Following on from previous work [J.-Å. Larsson, Phys. Rev. A 67, 022108 (2003)], Bell inequalities based on correlations between binary digits are considered for a particular entangled state involving $2N$ trapped ions. These inequalities involve applying displacement operations to half of the ions and then measuring correlations between pairs of corresponding bits in the binary representations of the number of center-of-mass phonons of $N$ particular ions. It is shown that the state violates the inequalities and thus displays nonclassical correlations. It is also demonstrated that it violates a Bell inequality when the displacements are replaced by squeezing operations.

In a fundamental test of quantum mechanics, we have observed $\mathrm{228\hspace{0.17em}000}$ quantum jumps of a single trapped and laser cooled ${}^{88}\mathrm{Sr}^{+}$ ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for nonrandomness in quantum-mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated multiparticle effects and providing near-unit detection efficiency of transitions. We measure the fractional reduction in the entropy of information to be $<6.5\times {10}^{-4}$ when the value of any interval between quantum jumps is known. We also find that the number of runs of successively increasing or decreasing interval times agrees with the theoretically expected values. Furthermore, we analyze $\mathrm{238\hspace{0.17em}000}$ quantum jumps from two simultaneously confined ions and find that the number of apparently coincidental transitions is as expected. Finally, we observe 8400 spontaneous decays of two simultaneously trapped ions and find that the number of apparently coincidental decays from the metastable state agrees with the expected value. We find no evidence for short- or long-term correlations in the intervals of the quantum jumps or in the decay of the quantum states, in agreement with quantum theory.

We present networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our networks can estimate the LU invariants for multiparty states, where each party can have a Hilbert space of arbitrary dimension and the SLOCC invariants for multiqubit states. We analyze the statistical efficiency of our networks compared to methods based on estimating the state coefficients and calculating the invariants.

Based on the positive maps separability criterion, we present a method for the detection of quantum entanglement of a shared bipartite quantum state, within the “distant labs” paradigm, using only local operations and classical communication.

In the optical Stern-Gerlach effect the two branches in which the incoming atomic packet splits up can display interference pattern outside the cavity when a field measurement is made which erases the which-way information on the quantum paths the system can follow. On the contrary, the mere possibility to acquire this information causes a decoherence effect which cancels out the interference pattern. A phase-space analysis is also carried out to investigate on the negativity of the Wigner function and on the connection between its covariance matrix and the distinguishability of the quantum paths.

We present first-principles calculations for the tunnel ionization rate of some atoms and molecules in a static intense electric field. The Gamow state is calculated to describe the ionization process in the Kohn-Sham formalism with the self-interaction correction. The tunnel ionization rate is obtained from the imaginary part of the Gamow state eigenvalue. The ionization rates of rare-gas atoms Ar and Xe and diatomic molecules ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{F}}_2$ are investigated. The calculations describe well the observed behavior of the tunnel ionization. The results also show good correspondence with the Ammosov-Delone-Krainov model for rare-gas atoms. We find that the properties of the highest occupied orbital have significant effects on the ionization rate. In particular, our calculation reproduces the suppression of the ionization rate of ${\mathrm{O}}_2$ molecule in comparison with that of Xe atom. We also find that the ionization rates of ${\mathrm{O}}_2$ and ${\mathrm{F}}_2$ molecules are very sensitive to the relative angle between the electric field and the molecular axis, reflecting properties of the highest occupied orbital.

Resonant Raman coupling between internal levels can create double-well momentum-space potentials for multilevel “periodically-dressed” atoms. We develop a many-body formalism for a weakly interacting, trapped periodically dressed Bose gas which illustrates how a tunable exchange interaction yields correlated many-body ground states. In contrast to the case of a position-space double well, the ground state of stable periodically-dressed Bose gases with repulsive interactions tends toward a macroscopic superposition state in the regime where interactions dominate the momentum-space tunneling induced by the external trapping potential. We discuss how real-time control of experimental parameters can be used to create macroscopic quantum superpositions of either momentum or internal states, and how these states could be dynamically controlled, opening the way toward highly sensitive interferometry and frequency metrology.

