Spin asymmetry of ground states is studied in trapped spin-degenerate (two-component) gases of fermionic atoms with repulsive interaction between different components; and, for a large particle number, the asymmetric (collective ferromagnetic) states are shown to be stable because it can be energetically favorable to increase the Fermi energy of one component rather than increase the interaction energy between up-down components. We formulate the Thomas-Fermi equations and give algebraic methods to solve them. From the Thomas-Fermi solutions, we find three kinds of ground states in the finite system: (1) paramagnetic (spin-symmetric), (2) ferromagnetic (equilibrium), and (3) ferromagnetic (nonequilibrium) states. We present the density profiles and the critical atom numbers for these states obtained analytically, and, in ferromagnetic states, the spin asymmetries are shown to occur in the central region of the trapped gas, and increase with increasing particle number. Based on the obtained results, we discuss the experimental conditions and current difficulties in realizing the ferromagnetic states of the trapped atom gas, which should be overcome.

Molecular band spectra reveal a left-right symmetry for atoms [Van Hooydonk, Spectrochim. Acta A 56, 2273 (2000)]. Intra-atomic left-right symmetry points to antiatom states and, to make sense, this must also show in line spectra. H Lyman $\mathrm{ns}$ singlets show a mirror plane at quantum number $n_0=\frac{1}{2}\pi .$ A symmetry-breaking oscillator $(1\mathrm{}-\frac{1}{2}\pi {/n)}^2$ means that some of these n states are antihydrogenic. This view runs ahead of CERN’s antiproton decelerator project on antihydrogen.

By using an exact solution to the time-dependent Schrödinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source with energy below the barrier height, and for distances larger than the penetration length, the probability density exhibits a forerunner associated with a nontunneling process, which propagates in space at exactly the semiclassical group velocity. We show that the time of arrival of the maximum of the forerunner at a given fixed position inside the potential is exactly the traversal time $\tau .$ We also show that the spatial evolution of this transient pulse exhibits an invariant behavior under a rescaling process. This analytic property is used to characterize the evolution of the forerunner, and to analyze the role played by the time of arrival $3^{-1/2}\tau$ found recently by Muga and Büttiker [Phys. Rev. A 62, 023808 (2000)].

Well-known nuclear magnetic resonance experiments show that the time evolution according to (truncated) dipole-dipole interactions between n spins can be inverted by simple pulse sequences. Independent of n, the reversed evolution is only two times slower than the original one. Here we consider more general spin-spin couplings with long range. We prove that some are considerably more complex to invert since the number of required time steps and the slow-down of the reversed evolutions are necessarily of the order n. Furthermore, the spins have to be addressed separately. We show for which values of the coupling parameters the phase transition between simple and complex time-reversal schemes occurs.

We present a procedure for quantum teleportation in a nuclear spin quantum computer in which quantum logic gates are implemented by using selective electromagnetic pulses. A sequence of pulses is combined with single-spin measurements in the ${\sigma }^z$ basis for fast transfer of information in a spin quantum computer. We simulated this procedure for quantum teleportation in a nuclear spin chain with a large number (201) of spins. The systematic errors generated in the process of teleportation due to the non-resonant effects are analyzed in detail. We demonstrate that a $“2\pi k”$ method provides a significant reduction of errors.

Energies of ${2s}^2{2p}^5{3l3l}^{\prime }$ and ${2s2p}^6{3l3l}^{\prime }$ states for sodiumlike ions with $Z=14\mathrm{}–100$ are evaluated to second order in relativistic many-body perturbation theory starting from a neonlike Dirac-Fock potential. Second-order Coulomb and Breit interactions are included. Correction for the frequency dependence of the Breit interaction is taken into account in the lowest order. The Lamb shift correction to energies is also included in the lowest order. Intrinsic particle-particle-hole contributions to energies are found to be 20–30 % of the sum of one- and two-body contributions. Comparisons are made with available experimental data. These calculations are presented as a theoretical benchmark for comparison with experiment and theory.

The polarization of Lyman-β radiation, produced by electron-impact excitation of atomic hydrogen, has been measured over the extended energy range from near threshold to 1000 eV. Measurements were obtained in a crossed-beams experiment using a silica-reflection linear polarization analyzer in tandem with a vacuum ultraviolet monochromator to isolate the emitted line radiation. Our data are in excellent agreement with convergent close-coupling calculations over the entire energy range. The data are broadly similar to the earlier measurements of H Lyman-α polarization reported from the Jet Propulsion Laboratory.

