In homonuclear molecules, such as ${\mathrm{H}}_2$, the electric dipole transitions are strongly forbidden, and the transitions between rovibrational states are of the electric quadrupole type. We show, however, that magnetic dipole transitions also take place, although they are significantly weaker. We evaluate the probabilities of such transitions between several of the lowest rotational states and compare them with those of the corresponding electric quadrupole transitions.

We demonstrate that the third-order dispersion drastically changes the phase-sensitive parametric gain in cw-pumped fiber systems. We analytically calculate the phase-sensitive gain as a function of the frequency for amplification of two weak monochromatic fields with spectral components symmetric with respect to the pump field. In the absence of the third-order dispersion, the phase-sensitive gain is symmetric with respect to the frequency. When the third-order dispersion is present, the gain has an asymmetric shape. This asymmetry has its origin in the phase-sensitive nature of the parametric gain.

Local variables cannot describe the quantum correlations observed in tests of Bell inequalities. Likewise, we show that deterministic nonlocal variables cannot describe quantum correlations in a relativistic time-order-invariant way.

We explore the physical limits of pulsed dynamical decoupling methods for decoherence control as determined by finite timing resources. By focusing on a decohering qubit controlled by arbitrary sequences of $\pi$ pulses, we establish a nonperturbative quantitative upper bound to the achievable coherence for specified maximum pulsing rate and noise spectral bandwidth. We introduce numerically optimized control “bandwidth-adapted” sequences that saturate the performance bound and show how they outperform existing sequences in a realistic excitonic-qubit system where timing constraints are significant. As a by-product, our analysis reinforces the impossibility of fault-tolerance accuracy thresholds for generic open quantum systems under purely reversible error control.

We present an experimental demonstration of nonresonant manipulation of vibrational states in a molecule by an intense ultrashort laser pulse. A vibrational wave packet is generated in ${\mathrm{D}}_2{}^{+}$ through tunnel ionization of ${\mathrm{D}}_2$ by a few-cycle pump pulse. A similar control pulse is applied as the wave packet begins to dephase so that the dynamic Stark effect distorts the electronic environment of the nuclei, transferring vibrational population. The time evolution of the modified wave packet is probed via the ${\mathrm{D}}_2{}^{+}$ photodissociation yield that results from the application of an intense probe pulse. Comparing the measured yield with a quasiclassical trajectory model allows us to determine the redistribution of vibrational population caused by the control pulse.

We address the concept of direct multiphoton multiple ionization in atoms exposed to intense, short-wavelength radiation and explore the conditions under which such processes dominate over the sequential. Their contribution is shown to be quite robust, even under intensity fluctuations and interaction volume integration, and reasonable agreement with experimental data is also found.

Dynamical $A$ and $B$ maps have been employed extensively by Sudarshan and co-workers to investigate open-system evolution of quantum systems. A canonical structure of the $A$ map is introduced here. It is shown that this canonical $A$ map enables us to investigate whether the dynamics is completely positive (CP) or not completely positive (NCP) in an elegant way and, hence, it subsumes the basic results on open-system dynamics. Identifying memory effects in open-system evolution is gaining increasing importance recently and, here, a criterion of non-Markovianity, based on the relative entropy of the dynamical state is proposed. The relative entropy difference of the dynamical system serves as a complementary characterization—though not related directly—to the fidelity difference criterion proposed recently. Three typical examples of open-system evolution of a qubit, prepared initially in a correlated state with another qubit (environment), and evolving jointly under a specific unitary dynamics—which corresponds to a NCP dynamical map—are investigated by employing both the relative entropy difference and fidelity difference tests of non-Markovianity. The two-qubit initial states are chosen to be (i) a pure entangled state, (ii) the Werner state, which exemplifies both entangled and separable states of qubits, depending on a real parameter, and (iii) a separable mixed state. Both the relative entropy and fidelity criteria offer a nice display of how non-Markovianity manifests itself in all three examples.

