We use the forward-backward angular asymmetry in the electron emission cross sections in fast ion impact ionization of ${\mathrm{H}}_2$ as a probe of the inversion symmetric coherence in homonuclear diatomic molecules. The electron energy dependence of the asymmetry parameter for ${\mathrm{H}}_2$ exhibits oscillatory structure due to Young-type interference in contrast to atomic targets such as He. The asymmetry parameter technique provides a self-normalized method to reveal the interference oscillation independent of theoretical models and complementary measurements on atomic H target.

We report a way of manipulating the spontaneous emission process leading to a spatial modulation of spontaneous decay. The effect is observed in the case of coherently driven atoms separated by less than a transition wavelength. It is quantified by Glauber’s photon-photon second-order correlation function. We show that the photon arrival time, usually regarded as an entirely random process, depends not only on where a photon is detected but also on where a former photon had been recorded previously. Our results shed light on the unexpected consequences of state reduction and entanglement for the fundamental process of spontaneous emission.

Resonant energy transfer between cold Rydberg atoms was used to determine Rydberg atom energy levels, at precisions approaching those obtainable in microwave spectroscopy. Laser cooled ${}^{85}\mathrm{Rb}$ atoms from a magneto-optical trap were optically excited to $32d_{5∕2}$ Rydberg states. The two-atom process $32d_{5∕2}+32d_{5∕2}\to 34p_{3∕2}+30g$ is resonant at an electric field of approximately $0.3\mathrm{V}∕\mathrm{cm}$. This process is driven by the electric dipole-dipole interaction, which is allowed due to the partial $f$ character that the $g$ state acquires in an electric field. The experimentally observed resonant field, together with the Stark map calculation is used to make a determination of the ${}^{85}\mathrm{Rb}$ $ng$-series quantum defect ${\delta }_g(n=30)=0.00405\left(6\right)$.

High harmonic generation from diatomic molecules in a linearly polarized intense laser field is investigated and the emission time of the harmonics is discussed with the time-frequency analysis method. It is shown that high harmonic generation from molecules at equilibrium distance is similar to that from atoms. Only the harmonics in the cutoff are synchronized, i.e., well phase-locked, whereas the other harmonics are not phase-locked. For the molecule stretched well beyond its equilibrium distance, the harmonics exhibit distinct time-frequency characteristics. The harmonic spectrum can be extended to $I_p+8U_p$, where $I_p$ and $U_p$ are the ionization and ponderomotive potential, and the harmonics with energies below $I_p+3.17U_p$ are not phase-locked and the harmonics with energies beyond $I_p+3.17U_p$ are well phase-locked. Thus a large range of harmonics which are well phase-locked are produced, and a train of clean attosecond (as) pulses with a single $90\text{−}\mathrm{as}$ pulse in each half optical cycle can be generated with a multicycle laser pulse. Using a few-cycle laser pulse, an isolated attosecond pulse with a duration of about $95\mathrm{as}$ is obtained.

We provide additional evidence for the existence of zero-width resonances in the intense-field photodissociation of ${{\mathrm{H}}_2}^{+}$. In a previous investigation [Atabek, Chrysos, and Lefebvre, Phys. Rev. A 49, R8 (1994)] the situation, in a two-channel dressed picture, corresponded to a diabatic crossing point classically reachable in both adiabatic potentials. A semiclassical explanation could be modeled after that developed for predissociation in the intermediate-coupling regime. At higher frequencies the crossing point lies between the two turning points. A numerical study shows that zero-width resonances exist also in such a case. An extension of the semiclassical approach provides an explanation for the occurrence of these resonances. It is shown that they survive even when going to a multichannel description. The associated wave functions and probability densities are studied: they are very similar to those of the upper adiabatic potential, with a minor component in the lower adiabatic channel. Some conditions for the production of such long-lived dressed molecular species are stated.

A procedure is proposed to prepare the average and width of the velocity distribution of ultracold atoms. The atoms are set initially in the ground state of an optical trap formed by an inner red-detuned-laser well and an outer blue-detuned-laser barrier. Then the well and barrier parameters are changed until the ground state becomes a Breit-Wigner tunneling resonance. An optimal time dependence of the switching process, between the sudden and adiabatic limits, adjusts the final translational energies of the leaking atoms to the Lorentzian distribution of the resonance state.

Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.

The Bogoliubov equations are solved for a three-dimensional Bose-Einstein condensate containing a doubly quantized vortex, trapped in a harmonic potential. Complex frequencies, signifying dynamical instability, are found for certain ranges of parameter values. The existence of alternating windows of stability and instability, respectively, is explained qualitatively and quantitatively using variational calculus and direct numerical solutions. It is seen that the windows of stability disappear in the limit of a cigar-shaped condensate, which is consistent with recent experimental results on the lifetime of a doubly quantized vortex in that regime.

In a recent paper [Bressanini et al. Phys. Rev. Lett. 95, 110201 (2005)] it was pointed out that “the nodes of even simple wave functions are largely unexplored.” Here we show that for $N$-particle wave functions nodal surfaces arise from the spin and orbital entanglement of constituent two-particle wave functions and derive, for two-electron atoms, 11 exact nodal rules applicable in $LS$ coupling. In addition, the “higher symmetry” identified numerically in the above paper is shown to be an approximate dynamical symmetry described by a molecular model or a classical unstable periodic orbit. We show that the analysis is readily extended to four-particle wave functions and consider the case of the hydrogen molecule, both fixed in space and rotating.

Based on a geometrical argument introduced by Żukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results. Moreover, a necessary and sufficient condition for the violation of this inequality is presented. It turns out that the class of nonseparable states which do not admit local realistic description is extended when compared to the two-setting inequalities. However, supporting the conjecture of Peres, quantum states with positive partial transposes with respect to all subsystems do not violate the inequality. Additionally, we follow a general link between Bell inequalities and communication complexity problems, and present a quantum protocol linked with the inequality, which outperforms the best classical protocol.

The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it corresponds to making measurements diagonal in a corresponding Schmidt basis. More generally, it is shown that the maximum correlation may be characterized in terms of a correlation basis for the joint density operator, which defines the corresponding (nondegenerate) optimal measurements. The maximum coincidence rate for spin measurements on two-qubit systems is determined to be $(1+s)∕2$, where $s$ is the spectral norm of the spin correlation matrix, and upper bounds are obtained for $n$-valued measurements on general bipartite systems. It is shown that the maximum coincidence rate is never greater than the computable cross norm measure of entanglement, and a much tighter upper bound is conjectured. Connections with optimal state discrimination and entanglement bounds are briefly discussed.

We study quantum information processing in complex disordered many body systems that can be implemented by using lattices of ultracold atomic gases and trapped ions. We demonstrate, first in the short range case, the generation of entanglement and the local realization of quantum gates in a disordered magnetic model describing a quantum spin glass. We show that in this case it is possible to achieve fidelities of quantum gates higher than in the classical case. Complex systems with long range interactions, such as ions chains or dipolar atomic gases, can be used to model neural network Hamiltonians. For such systems, where both long range interactions and disorder appear, it is possible to generate long range bipartite entanglement. We provide an efficient analytical method to calculate the time evolution of a given initial state, which in turn allows us to calculate its quantum correlations.

We propose the concept of SLOCC-equivalent basis in the multiqubit space. In particular, two special SEBs, the Greenberger-Horne-Zeilinger–(GHZ-) type and the $W$-type basis are introduced. They can make up a more general family of multiqubit states, the GHZ-$W$-type states, which is a useful kind of entanglement for quantum teleportation and error correction. We completely characterize the property of this type of state, and mainly classify the GHZ-type and the $W$-type states in a regular way, which is related to the enumerative combinatorics. Many concrete examples are given to exhibit our method of classification. We also propose the condition on which two GHZ-$W$-type states are interconvertible with probability 1.

We investigate the problem of enhancement of mutual information by encoding classical data into entangled input states of arbitrary length and show that while there is a threshold memory or correlation parameter beyond which entangled states outperform the separable states, resulting in a higher mutual information, this memory threshold increases toward unity as the length of the string increases. These observations imply that encoding classical data into entangled states may not enhance the classical capacity of quantum channels.