The radiative recombination of an electron with H- and Li-like ${}^{238}\mathrm{U}$ in its ground state is studied. An experiment is proposed in which both the electron and the ion are polarized in the same direction, along or opposite to the initial electron momentum. Since, owing to the Pauli principle, the electron can be captured into the ground state of He- and Be-like uranium, respectively, only via a spin-flip transition, one may uniquely identify spin-flip transitions for arbitrary photon emission angles. The cross section of the process is calculated for a wide range of initial electron energies.

We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics, this Hamiltonian does not have a power expansion in the fields and the conversion length decreases with decreasing input power. We analyze the stationary wave-mixing process in the forward scattering configuration using an exact numerical analysis for up to ${10}^3$ input photons and compare the results with a mean-field approach. Due to quantum effects, complete conversion from the two pump fields into the signal and idler modes is achieved only asymptotically for large coherent pump intensities or for pump fields in few-photon Fock states. The signal and idler fields are perfectly quantum correlated which has potential applications in quantum communication schemes. We also discuss the implementation of a single-photon phase gate for continuous quantum computation.

For the special case of freely evolving Dirac electrons in $\mathrm{}(1+1)\mathrm{}$ dimensions, Feynman checkerboard paths have previously been used to derive Wigner’s arrival-time distribution which includes all arrivals. Here, an attempt is made to use these paths to determine the corresponding distribution of first-arrival times. Simple analytic expressions are obtained for the relevant components of the first-arrival propagator. These are used to investigate the relative importance of the first-arrival contribution to the Wigner arrival-time distribution and of the contribution arising from interference between first and later (i.e., second, third, etc.) arrivals. It is found that a distribution of (intrinsic) first-arrival times for a Dirac electron cannot in general be consistently defined using checkerboard paths, not even approximately in the nonrelativistic regime.

There have been recent suggestions for searching for the electron electric dipole moment, using solid state experiments with compounds containing ${\mathrm{Gd}}^{3+}$ ions. These experiments could improve the sensitivity compared to present atomic and molecular experiments by several orders of magnitude. The analysis of the problem requires a calculation of the enhancement coefficient K for the electron electric dipole moment in the ${\mathrm{Gd}}^{3+}$ ion. In the present work we perform this calculation. The result is $K\approx 6.4$ or $K\approx 3.3,$ depending on different assumptions on the ${\mathrm{Gd}}^{3+}$ excitation spectra. We formulate which quantities have to be measured and/or calculated to improve the accuracy.

In order to study multipartite quantum cryptography, we introduce quantities which vanish on product probability distributions, and which can only decrease if the parties carry out local operations or public classical communication. These “secrecy monotones” therefore measure how much secret correlation is shared by the parties. In the bipartite case we show that the mutual information is a secrecy monotone. In the multipartite case we describe two different generalizations of the mutual information, both of which are secrecy monotones. The existence of two distinct secrecy monotones allows us to show that in multipartite quantum cryptography the parties must make irreversible choices about which multipartite correlations they want to obtain. Secrecy monotones can be extended to the quantum domain and are then defined on density matrices. We illustrate this generalization by considering tripartite quantum cryptography based on the Greenberger-Horne-Zeilinger state. We show that before carrying out measurements on the state, the parties must make an irreversible decision about what probability distribution they want to obtain.

A continuous, analog version of the Grover algorithm is realized using NMR. The system studied is ${}^{23}\mathrm{Na}$ in a liquid-crystal medium. The presence of quadrupolar coupling makes the spin $I=3/2\mathrm{}$ nucleus a two-qubit system. Applying a specially designed pulse sequence, the time evolution of the spin-density operator is described in an interaction representation that has no external time-dependent radio-frequency fields. This approach is used to implement one instance of the continuous Grover search for the transform of a uniform state to a target state, and the implementation provides a clear physical interpretation of the algorithm. The experimental results are in good agreement with the theory.

