Any deterministic bipartite-entanglement transformation involving finite copies of pure states and carried out using local operations and classical communication (LOCC) results in a net loss of entanglement. We show that for almost all such transformations, partial recovery of lost entanglement is achievable by using $2\times 2$ auxiliary entangled states, no matter how large the dimensions of the parent states are. For the rest of the special cases of deterministic LOCC transformations, we show that the dimension of the auxiliary entangled state depends on the presence of equalities in the majorization relations of the parent states. We show that genuine recovery is still possible using auxiliary states in dimensions less than that of the parent states for all patterns of majorization relations except only one special case.

We sympathetically cool a trapped ${}^{112}{\mathrm{Cd}}^{+}$ ion by directly Doppler cooling a ${}^{114}{\mathrm{Cd}}^{+}$ ion in the same trap. This is the first demonstration of optically addressing a single trapped ion being sympathetically cooled by a different species ion. Notably, the experiment uses a single laser source, and does not require strong focusing. This paves the way toward reducing decoherence in an ion trap quantum computer based on ${\mathrm{Cd}}^{+}$ isotopes.

Using a “monochromatic” (single-axial-velocity) and slow (250 m/s) beam of metastable helium atoms, we realize up to eighth-order Bragg scattering and obtain a splitting angle of 6 mrad at low laser power (3 mW). This corresponds to a truly macroscopic separation of 12 mm on the detector. For fifth-order scattering, we have observed several oscillations of the splitting ratio when varying the laser power (“Pendellösung oscillations”). The large splitting angle, the adjustable splitting ratio, and the cleanness of the split beams, with $200-\mu \mathrm{m}$ rms width each, make the beam splitter ideal for a large-enclosed-area atom interferometer.

We demonstrate that the mode dispersion of gas-filled waveguides can be used to match group velocities of guided laser pulses. The synchronism is attained by balancing normal dispersion of the gas with geometry-dependent negative waveguide dispersion. By applying this approach to the process of Raman sideband generation in an impulsively excited ${\mathrm{SF}}_6,$ a multifold increase in the scattering efficiency was achieved, with the number of generated phase-locked Raman components sufficient to approach the attosecond regime of optical-field synthesis.

We show that the interaction between Rydberg atomic states can provide continuous spin squeezing of atoms with two ground states. The interaction prevents the simultaneous excitation of more than a single atom in the sample to the Rydberg state, and we propose to utilize this blockade effect to realize an effective collective spin Hamiltonian $J_x^2-J_y^2.$ With this Hamiltonian the quantum-mechanical uncertainty of the spin variable $J_x-J_y$ can be significantly reduced.

We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle’s wave function. The wave function in the presence of such a detector vanishes on the detector. The trace the absorbed particles leave on the detector is identified as the absorption current density on the detector. This density is calculated from the solution of Schrödinger’s equation with a reflecting boundary at the detector. This current density is not the usual Schrödinger current density. We define the probability distribution of the time of arrival to a detector in terms of the absorption current density. We define coordinate measurement by an absorbing wall in terms of four postulates. In the resulting theory the quantum-mechanical collapse of the wave function is replaced with the usual collapse of the probability distribution after observation. Two measurement experiments are proposed to measure time of arrival and the probability density function of a freely propagating two-dimensional Gaussian packet from the measurement of the absorption current on two planes.

Breakdown of quantum-classical correspondence is studied on an experimentally realizable example of a one-dimensional periodically driven system. Two relevant time scales are identified in this system: the short Ehrenfest time $t_{ħ}\sim \ln \left({ħ}^{-1}\right)$ and the typically much longer localization time scale $T_L\sim {ħ}^{-2}.$ It is shown that surprisingly weak modification of the Hamiltonian may eliminate the more dramatic symptoms of localization without effecting the more subtle but ubiquitous and rapid loss of correspondence at $t_{ħ}.$

We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the state vector, white-noise stochastic processes with nonwhite ones. We prove that such a modification can be consistently performed without altering the most interesting features of the previous models. One of the reasons to discuss this matter derives from the desire of being allowed to deal with physical stochastic fields, such as the gravitational one, which cannot give rise to white noises. From our point of view, the most relevant motivation for the approach we propose here derives from the fact that in relativistic models intractable divergences appear as a consequence of the white nature of the noises. Therefore, one can hope that resorting to nonwhite noises, one can overcome such a difficulty. We investigate stochastic equations with nonwhite noises, we discuss their reduction properties and their physical implications. Our analysis has a precise interest not only for the above-mentioned subject but also for the general study of dissipative systems and decoherence.