Phonon like excitations can be imprinted into a trapped Bose-Einstein condensate of cold atoms using light scattering. If the condensate is suddenly let to freely expand, the initial phonons lose their collective character by transferring their energy and momentum to the motion of individual atoms. The basic mechanisms of this evaporation process are investigated by using the Gross-Pitaevskii theory and dynamically rescaled Bogoliubov equations. Different regimes of evaporation are shown to occur depending on the phonon wavelength. Distinctive signatures of the evaporated phonons are visible in the density distribution of the expanded gas, thus providing a new type of spectroscopy of Bogoliubov excitations.

When a four-level $\mathsf{Y}$-type atom with two highest nearly degenerate lying levels interacts with the same vacuum radiation field, its excited levels have vacuum-induced coherence due to the quantum interference between the spontaneous decay channels. We consider the effects of the vacuum-induced coherence on the electromagnetically induced transparency against single- and two-photon absorption in the atomic system. We find that the vacuum-induced coherence can lead to probe gain without incoherent pumping. On the other hand, the coherence can suppress the two-photon transparency, even in some cases where it can enhance the two-photon absorption. Another important result is the finding of the crucial role played by the relative phase between the probe and coupling fields: the two-photon transparency and the probe gain spectra can be modulated by this phase.

The Bethe logarithm is calculated for the $S$ and $P$ states of the helium atom. The calculations are based on variational expansion with randomly chosen exponents. The exponentially growing exponents in the variational basis set of the intermediate states were used to reach high convergence rate. This approach is similar to the strategy used by Drake and Goldman [Can. J. Phys. 77, 835 (1999)]. The estimated accuracy of obtained values is about 11–12 significant digits.

Manipulation of the quantum states of two-level atoms has been investigated using laser-controlled geometric phase change, which has the potential to build robust quantum logic gates for quantum computing. For a qubit based on two electronic transition levels of an atom, two basic quantum operations that can make any universal single qubit gate have been designed employing resonant laser pulses. An operation equivalent to a phase gate has been demonstrated using ${\mathrm{Tm}}^{3+}$ doped in a yttrium aluminum garnet crystal.

Reconstruction of a reduced density operator for weakly coupled systems of spins $\frac{1}{2}$ from fits to nuclear magnetic resonance spectra is described in detail. Particular emphasis is placed on data treatment procedures that specify fewer than the $3^n$ complete spectra that are implicitly prescribed in published references to state tomography on $n$-spin systems. It is shown that if the density operator is expanded in the so-called product-operator basis, it is always possible to estimate a desired coefficient in the expansion by measuring a single spectral multiplet. This simple observation can substantially reduce the experimental effort required for either complete density-matrix reconstruction or estimation of subsets of the coefficients in the product-operator expansion. A simple iterative algorithm can be used to produce reduced measurement procedures for experiments involving small numbers of qubits.

We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits are in pure states while other qubits are in mixed states. It enables a single ensemble quantum computer to perform “single-instruction-multidata” type of parallel computation. Parallel quantum computing can provide additional speedup in Grover’s algorithm and Shor’s algorithm. In addition, it also makes a fuller use of qubit resources in an ensemble quantum computer. As a result, some qubits discarded in the preparation of an effective pure state in the Schulman-Varizani and the Cleve-DiVincenzo algorithms can be reutilized.

Isotopic effects on double-excitation resonances in ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ were observed in photoionization spectra using synchrotron radiation with high monochromator resolution. In ${}^3\mathrm{He}$, the resonances were found to be shifted to lower energies with respect to ${}^4\mathrm{He}$ by $\Delta E=3.06\pm 0.07\text{meV}$, in good agreement with theoretical expectations based on normal and specific mass shifts. From the experimental data, the resonance parameters $E_r$, $\Gamma$, and $q$ of the resonances $2,-1_3,$ $2,1_4,$ and $2,0_7$ were analyzed in detail using a double-convolution fit procedure that considers the different Doppler broadenings of the states in ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$. In this way, the resolution function of the monochromator could be derived, which can be accounted for in a quantitative way on the basis of the properties of undulator radiation and the optical design of the monochromator.