We observed broadband emission spectra of Cs-He excimers $\left({\mathrm{Cs}}^{*}\mathrm{He}\right)$ in cold He gas $(1.3\mathrm{}–100\mathrm{K}),$ when Cs atoms were excited to the $6{}^{2}P$ states. We calculated the emission spectrum from each vibrational state of ${\mathrm{Cs}}^{*}\mathrm{He}$ using Pascale’s semiempirical Cs-He potential energy curves [J. Pascale, Phys. Rev. A $28,$ 632 (1983)], and compared the results with the observed spectra. From the measured spectral shape, we estimated the relative populations of the vibrational states of ${\mathrm{Cs}}^{*}\mathrm{He}$ at various He gas densities, and estimated the predissociation rate of ${\mathrm{Cs}}^{*}\mathrm{He}$ in the $A{}^2{\Pi }_{1/2}$ state. Moreover, a broadband emission spectrum of ${\mathrm{Cs}}^{*}{\mathrm{He}}_2$ was also observed, which was compared with that observed in liquid He.

The development of buffer-gas trapping and magnetized beam formation has provided positron beams with significantly improved energy resolution $(\Delta E<~0.025\mathrm{eV})$ compared to those available previously. Analysis techniques have been developed to take advantage of the fact that the beam is in a magnetic field of $\sim 0.1\mathrm{T}.$ This has enabled scattering experiments at lower energies and with significantly improved state selectivity for excitation experiments than had been possible previously. A detailed description of these techniques is presented. Data are presented for a variety of cross sections for scattering of positrons from atomic and molecular targets.

We calculate potential energy curves for heavy alkali-metal dimers, ${\mathrm{Rb}}_2$ and ${\mathrm{Cs}}_2$ in which one of the atoms is in a highly excited Rydberg states. The method combines numerical integration of coupled equations, describing interaction of electron with the ground-state atom in the field of the Coulomb core of the Rydberg atom, with subsequent matching of the obtained wave function with the Coulomb Green’s function in the form of the Kirchhoff integral. The spin-orbit interaction for the Rydberg electron is also included. The results show the existence of several groups of states. Most interesting of them are dominated either by the ${}^{3}S$ symmetry near the ground-state atom or by the ${}^3{P}_J$ symmetry, $J=0,1,2.\mathrm{}$ All states, except the ${}^3{P}_1$ state, exhibit oscillatory dependence of energy on the internuclear distance that can support long-range molecular Rydberg states [e.g., “trilobite states” for the ${}^{3}S$ symmetry, Greene et al., Phys. Rev. Lett. 85, 2458 (2000)]. These states possess large diagonal and transition dipole moments which are expressed analytically in terms of the Coulomb wave functions and calculated in a broad range of internuclear separations.

In recent work, the formation of ring-shaped electron distributions for hydrogen atoms in resonant static magnetic-laser fields has exclusively been associated with the impact of relativity. In this note we will generalize this statement and show that the nonlinearity associated with the nuclear binding force can trigger similarly shaped steady-state charge clouds in atoms under suitable conditions. The dephasing model, based on modeling the quantum-mechanical state by a classical ensemble of quasiparticles evolving with slightly different cyclotron periods, can recover features in the two lowest-order resonances as well as the Coulomb-field-induced charge distributions.

We study the effect of going beyond the Gross-Pitaevskii theory on the frequencies of collective oscillations of a trapped Bose gas in the large gas parameter regime. We go beyond the Gross-Pitaevskii regime by including a higher-order term in the interatomic correlation energy. To calculate the frequencies we employ the sum-rule approach of many-body response theory coupled with a variational method for the determination of ground-state properties. We show that going beyond the Gross-Pitaevskii approximation introduces significant corrections to the collective frequencies of the compressional mode.

We present a method for reducing the inhomogeneous frequency broadening in the hyperfine splitting of the ground state of optically trapped atoms. This reduction is achieved by the addition of a weak light field, spatially mode matched with the trapping field and whose frequency is tuned in between the two hyperfine levels. We experimentally demonstrate the new scheme with ${}^{85}\mathrm{Rb}$ atoms, and report a 50-fold narrowing of the rf spectrum.

We experimentally demonstrate the transformation from two-photon time entanglement to polarization entanglement using unbalanced interferometers. The polarization states of down-converted photon pairs from the interferometer depend on the path they have experienced. Therefore, the polarization entanglement is achieved by the coincidence measurement. We also show that our scheme can be used for the probabilistic manipulation of down-converted photon pairs and experimentally simulate an operation of quantum logic gate known as controlled-NOT gate. Availability of our method to the quantum information and the relation to the local realism are discussed.