We construct a probabilistic cloning and deleting machine which, taking several copies of an input quantum state, can output a linear superposition of multiple cloning and deleting states. Since the machine can perform cloning and deleting in a single unitary evolution, the probabilistic cloning and other cloning machines proposed in the previous literature can be thought of as special cases of our machine. A sufficient and necessary condition for successful cloning and deleting is presented, and it requires that the copies of an arbitrarily presumed number of the input states are linearly independent. This simply generalizes some results for cloning. We also derive an upper bound for the success probability of the cloning and deleting machine.

A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This phase shift does not destroy the decoherence-free (DF) property of the subspace because the associated fidelity is $1.$ This permits a universal formalism to be presented—the eigenprojectors of the free part of the Hamiltonian for the system and bath may be used to construct a DF projected subspace based on the SKE. To eliminate possible phase or unitary errors induced by the change in the eigenvalues, a cancellation technique is proposed, using the adjustment of the coupling time, and applied to a two-qubit computing system. A general criteria for constructing a DF-projected subspace from the SKE is discussed. Finally, a proposal for using triangulation to realize a decoherence-free subsystem based on SKE is presented. The concrete formulation for a two-qubit model is given exactly. Our approach is general and appears to be applicable to any type of decoherence.

The dynamics of the entanglement for coherent excitonic states in the system of two, coupled, large semiconductor quantum dots ${(R/a}_B\gg 1)$ mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is present in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of the excitons.

We introduce a formalism that connects entanglement witnesses and the distillation and activation properties of a state. We apply this formalism to two cases: First, we rederive the results presented in Eggeling et al. (e-print quant-ph/0104095), namely, that one copy of any bipartite state with nonpositive partial transpose (NPPT) is either distillable, or activatable. Second, we show that there exist three-partite NPPT states, with the property that two copies can neither be distilled, nor activated.

We consider the environment-affected dynamics of N self-interacting particles living in one-dimensional double wells. Two topics are dealt with. First, we consider the production of entangled states of two-level systems. We show that by adiabatically varying the well biases, we may dynamically generate maximally entangled states, starting from initially unentangled product states. Entanglement degradation due to a common type of environmental influence is then computed by solving a master equation. However, we also demonstrate that entanglement production is unaffected if the system-environment coupling is of the type that induces “motional narrowing.” As our second but related topic, we construct a different master equation that seamlessly merges error protection/detection dynamics for quantum information with the environmental couplings responsible for producing the errors in the first place. Adiabatic avoided crossing schemes are used in both topics.

For nearly all the states dissociating below the ionic limit [i.e., Rb $(5s,$ $5p,$ $4d,$ $6s,$ $6p,$ $5d,$ $7s,$ and $4f)+\mathrm{H}$ $\mathrm{}\left(1s\right)\mathrm{}]$ in ${}^1{\Sigma }^{+}$ and ${}^3{\Sigma }^{+}$ symmetries, we present an adiabatic and diabatic study. Adiabatic results are also reported for ${}^1\Pi ,$ ${}^3\Pi ,$ ${}^1\Delta ,$ and ${}^3\Delta$ symmetries. The ab initio calculations rely on pseudopotential, operatorial core-valence correlation, and full valence configuration-interaction approaches, combined to an efficient diabatization procedure. For the low-lying states, our vibrational level spacings and spectroscopic constants are in good agreement with the available experimental data. Diabatic potentials and dipole moments are analyzed, revealing the strong imprint of ionic state in the ${}^1{\Sigma }^{+}$ adiabatic states while improving the results. As for LiH, vibrational spacing of the A state is bracketed by our results, with and without the improvement, taking into account the diabatic representation. Experimental suggestions are also given.

Unit transition probability occurs when a bound state works as a doorway state between two continua. It is shown that in the limit of small coupling this is still true if there is direct coupling between the continua. A cancellation of this coupling occurs in the appropriate element of the transition operator.