We investigate the scenario where spatially separated parties perform measurements in randomly chosen bases on an $N$-partite Greenberger-Horne-Zeilinger state. We show that without any alignment of the measurements, the observers will obtain correlations that violate a Bell inequality with a probability that rapidly approaches 1 as $N$ increases and that this probability is robust against noise. We also prove that restricting these randomly chosen measurements to a plane perpendicular to a common direction will always generate correlations that violate some Bell inequality. Specifically, if each observer chooses their two measurements to be locally orthogonal, then the $N$ observers will violate one of two Bell inequalities by an amount that increases exponentially with $N$. These results are also robust against noise and perturbations of each observer’s reference direction from the common direction.

We propose an analytical study of relativistic tunneling through opaque barriers. We obtain a closed formula for the phase time. This formula is in excellent agreement with the numerical simulations and corrects the standard formula obtained by the stationary phase method. An important result is found when the upper limit of the incoming energy distribution coincides with the upper limit of the tunneling zone. In this case, the phase time is proportional to the barrier width.

We calculate an achievable secret key rate for quantum key distribution with a finite number of signals by evaluating the quantum conditional min-entropy explicitly. The min-entropy for a classical random variable is the negative logarithm of the maximal value in its probability distribution. The quantum conditional min-entropy can be expressed in terms of the guessing probability, which we calculate for $d$-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find nonzero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to nonzero key rates for only ${10}^4$–${10}^5$ signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states, the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.

Characterizing the transformation and classification of multipartite entangled states is a basic problem in quantum information. We study the problem under the two most common environments, local operations and classical communications (LOCC), stochastic LOCC and two more general environments, multicopy LOCC (MCLOCC), and multicopy SLOCC (MCSLOCC). We show that two transformable multipartite states under LOCC or SLOCC are also transformable under MCLOCC and MCSLOCC. What is more, these two environments are equivalent in the sense that two transformable states under MCLOCC are also transformable under MCSLOCC, and vice versa. Based on these environments we classify the multipartite pure states into a few inequivalent sets and orbits, between which we build the partial order to decide their transformation. In particular, we investigate the structure of SLOCC-equivalent states in terms of tensor rank, which is known as the generalized Schmidt rank. Given the tensor rank, we show that Greenberger-Horne-Zeilinger states can be used to generate all states with a smaller or equivalent tensor rank under SLOCC, and all reduced separable states with a cardinality smaller than or equivalent to the tensor rank under LOCC. Using these concepts, we extended the concept of the “maximally entangled state” in the multipartite system.

Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We specifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that ${}^{15}\mathrm{N}$H is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar coupling term. At higher energies and fields, intramolecular spin-spin coupling becomes increasingly important. Our qualitative results and conclusions are fairly independent of the exact form of the potential and of the size of the channel basis set.

When highly charged ions are incident on a surface, part of their potential energy is emitted as characteristic radiation. The energies and yields of these characteristic x rays have been measured for a series of elements at the Tokyo electron-beam ion trap. These data have been used to develop a simple model of the relaxation of the hollow atoms which are formed as the ion approaches the surface, as well as a set of semiempirical scaling laws, which allow for the ready calculation of the $K$-shell x-ray spectrum which would be produced by an arbitrary slow bare or hydrogenlike ion on a surface. These semiempirical scaling laws can be used to assess the merit of highly charged ion fluorescence x-ray generation in a wide range of applications.

Recently, it was predicted theoretically and verified experimentally that a pair of delayed and cross-polarized short laser pulses can create molecular ensembles with a well-defined sense of rotation (clockwise or counterclockwise). Here we provide a comparative study of the classical and quantum aspects of the underlying mechanism for linear molecules and for symmetric tops, like benzene molecules, that were used for the first experimental demonstration of the effect. Very good quantitative agreement is found between the classical description of the process and the rigorous quantum-mechanical analysis at the relevant experimental conditions. Both approaches predict the same optimal values for the delay between pulses and the angle between them, and deliver the same magnitude of the induced oriented angular momentum of the molecular ensemble. As expected, quantum and classical analyses substantially deviate when the delay between pulses is comparable with the period of quantum rotational revivals. However, time-averaged characteristics of the excited molecular ensemble are equally well described by these two approaches. This is illustrated by calculating the anisotropic time-averaged angular distribution of the double-pulse excited molecules, which reflects persistent confinement of the molecular axes to the rotation plane defined by two polarization vectors of the pulses.

