We construct a model which describes a recently performed experiment [Phys. Rev. A 64, 050301(R) (2001)] in which an entangled state between two modes of a single cavity is built. Environmental effects are taken into account and the results agree with the experimental findings. Moreover, the model predicts, for different conditions of the same experiment, a decoherence-free subspace. These conditions are analyzed and slightly different experiments suggested in order to test its viability.

Atomic wave packets are coherently split into two components evolving on different adiabatic potentials of a near-resonant gray optical lattice. The components follow separated paths and overlap periodically. Wave-packet interference is observed at times when the components overlap. The wave-packet splitting and recombination mechanisms are quantum projection and nonadiabatic coupling. Experimental results are in agreement with the results of a detailed theoretical model.

A trapped degenerate Bose gas exhibits superfluidity with spatially nonuniform superfluid density. We show that the vortex distribution in such a highly inhomogeneous rotating superfluid is nevertheless nearly uniform. The inhomogeneity in vortex density, which diminishes in the rapid-rotation limit, is driven by the discrete way vortices impart angular momentum to the superfluid. This effect favors the highest vortex density in regions where the superfluid density is most uniform (e.g., the center of a harmonically trapped gas). A striking consequence of this is that the boson velocity deviates from a rigid-body form exhibiting a radial-shear flow past the vortex lattice.

It is well known that optical nonlinearities are extremely weak at the quantum, or single-photon, level. This has been one of the major difficulties for optical implementations of universal, scalable quantum computation. Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] showed, among other things, that one could perform the elusive two-qubit logic gates with only linear-optical elements if one also uses extra single photons and measurement. In this work, we apply linear-optics techniques to produce effects in few-photon beams that are more familiar to strong-field nonlinear optics. Specifically, we show that these methods are sufficient to change the spatial (or temporal) properties of a light beam with strong dependence on its constituent number of photons; such phenomena cannot occur via linear optics alone.

Complete sets of commuting observables (CSCOs) of the form ${\Sigma }_N={\Pi }_{i=1}^N{\sigma }_{i{\alpha }_i}({\alpha }_i=x,y,z)$ for an $N$-qubit system are extracted by a simple graphic approach. One can construct $2\times 3^N$ sets of operators, each set consisting of $K_N$ commuting ${\Sigma }_N$, $K_N=2^{N-1}+1$ for even $N$, and $2^{N-1}$ for odd $N$. Any $N$ functional-independent operators among the $K_N$ operators may be adopted as a CSCO, whose simultaneous eigenstates (SEs) span an orthonormal basis of $N$-qubit space. These SEs have reduced density matrix of rank 2 and can be reduced to the Greenberger-Horne-Zeilinger (GHZ) state form of Eq. (2) in suitable representations. The all-versus-nothing demolition of the elements of reality holds for each basis of the form of Eq. (2) for $N$-qubit $\left(N⩾3\right)$ systems. ${\Sigma }_N$ may be considered as the infinitesimal operator of rotational operator $R({\alpha }_1,{\alpha }_2,\dots {\alpha }_N)={\Pi }_{i=1}^N\exp \left[-i\pi {\sigma }_{i{\alpha }_i}∕2\right]$ , whose eigenvalue (signature) $r=e^{-i\pi \alpha }$, or signature exponent $\alpha$, may be equivalently used for characterizing each basis.

A system consisting of two neutral spin-1/2 particles is analyzed for two magnetic field perturbations: (1) an inhomogeneous magnetic field over all space, and (2) external fields over a half space containing only one of the particles. The field is chosen to point from one particle to the other, which results in essentially a one-dimensional problem. A number of interesting features are revealed for the first case: the singlet, which has zero potential energy in the unperturbed case, remains unstable in the perturbing field. The spin-zero component of the triplet evolves into a bound state with a double well potential, with the possibility of tunneling. Superposition states can be constructed which oscillate between entangled and unentangled states. For the second case, we show that changes in the magnetic field around one particle affect measurements of the spin of the entangled particle not in the magnetic field nonlocally. By using protective measurements, we show it is possible in principle to establish a nonlocal interaction using the two particles, provided the dipole-dipole potential energy does not vanish and is comparable to the potential energy of the particle in the external field.