Low-energy electron emission spectra are studied in collisions of 3.6 MeV/amu ${\mathrm{Au}}^{53+}$ ions with neon and argon atoms for well-defined degrees of target ionization. We calculate doubly differential cross sections as functions of the recoil-ion charge state in the continuum-distorted-wave with eikonal initial-state approximation using a binomial analysis of the total and differential ionization probabilities, and compare them with the present and with previously published experimental data. Very good agreement is found for the single-ionization spectra and for double ionization of neon, while some discrepancies are observed in the spectra for double and triple ionization of argon.

We introduce the “shaped-adiabatic-passage” method that allows one to realize a complete population transfer from a given state $|1〉$ to superpositions of energy eigenstates $|\Psi 〉={\sum }_k{c}_k{e}^{-i{\omega }_{k}t}|k〉$ of any desired composition. This objective can be achieved by using a “shaped” (dump or Stokes) laser pulse, formed by simultaneous monochromatic pulses of the same smooth profile, resonantly coupling the states $|k〉$ with a single intermediate state $|2〉,$ followed by a (pump or anti-Stokes) pulse, coupling this intermediate state with the initial state $|1〉.$ The pulse shapes can be obtained from first-order perturbation theory, so the method can be used for efficient information coding in the form of superpositions of atomic Rydberg states or of molecular vibrational states.

Analytical expressions for the energy eigenstates of the boson-Hubbard (or quantum discrete-nonlinear Schrödinger) dimer are obtained by applying perturbation theory in the small-tunneling-amplitude limit. The results are relevant for a Bose-Einstein condensate trapped in a double-well potential. A detailed comparison with the numerical solutions arising from the direct diagonalization of the Hamiltonian (for even or odd numbers of bosons) is presented, and the limits of validity of the perturbative results are determined. For fixed values of the tunneling amplitude, the accuracy of the perturbative calculation varies with the total number of bosons in different ways, depending on the particular energy level. Results for the fluctuations of the boson-number difference in each eigenstate are also presented.

We consider many-body effects on particle scattering in one-, two-, and three-dimensional (3D) Bose gases. We show that at $T=0\mathrm{}$ these effects can be modeled by the simpler two-body T matrix evaluated off the energy shell. This is important in 1D and 2D because the two-body T matrix vanishes at zero energy and so mean-field effects on particle energies must be taken into account to obtain a self-consistent treatment of low-energy collisions. Using the off-shell two-body T matrix we obtain the energy and density dependence of the effective interaction in 1D and 2D and the appropriate Gross-Pitaevskii equations for these dimensions. Our results provide an alternative derivation of those of Kolomeisky and co-workers. We present numerical solutions of the Gross-Pitaevskii equation for a 2D condensate of hard-sphere bosons in a trap. We find that the interaction strength is much greater in 2D than for a 3D gas with the same hard-sphere radius. The Thomas-Fermi regime is, therefore, approached at lower condensate populations and the energy required to create vortices is lowered compared to the 3D case.

Tunneling of atoms between two trapped Bose-condensed gases at finite temperatures is explored using a many-body linear-response tunneling formalism similar to that used in superconductors. To lowest order, the tunneling currents can be expressed quite generally in terms of the single-particle Green’s functions of isolated Bose gases. A coherent first-order tunneling Josephson current between two atomic Bose-Einstein condensates is found, in addition to coherent and dissipative contributions from second-order condensate-noncondensate and noncondensate-noncondensate tunneling. Our work is a generalization of Meier and Zwerger, who recently treated tunneling between uniform atomic Bose gases. We apply our formalism to the analysis of an out-coupling experiment induced by light wave fields, using a simple Bogoliubov-Popov quasiparticle approximation for the trapped Bose gas. For tunneling into the vacuum, we recover the results of Japha, Choi, Burnett, and Band, who recently pointed out the usefulness of studying the spectrum of out-coupled atoms. In particular, we show that the small tunneling current of noncondensate atoms from a trapped Bose gas has a broad spectrum of energies, with a characteristic structure associated with the Bogoliubov quasiparticle $u^2$ and $v^2$ amplitudes.