Dipolar coupled homonuclear spins present challenging, yet useful systems for quantum-information processing. In such systems, the eigenbasis of the system Hamiltonian is the appropriate computational basis and coherent control can be achieved by specially designed strongly modulating pulses. In this paper we describe the first experimental implementation of the quantum algorithm for numerical gradient estimation by nuclear magnetic resonance, using the eigenbasis of a four spin system.

There exist absorption windows (i.e., Cooper-minima) in the photoabsorption cross sections of some atomic systems because of the relative phase shifts between the initial and final state wave functions due to the atomic screening potentials in contrast to the Coulomb potentials. Such window positions are sensitive to the accuracy of the initial and final state wave functions. Using our modified Breit-Pauli $R$-matrix code, the photoionization cross sections of ground Na are calculated. Our calculated cross sections and minimum position in the low photoelectron energy range $(<9\mathrm{eV})$ are in excellent agreement with the experimental results. In the high energy range $(>9\mathrm{eV})$, there is an abnormal bump in the experimental measurements, which is a long-standing experimental puzzle. It is interesting to note that there is also an absorption window in the photoabsorption (i.e., photodissociation) cross sections of $\mathrm{Na}_2{}^{+}$. Such an absorption window provides an answer to the puzzle.

The high-energy electron impact excitation cross sections are directly proportional to the generalized oscillator strengths (GOSs) of the target (an atom or molecule). In the present work, the GOSs of helium from the ground state to $n{}^{1}S$, $n{}^{1}P$, $n{}^{1}D$ $(n\to \infty )$ and adjacent continuum excited states are calculated by a modified $R$-matrix code within the first Born approximation. In order to treat the bound-bound and bound-continuum transitions in a unified manner, the GOS density (GOSD) is defined based on the quantum defect theory. The GOSD surfaces of ${}^{1}S$, ${}^{1}P$, and ${}^{1}D$ channels are calculated and tested stringently by the recent experiments. With the recommended GOSD surfaces with sufficient accuracy, the GOSDs (i.e., GOSs) from the ground state into all $n{}^{1}S$, $n{}^{1}P$, and $n{}^{1}D$ excited states of helium can be obtained by interpolation. Thus, the high-energy electron impact excitation cross sections of all these excited states can be readily obtained. In addition to the high-energy electron impact excitation cross sections, a scheme to calculate the cross sections in the entire incident energy range is discussed.

We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that when the potential is turned on nonadiabatically, the system explores a number of transient states whose periodicity is a fraction of that of the lattice. We illustrate the origin of fractional-period states analytically by treating them as resonant states of a parametrically forced Duffing oscillator and discuss their transient nature and potential observability.

Dynamics of the spontaneous emission from a two-level atom embedded in a bisphere microcavity is analyzed theoretically. A bisphere supports a morphology-dependent resonance having such a high quality factor with local field enhancement that the strong coupling between the atom and the cavity can be realized. By taking full account of the photon degree of freedom, we derive theoretically the coupling constant between the atom and the cavity as well as the radiation damping constants, which are used in the conventional cavity QED approach. In addition, we show that the power spectrum of the spontaneous emission at a local observation point is strongly affected by the photon Green function.

We present a general theory on the interference of a two-photon wave packet associated with spatial modes at a beam splitter. We find that the topological symmetry of the two-photon angular spectrum governs the nature of the two-photon interference. We distinguish between the coalescence interference and anticoalescence interference according to the decrease or increase of the coincidence probability in the absence of interference, respectively, and demonstrate that the symmetric and antisymmetric two-photon angular spectra are responsible for perfect coalescence interference and anticoalescence interference, respectively. Then we prove that anticoalescence interference never occurs for two independent photons, and it turns out that anticoalescence interference is the signature of two-photon entanglement. On the basis of this feature, we propose a special Mach-Zehnder interferometer, incorporated with two spiral phase plates, which can change the interference from a coalescence to an anticoalescence type only for a two-photon entangled state. The scheme is simple and straightforward compared with a test of Bell’s inequality.