We consider an ensemble of trapped atoms interacting with a continuous-wave laser field. For sufficiently polarized atoms and for a polarized light field, we may approximate the nonclassical components of the collective spin angular momentum operator for the atoms and the Stokes vectors of the field by effective position and momentum variables for which we assume a Gaussian state. Within this approximation, we present a theory for the squeezing of the atomic spin by polarization rotation measurements on the probe light. We derive analytical expressions for the squeezing with and without inclusion of the noise effects introduced by atomic decay and by photon absorption. The theory is readily adapted to the case of inhomogeneous light-atom coupling [A. Kuzmich and T.A.B. Kennedy, Phys. Rev. Lett. 92, 030407 (2004)]. As a special case, we show how to formulate the theory for an optically thick sample by slicing the gas into pieces, each having only small photon absorption probability. Our analysis of a realistic probing and measurement scheme shows that it is the maximally squeezed component of the atomic gas that determines the accuracy of the measurement.

Electrostatic and dispersive interactions of polarizable molecules are expressed in terms of generalized (nonretarded) charge-density response functions of the isolated molecules, which in turn are expanded using the collective electronic oscillator (CEO) eigenmodes of linearized time-dependent density-functional theory. Closed expressions for the intermolecular energy are derived to sixth order in charge fluctuation amplitudes.

A connectivity analysis of controlled quantum systems assesses the feasibility of a field existing that can transfer at least some amplitude between any specified pair of states. Although Hamiltonians with special structure or symmetry may not produce full connectivity, it is argued and demonstrated that virtually any Hamiltonian is expected to be connected. The connectivity of any particular system is generally revealed in the quantum evolution over a single or at most a few time steps. A connectivity analysis is inexpensive to perform and it can also identify statistically significant intermediate states linking a specified initial and final state. These points are illustrated with several simple systems. The likelihood of an arbitrary system being connected implies that at least some product yield can be expected in the laboratory for virtually all systems subjected to a suitable control.

The accuracy of classical trajectory Monte Carlo treatments of electron capture is studied, by focusing on collisions on $\mathrm{H}\left(1s\right)$ targets by ${\mathrm{Li}}^{3+}$ and ${\mathrm{Ne}}^{10+}$ projectiles, treated in a separate paper. We examine how the choice of the initial distribution, and the partition of phase space usually employed to calculate partial cross sections, influence the accuracy of the method. With respect to the former, an improvement over the single-microcanonical choice is advisable, but further refinements based on the electron density are not worthwhile. Regarding the latter, we illustrate the accuracy of the “binning” method for $n>2$. We show that classical and semiclassical mechanisms are essentially the same, although at low velocities the method is unable to describe the fall of the cross section.

Theoretical calculations and experimental crossed-beam measurements are compared for electron-impact single ionization of ${\mathrm{Bi}}^{q+}$ for $q=1–10$. The configuration-average distorted-wave calculations include both direct ionization and indirect excitation-autoionization contributions. For ${\mathrm{Bi}}^{2+}$ it is necessary to account for levels within an excited configuration that straddle the ionization threshold. This was included via level-resolved atomic structure calculations, from which statistical partitions of the configuration-averaged cross sections could then be made. Evidence is found for ionization contributions from an excited configuration in ${\mathrm{Bi}}^{3+}$ and ${\mathrm{Bi}}^{5+}$. Good agreement is found between theory and experiment for all the ionization stages of Bi studied.

The translational motion of molecular ions can be effectively cooled sympathetically to translational temperatures below $100\mathrm{mK}$ in ion traps through Coulomb interactions with laser-cooled atomic ions. The rovibrational degrees of freedom, however, are expected to be largely unaffected during translational cooling. We have previously proposed schemes for cooling of the internal degrees of freedom of such translationally cold but internally hot heteronuclear diatomic ions in the simplest case of ${}^1\Sigma$ electronic ground-state molecules. Here we present a significant simplification of these schemes and make a generalization to the most frequently encountered electronic ground states of heteronuclear molecular ions: ${}^1\Sigma$, ${}^2\Sigma$, ${}^3\Sigma$, and ${}^2\Pi$. The schemes are relying on one or two laser-driven transitions with the possible inclusion of a tailored incoherent far-infrared radiation field.

