We show that private shared reference frames can be used to perform private quantum and private classical communication over a public quantum channel. Such frames constitute a type of private shared correlation, distinct from private classical keys or shared entanglement, useful for cryptography. We present optimally efficient schemes for private quantum and classical communication given a finite number of qubits transmitted over an insecure channel and given a private shared Cartesian frame and∕or a private shared reference ordering of the qubits. We show that in this context, it is useful to introduce the concept of a decoherence-full subsystem, wherein every state is mapped to the completely mixed state under the action of the decoherence.

We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for the maximal achievable average fidelity and we explicitly show how to construct a probabilistic operation that achieves this fidelity. We illustrate our method on several examples such as the phase covariant cloning of qubits, cloning of coherent states, and purification of qubits transmitted via depolarizing channel and amplitude damping channel. Our examples reveal that the probabilistic cloner may yield higher fidelity than the best deterministic cloner even when the states that should be cloned are linearly dependent and are drawn from a continuous set.

The advantage of using a discrete variable representation (DVR) is that the Hamiltonian of two interacting particles can be constructed in a very simple form. However, the DVR Hamiltonian is approximate and, as a consequence, the results cannot be considered as variational ones. We will show that the variational character of the results can be restored by performing a reduced number of integrals. In practice, for a variational description of the lowest $n$ bound states only $n(n+1)∕2$ integrals are necessary whereas $D(D+1)∕2$ integrals are enough for the scattering states ($D$ is the dimension of the $S$ matrix). Applications of the method to the study of dimers of He, Ne and Ar, for both bound and scattering states, are presented.

Resolution plays a vital role in spectroscopic studies. In the usual recoil-ion momentum spectroscopy (RIMS), Q-value resolution is relied upon to distinguish between different collision channels: The better the Q-value resolution, the better one is able to resolve energetically similar channels. Although traditional COLTRIMS greatly improves Q-value resolution by cooling the target and thus greatly reducing the initial target momentum spread, the resolution of the technique is still limited by target temperature. However, with the recent development in RIMS, namely, magneto-optical trap recoil ion momentum spectroscopy (MOTRIMS) superior recoil ion momentum resolution as well as charge transfer measurements with laser excited targets have become possible. Through MOTRIMS, methods for the measurements of target excited state fraction and kinematically complete relative charge transfer cross sections have been developed, even for some systems having energetically degenerate or nearly degenerate channels. In the present work, the systems of interest having energy degeneracies or near degeneracies are ${\mathrm{Rb}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{Li}}^{+}$ colliding with trapped $\mathrm{Rb}\left(5l\right)$, where $l=s$ and $p$.

Single and double ionization of ground state $\mathrm{Mg}$ atoms is observed in an atomic beam experiment in the $584–596\mathrm{nm}$ spectral range with a maximum intensity of $9\times {10}^{11}\mathrm{W}∕{\mathrm{cm}}^2$ and pulses of ns duration. The ${\mathrm{Mg}}^{+}$ spectrum consists of a single broad resonance whose position is very sensitive to laser intensity and it is attributed to the four-photon excitation of the doubly excited $3p^2{}^{1}S_0$ state. For intensities higher than $2\times {10}^{11}\mathrm{W}∕{\mathrm{cm}}^2$ a considerable double ionization yield is obtained. The ${\mathrm{Mg}}^{2+}$ spectra are composed of two lobes, each one dominating at different intensities. These observations can be interpreted by a sequential mechanism in which doubly charged ions are created by multiphoton resonant ionization of the excited $3p_{1∕2,3∕2}$ ${\mathrm{Mg}}^{+}$ states (with negligible contribution from the $3s_{1∕2}$ ionic ground state) after the single ion production has saturated. The population of these excited ionic states suggests the absorption of two photons above the first ionization threshold of $\mathrm{Mg}$. This interpretation is unambiguously confirmed by a complementary fluorescence experiment. Moreover, both ionization and fluorescence spectra as well as ionization yields are very well reproduced by a theoretical model based on a combination of density matrix and rate equations, taking into account the near-resonant coupling between the $3p^2{}^{1}S_0$ and $3p3d{}^{1}P_1$ autoionizing states and employing calculated parameters for both $\mathrm{Mg}$ and ${\mathrm{Mg}}^{+}$. It is thus pointed out that for visible ns pulses of moderate intensity the autoionizing resonances play a crucial role in the multiphoton sequential double ionization of alkaline-earth-metal atoms.

We investigate the evolution of a quantum system under the influence of sequential measurements. The measurement scheme distinguishes whether or not the system is in a specified state $\mid f_n⟩$ at the $n$th step, where $\mid f_n⟩$ varies with $n$. Dark evolution corresponds to the situation when all measurements give negative results. We show that dark evolution is unitary in the continuous measurement limit. We derive the effective Hamiltonian, and indicate how $\mid f_n⟩$ controls quantum state transport.