We have recorded the double photoionization spectrum of atomic Cd at four different photon energies in the range 40–200 eV. The main channel is single ionization and subsequent decay of excited Cd${}^{+}$ states, some involving Coster-Kronig processes, whereas direct double ionization is found to be weak. The decay of the excited Cd${}^{+}$ states shows a strong selectivity, related to the configuration of the final state. Double ionization leading to the Cd${}^{2+}$ ground state is investigated in some detail and is found to proceed mainly through ionization and decay of $4d$ correlation satellites. The most prominent autoionization peaks have been identified with the aid of quantum-mechanical calculations.

We investigate in detail the effects of nonlinearity on optical diffraction of Bose-Einstein condensates (BECs). By directly integrating the optically coupled two-component Gross-Pitaevskii equation in real space-time, comprehensive analyses of BEC optical diffraction phenomena are done under various conditions of light-pulse irradiation, total number of BEC atoms, etc., without using the adiabatic elimination approximation for an atomic excited state. Calculation results for the optical diffraction of ${}^{87}\text{Rb}$ BECs revealed that (1) the effect of nonlinearity on the atomic states causes the “nonkinetic” nonlinear effect in the Raman-Nath regime of diffraction, while the dynamics of BEC atoms due to the nonlinearity-induced repulsive forces works dominantly to produce the “kinetic” nonlinear effect in the Bragg regime of diffraction; (2) nonlinearity reduces the amplitude and frequency of the two-photon Rabi oscillation between BEC stationary and moving states, suggesting limitations in implementing the BEC Mach-Zehnder interferometer; and (3) the observed nonlinear effects are free from kinetic effects of the atomic excited state and not responsible for the optical transition process.

By direct numerical simulation and variational solution of the Gross-Pitaevskii equation, we studied the stationary and dynamic characteristics of a cigar-shaped, localized, collisionally inhomogeneous Bose-Einstein condensate trapped in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a Bose-Einstein condensate [Roati et al., Nature (London) 453, 895 (2008)]. The effective potential characterizing the spatially modulated nonlinearity is obtained. It is found that the collisional inhomogeneity has influence not only on the central region but also on the tail of the Bose-Einstein condensate. The influence depends on the sign and value of the spatially modulated nonlinearity coefficient. We also demonstrate the stability of the stationary localized state by performing a standard linear stability analysis. Where possible, the numerical results are shown to be in good agreement with the variational results.

We study the convergence of a functional renormalization group technique by looking at the ratio between the fermion-fermion scattering length and the dimer-dimer scattering length for a system of nonrelativistic fermions. We find that in a systematic expansion in powers of the fields there is a rapid convergence of the result that agrees with known exact results.

We study the supercounterfluid (SCF) states in the two-component hard-core Bose-Hubbard model on a square lattice, using the quantum Monte Carlo method based on the worm (directed-loop) algorithm. Since the SCF state is a state of a pair condensation characterized by $\langle a^{†}b\rangle \ne 0,\langle a\rangle =0$, and $\langle b\rangle =0$, where $a$ and $b$ are the order parameters of the two components, it is important to study behaviors of the pair-correlation function $\langle a_i{b}_i^{†}{a}_j^{†}{b}_j\rangle$. For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair correlation, we confirm the Kosterlitz-Thouless character of the SCF phase. The simulation efficiency is also improved in the SCF phase.

We consider an ultracold dipolar Bose gas in a one-dimensional lattice. For a sufficiently large lattice recoil energy, such a system becomes a series of nonoverlapping Bose-Einstein condensates that interact via the long-range dipole-dipole interaction (ddi). We model this system via a coupled set of nonlocal Gross-Pitaevskii equations (GPEs) for lattices of both infinite and finite extent. We find significantly modified stability properties in the lattice due to the softening of a discrete roton-like mode, as well as “islands” in parameter space where biconcave densities are predicted to exist and that only exist in the presence of the other condensates on the lattice. We solve for the elementary excitations of the system to check the dynamical stability of these solutions and to uncover the nature of their collapse. By solving a coupled set of GPEs exactly on a full numeric grid, we show that this emergent biconcave structure can be realized in a finite lattice with atomic ${}^{52}\mathrm{Cr}$.