We calculate the effect of the interaction between an optically active material and a Bose-Einstein condensate on the collective oscillations of the condensate. We provide explicit expressions for the frequency shift of the center-of-mass oscillation in terms of the potential generated by the substrate and of the density profile of the gas. The form of the potential is discussed in detail and various regimes (van der Waals–London, Casimir-Polder, and thermal regimes) are identified as a function of the distance of atoms from the surface. Numerical results for the frequency shifts are given for the case of a sapphire dielectric substrate interacting with a harmonically trapped condensate of ${}^{87}\mathrm{R}\mathrm{b}$ atoms. We find that at distances of $4–8\mu \mathrm{m}$, where thermal effects become visible, the relative frequency shifts produced by the substrate are of the order ${10}^{-4}$ and hence accessible experimentally. The effects of nonlinearities due to the finite amplitude of the oscillation are explicitly discussed. Predictions are also given for the radial breathing mode.

We demonstrate that a triangular optical lattice of two atomic species, bosonic or fermionic, can be employed to generate a variety of spin-$1∕2$ Hamiltonians. These include effective three-spin interactions resulting from the possibility of atoms tunneling along two different paths. Such interactions can be employed to simulate particular one- or two-dimensional physical systems with ground states that possess a rich structure and undergo a variety of quantum phase transitions. In addition, tunneling can be activated by employing Raman transitions, thus creating an effective Hamiltonian that does not preserve the number of atoms of each species. In the presence of external electromagnetic fields, resulting in complex tunneling couplings, we obtain effective Hamiltonians that break chiral symmetry. The ground states of these Hamiltonians can be used for the physical implementation of geometrical or topological objects.

We find a set of different orthonormalized states of a nonstationary harmonic oscillator and use them to expand the solution of the Gross-Pitaevskii equation with harmonic potential. The expansion series describes wave-packet trains of a Bose-Einstein condensate, which may be induced initially by the modulational instability. The center of any wave-packet train oscillates like a classical harmonic oscillator of frequency $\omega$. The width and height of the wave packet and the distance between two wave packets change simultaneously like an array of breathers with frequency $2\omega$. We demonstrate analytically and numerically that for a set of suitable parameters the wave-packet trains can be more exactly fitted to the matter-wave soliton trains observed by Strecker et al. and reported in Nature (London) 417, 150 (2002).

We propose a method using “light storage” and fractional stimulated Raman adiabatic passage (F-STIRAP) to get entangled multiple Fock states from a single photon. A light storage technique is used to store the quantum information of a single-photon pulse in atoms. F-STIRAP pulses then split the stored coherence, such that reading pulses retrieve the quantum information from this new coherence. Since each reading pulse only retrieves part of the total coherence, we can obtain entangled multiple Fock states with arbitrary relative amplitude. This method to create entanglement is versatile for obtaining frequency, time, and∕or spatial entanglement. Indeed, we obtain a multiple beam splitter with easily adjustable parameters.

We propose a scheme for teleporting an unknown atomic state in cavity QED. Our scheme does not involve the Bell-state measurement. During the interaction between atom and cavity, the cavity is only virtually excited and thus the scheme is insensitive to the cavity field states and cavity decay. The idea can also be used in the case of teleporting an unknown atomic entangled state.

It is shown that the order property of pure bipartite states under stochastic local operations and classical communications (SLOCC) changes radically when dimensionality shifts from finite to infinite. In contrast to finite-dimensional systems where there is no pure incomparable state, the existence of infinitely many mutually SLOCC incomparable states is shown for infinite-dimensional systems even under the bounded energy and finite information exchange condition. These results show that the effect of the infinite dimensionality of Hilbert space, the “infinite workspace” property, remains even in physically relevant infinite-dimensional systems.

We consider the entanglement of spins for two electrons contributing to the acoustoelectric current driven by a surface acoustic wave (SAW) in two adjacent narrow channels by calculating their exchange energy $\left(J\right)$. The channels belong to an acoustic nanocircuit which comprises a network of quasi-one-dimensional pinched-off channels serving as wires along which SAW quantum dots transport electrons. This is motivated by possible practical applications involving quantum information processing and quantum computers. We calculate $J$ as a function of time as the electrons travel side-by-side in the adjacent channels and as a function of the distance between the centers of the channels. The leakage from the state in which the system is prepared, is calculated. The oscillations in the leakage indicate the probability for the electron system to make transitions between the ground and excited states, or for an electron to hop back and forth between channels.