Theories are developed to evaluate Larmor frequency shifts, derived from geometric phases, in experiments to measure electric dipole moments (EDM’s) of trapped, atoms, molecules, and neutrons. A part of these shifts is proportional to the applied electric field and can be interpreted falsely as an electric dipole moment. A comparison is made between our theoretical predictions for these shifts and some results from our recent experiments, which shows agreement to within the experimental errors of 15%. The comparison also demonstrates that some trapped particle EDM experiments have reached a sensitivity where stringent precautions are needed to minimize and control such false EDM’s. Computer simulations of these processes are also described. They give good agreement with the analytical results and they extend the study by investigating the influence of varying surface reflection laws in the hard-walled traps considered. They also explore the possibility to suppress such false EDM’s by introducing collisions with buffer gas particles. Some analytic results for frequency shifts proportional to the square of the $\mathbf{E}$ field are also given and there are results for the averaging of the $\mathbf{B}$ field in the absence of an $\mathbf{E}$ field.

Electron capture and direct elastic scattering in collisions of ${\mathrm{H}}^{+}$ ions with ${\mathrm{CH}}_2$ molecules between 0.5 and $1.5\mathrm{keV}$ are theoretically investigated. A molecular representation is adopted within a fully quantum-mechanical approach. We consider the following four different molecular configurations for collision dynamics: (I) the proton approaches the $\mathrm{C}$ atom along the bisector of the $\mathrm{H}—\mathrm{C}—\mathrm{H}$ bond angle, passing the midpoint of the $\mathrm{H}\text{−}\mathrm{H}$ line, (II) it comes along the same line as in (I), but in the opposite direction, (III) the proton approaches the $\mathrm{C}$ atom in the $\mathrm{H}-\mathrm{C}-\mathrm{H}$ plane and perpendicularly to the bisector of the $\mathrm{H}—\mathrm{C}—\mathrm{H}$ bond angle, and (IV) the proton approaches the $\mathrm{C}$ atom perpendicularly to the $\mathrm{H}-\mathrm{C}-\mathrm{H}$ plane. Differential cross sections for elastic scattering and electron capture are calculated at 1.5 and $0.5\mathrm{keV}$ for these different molecular orientations. Total cross sections for these four orientations as well as orientation-averaged total cross sections are also calculated. Our results indicate that electron capture dynamics and corresponding electron-capture cross sections depend substantially on the molecular configuration, thus revealing a strong steric effect.

This work presents the results of computer simulations for the energy spectra of original versus recombined $\mathrm{H}_2{}^{+}$ molecular ions transmitted through thin amorphous carbon foils, for a broad range of incident energies. A detailed description of the projectile motion through the target has been done, including nuclear scattering and Coulomb repulsion as well as electronic self-retarding and wake forces; the two latter are calculated in the dielectric formalism framework. Differences in the energy spectra of recombined and original transmitted $\mathrm{H}_2{}^{+}$ molecular ions clearly appear in the simulations, in agreement with the available experimental data. Our simulation code also differentiates the contributions due to original and to recombined $\mathrm{H}_2{}^{+}$ molecular ions when the energy spectra contain both contributions, a feature that could be used for experimental purposes in estimating the ratio between the number of original and recombined $\mathrm{H}_2{}^{+}$ molecular ions transmitted through thin foils.

We report observations of backward and forward electron emission by a thin silicon crystal target traversed by $29\text{MeV}∕\mathrm{u}$ ${\mathrm{Pb}}^{56+}$ incident ions. For each incident ion we have performed measurements of backward and forward electron emission, of the energy loss and of the charge state of the transmitted ion. The crystal target was traversed by incident ions either in random incidence or in axial alignment conditions. In both cases these correlated measurements bring original information on electron emission. In random conditions, using an incident ion species with a charge quite far from equilibrium, we observe correlations between backward and forward electron emission, that we understand when analyzing the associated charge exchange and energy-loss data. In channeling conditions, we added electron emission measurements to simultaneous energy-loss and charge state measurements (that are known to characterize quite precisely the type of trajectory of a projectile transmitted through a thin crystal). This allowed us to observe the reduced electron emission due to hyperchanneled ions, that interact mainly with target valence electrons, and also the enhanced electron emission due to projectiles entering the crystal very close to atomic strings.