We report the theoretical evaluations of the static scalar polarizability of the ${}^{133}\mathrm{Cs}$ ground state and of the blackbody radiation shift induced on the transition frequency between the two hyperfine levels with $m_F=0$. This shift is of fundamental importance in the evaluation of the accuracy of the primary frequency standards based on atomic fountains and is employed in the realization of the SI second in the International Atomic Time scale at the level of $1\times {10}^{-15}$. Our computed value for the polarizability is ${\alpha }_0=(6.600\pm 0.016)\times {10}^{-39}{\mathrm{C}\mathrm{m}}^2∕\mathrm{V}$ in agreement at the level of $1\times {10}^{-3}$ with recent theoretical and experimental values. As regards the blackbody radiation shift we find for the relative hyperfine transition frequency $\beta =(-1.49\pm 0.07)\times {10}^{-14}$ at $T=300\mathrm{K}$ in agreement with frequency measurements reported by our group and by Bauch and Schröder [Phys. Rev. Lett. 78, 622 (1997)]. This value is lower by $2\times {10}^{-15}$ than that obtained with measurements based on the dc Stark shift and than the value commonly accepted up to now.

The interaction between an atom and a short laser pulse is studied in the case where both photon energies are smaller than the ionization potential and perturbation conditions prevail. Under these conditions, a full numerical solution of the time-dependent Schrödinger equation for a hydrogen atom initially in its ground state shows that secondary peaks show up in the above-threshold ionization (ATI) spectrum. We introduce here an easy-to-implement approximation that sheds light on these features. This approach, which is based on Coulomb-Volkov-type states, is an extension of a previous theory that applies only when photon energies are greater than the ionization potential. We show that introducing a coupling to intermediate bound states into the approach permits to nicely reproduce the full numerical electron spectrum for smaller photon energies. Further, it allows us to trace back unambiguously the secondary peaks to a manifold process, i.e., excitation of transient bound states followed by multiphoton absorption, and to show that the main ATI peaks may be enhanced by intermediate state contributions. When bound states with $1⩽n⩽4$ are included, the approach provides excellent predictions for photon energies as low as half the ionization potential.

We derive the finite-temperature oscillation modes of a harmonically confined Bose-Einstein condensed gas undergoing rigid body rotation supported by a vortex lattice in the condensate. The hydrodynamic modes separate into two classes corresponding to center of mass and relative oscillations of the thermal cloud and the condensate. These classes are independent of each other in the case where the thermal cloud is inviscid for all modes studied, except the radial pulsations which couple them because the pressure perturbations of the condensate and the thermal cloud are governed by different adiabatic indices. If the thermal cloud is viscous, the two classes of oscillations are coupled, i.e., each type of motion involves simultaneously mass and entropy currents. The relative oscillations are damped by the mutual friction between the condensate and the thermal cloud mediated by the vortex lattice. The damping is large for the values of the drag-to-lift ratio of the order of unity and becomes increasingly ineffective in either limit of small or large friction. An experimental measurement of a subset of these oscillation modes and their damping can provide information on the values of the phenomenological mutual friction coefficients and the quasiparticle-vortex scattering processes in dilute atomic Bose gases.

We study the effects of Feshbach resonant interactions in a rapidly rotating Bose gas. The resonant formation of molecules leads to the growth of pair correlations which modify the ground state of the gas. By an extension of the usual Chern-Simons theory, built of composite atoms and molecules, we are able to account for these resonance effects. Focusing on the $1∕2$ filling fraction, we find that the resulting ground state evolves from a Laughlin wave function to a unique paired wave function as one approaches the resonance.

We analyze the generation and mobility of discrete solitons in Bose-Einstein condensates confined in an optical lattice under realistic experimental conditions. We discuss first the creation of one-dimensional discrete solitons, for both attractive and repulsive interatomic interactions. We then address the issue of their mobility, focusing our attention on the conditions for the experimental observability of the Peierls-Nabarro barrier. Finally we report on the generation of self-trapped structures in two and three dimensions. Discrete solitons may open alternative routes for the manipulation and transport of Bose-Einstein condensates.

Analytical treatment of the self-phase-modulation of an ultrashort light pulse is extended beyond the slowly varying envelope approximation. The resulting wave equation is modified to include corrections to self-phase-modulation due to higher-order spatial and temporal derivatives. Analytical solutions are found in the limiting regimes of high nonlinearities and very short pulses. Our results reveal features that can significantly impact both pulse shape and the evolution of the phase.