19}$ and $q_I=35$ at $I={10}^{20}\mathrm{W}{\mathrm{cm}}^{-2}$. Electrostatic models and simulations, based on the cluster vertical ionization (CVI) initial conditions for Coulomb explosion of ${\left(D^{+}{I}^{q_I+}\right)}_{2171}$ and ${\left(H^{+}{I}^{q_I+}\right)}_{2171}$ ions with $q_I=25$ (corresponding to $I={10}^{19}\mathrm{W}{\mathrm{cm}}^{-2}$), reveal expanding, thin, two-dimensional spherical shells of the light $D^{+}$ or $H^{+}$ ions, with the monolayer expansion occurring on the femtosecond time scale. Under initial CVI conditions the model and the simulation results for the formation of femtosecond expanding nanoshells of light ions were confirmed by complete simulations involving both electron and nuclear dynamics in ${\left(HI\right)}_{2171}$ and ${\left(\mathrm{DI}\right)}_{2171}$ clusters subjected to a Gaussian laser pulse with $I={10}^{19}\mathrm{W}{\mathrm{cm}}^{-2}$. The energetic data for the light ions reveal high energies with a narrow energy distribution, e.g., average energy $E_{\mathit{av}}=23\mathrm{keV}$ at width $\Delta E∕E_{\mathit{av}}=0.16$ for Coulomb explosion of ${\left(D^{+}{I}^{q_I+}\right)}_{2171}$ clusters. These dynamic, structural and energetic data for light–heavy ${\left(A^{+}{I}^{q_I+}\right)}_n$ heteroclusters ($A=H$, $D$, and $T$) arise from kinematic overrun effects of the $A^{+}$ ions. Finally, we address the implications of these Coulomb explosion results of ${\left(D^{+}{I}^{q_I+}\right)}_n$ heteroclusters for $dd$ nuclear fusion driven by heterocluster Coulomb explosion, where the extremely charged $I^{q_I+}$ ions serve as most effective energetic and kinematic triggers for driving the expanding $D^{+}$ ions.

We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths that can be traversed adiabatically we also derive a differential equation which specifies the time dependence of the system parameters, for which transitions between distinct energy levels can be neglected. We also generalize the well-known geometric connections to the case of adiabatic paths containing arbitrarily many level-crossing points and degenerate levels.

We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped Bose-Einstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The simulations reveal previously unknown dynamical features of the vortex nucleation process, in which the condensate undergoes a strongly turbulent stage and the penetrating vortex lines vibrate rapidly. The vibrations arise from spontaneous excitation of Kelvin waves on the protovortices during a surface wave instability, caused by an inhomogeneity of the condensate density along the elongated axial direction.

A scheme of optical polarization modulation of a linearly polarized infrared probe field is studied in a degenerate four-level Yb atomic system. We have observed an anomalous transmission spectra of two circular polarization components of the probe field exhibiting an enhanced two-photon absorption and a three-photon gain with comparable magnitude, leading to the lossless transmission and enhanced circular dichroism. We carried out a proof-of-principle experiment of fast optical polarization modulation in such a system by modulating the polarization state of the coupling field. The observed enhanced two-photon absorption and three-photon gain of the probe field are due to the result of competing atomic coherence effects.

We propose how to generate macroscopic quantum superposition states using a microwave cavity containing a superconducting charge qubit. Based on the measurement of charge states, we show that the superpositions of two macroscopically distinguishable coherent states of a single-mode cavity field can be generated by a controllable interaction between a cavity field and a charge qubit. After such superpositions of the cavity field are created, the interaction can be switched off by the classical magnetic field, and there is no information transfer between the cavity field and the charge qubit. We also discuss the generation of the superpositions of two squeezed coherent states.

The molecular dianion $\mathrm{Li}{{\mathrm{F}}_3}^{2-}$ has been observed using accelerator mass spectrometry (AMS). This confirms the theoretical prediction that the lifetimes of the lowest vibrational states are at least long enough, greater than ${10}^{-5}\mathrm{s}$, for the dianion to be observed in mass spectrometers. The observed weakness of this dianion, compared with heavier dianions, also supports the detailed theoretical prediction that $\mathrm{Li}{{\mathrm{F}}_3}^{2-}$ has about one thousand times fewer vibrational states than the heavier dianion $\mathrm{Be}{{\mathrm{F}}_4}^{2-}$, which is readily observed. The relative intensity of $\mathrm{Li}{{\mathrm{F}}_3}^{2-}$ versus $\mathrm{Li}{{\mathrm{F}}_2}^{-}$, produced from a ${\mathrm{Cs}}^{+}$ sputter ion source on targets made of compressed ${}^6\mathrm{Li}\mathrm{F}$ and Ag powders, was estimated to be near $5\times {10}^{-13}$ under $27.5\mathrm{keV}{\mathrm{Cs}}^{+}$ bombardment at near $10\mu \mathrm{A}$ ion current. In addition, the ion $\mathrm{Li}{{\mathrm{F}}_3}^{-}$, with one fluorine atom above the superhalide anion $\mathrm{Li}{{\mathrm{F}}_2}^{-}$, could not be observed. The ratio of $\mathrm{Li}{{\mathrm{F}}_3}^{-}$ to $\mathrm{Li}{{\mathrm{F}}_2}^{-}$ was found to be below ${10}^{-8}$. The reasons why the $\mathrm{Li}{{\mathrm{F}}_3}^{2-}$ dianion has been difficult to observe are discussed briefly.