Ultracold molecules are associated from an atomic Bose-Einstein condensate by ramping a magnetic field across a Feshbach resonance. The reverse ramp dissociates the molecules. The kinetic energy released in the dissociation process is used to measure the widths of four Feshbach resonances in ${}^{87}\mathrm{Rb}$. This method to determine the width works remarkably well for narrow resonances even in the presence of significant magnetic-field noise. In addition, a quasimonoenergetic atomic wave is created by jumping the magnetic field across the Feshbach resonance.

We present an experimental approach to Bose-Einstein condensation by increasing the particle number of the system at almost constant temperature. In particular, the emergence of a new condensate is observed in multicomponent $F=1$ spinor condensates of ${}^{87}\mathrm{Rb}$. Furthermore, we develop a simple rate-equation model for multicomponent Bose-Einstein condensate thermodynamics at finite temperature which well reproduces the measured effects.

Semiclassical transformation theory implies an integral representation for stationary-state wave functions ${\psi }_m\left(q\right)$ in terms of angle-action variables ($\theta ,J$). It is a particular solution of Schrödinger’s time-independent equation when terms of order ${\hslash }^2$ and higher are omitted, but the preexponential factor $A(q,\theta )$ in the integrand of this integral representation does not possess the correct dependence on $q$. The origin of the problem is identified: the standard unitarity condition invoked in semiclassical transformation theory does not fix adequately in $A(q,\theta )$ a factor which is a function of the action $J$ written in terms of $q$ and $\theta$. A prescription for an improved choice of this factor, based on successfully reproducing the leading behavior of wave functions in the vicinity of potential minima, is outlined. Exact evaluation of the modified integral representation via the residue theorem is possible. It yields wave functions which are not, in general, orthogonal. However, closed-form results obtained after Gram-Schmidt orthogonalization bear a striking resemblance to the exact analytical expressions for the stationary-state wave functions of the various potential models considered (namely, a Pöschl-Teller oscillator and the Morse oscillator).

Extending the eavesdropping strategy devised by Zhang, Li, and Guo [Zhang, Li, and Guo, Phys. Rev. A 63, 036301 (2001)], we show that the multiparty quantum communication protocol based on entanglement swapping, which was proposed by Cabello (e-print quant-ph∕0009025), is not secure. We modify the protocol so that entanglement swapping can secure multiparty quantum communication, such as multiparty quantum key distribution and quantum secret sharing of classical information, and show that the modified protocol is secure against the Zhang-Li-Guo strategy for eavesdropping as well as the basic intercept-resend attack.

We find that the generally accepted security criteria are flawed for a whole class of protocols for quantum cryptography. This is so because a standard assumption of the security analysis, namely that the so-called square-root measurement is optimal for eavesdropping purposes, is not true in general. There are rather large parameter regimes in which the optimal measurement extracts substantially more information than the square-root measurement.

The response of very-high-$n$ strongly polarized potassium Rydberg atoms to a sequence of impulsive perturbations provided by a train of short unidirectional electric pulses is investigated. Each pulse, termed a half-cycle pulse (HCP), has a duration $T_p⪡T_n$, where $T_n$ is the classical electron orbital period. Pronounced differences in the survival probability are observed when the sequence of HCPs is directed parallel and antiparallel to the axis of polarization of the initial state. For impulses directed antiparallel to the initial state, Poincaré surfaces of section point to a mixed phase space with large stable islands embedded in a chaotic sea that can lead to dynamical stabilization. Stable islands are absent when the direction of the impulses is reversed. The system is globally chaotic leading to rapid ionization. We show that noise, i.e., random fluctuations in the temporal pulse-to-pulse spacing as well as in the pulse amplitude, plays a crucial role in the degree of dynamical stabilization. Reasonable agreement between experiment and theory is achieved.

The estimation of unknown qubit elementary gates and the alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as $1∕N^2$, can be asymptotically attained with a covariant protocol that exploits the quantum correlation of internal degrees of freedom instead of the more fragile entanglement between distant parties. This cuts by half the number of qubits needed to achieve the precision of the dense covariant coding protocol.

We discuss a possible experimental scheme for the implementation of a quantum walk. The scheme is based on the passage of an atom inside a high-$Q$ cavity. The chirality is characterized by the atomic states and the displacement is characterized by the photon number inside the cavity. The quantum steps are described by appropriate interactions with a sequence of classical and quantized cavity fields.

Data on $\overline{p}$ slowing down and capture in helium at 1 and $0.2\mathrm{mb}$ at room temperature are presented and compared to the corresponding previously publicated data in molecular hydrogen and deuterium. A Monte Carlo simulation containing a low-energy extrapolation of measured $\overline{p}$ electronic stopping power in helium gas, screened Rutherford collisions, and simple cascade mechanisms is able to reproduce the gross features of the data, but cannot explain some nontrivial details of the measured distributions.