We performed double resonance spectroscopy on the ground-state hyperfine splitting of ${}^{113}\mathrm{Cd}^{+}$ ions trapped in a rf linear trap. The ions were optically pumped by UV light from the ${}^{106}\mathrm{Cd}$ lamp and cooled by He buffer gas. The ground-state hyperfine splitting was measured to be $15199862855\mathrm{Hz}$ with the precision of $1.3\times {10}^{-11}$. The uncertainty stems from the error in extrapolation to zero magnetic field and from the resonance linewidth. This value is $3\mathrm{Hz}$ lower than the previous high-precision measurements by [Tanaka et al., Phys. Rev. A 53, 3982 (1996)], in which the laser light was used for optical excitation. The potential for a new microwave frequency standard based on the $15.2\text{−}\mathrm{GHz}$ ground-state hyperfine splitting of ${}^{113}\mathrm{Cd}^{+}$ ions is also discussed. Stability of the hyperfine frequency of ${}^{113}\mathrm{Cd}^{+}$ ion, with microwaves locked to the hydrogen maser, is $\sim 2\times {10}^{-13}{\tau }^{-1∕2}$.

We present elastic integral, differential, and momentum-transfer cross sections for electron collisions with ${\mathrm{N}}_2\mathrm{O}$. We show that, with a slight modification of a method of incorporating polarization effects proposed recently by us [Winstead, McKoy, and Bettega, Phys. Rev. A 72, 042721 (2005)] along with a flexible one-particle basis set, we can reproduce features in the experimental data that were not reproduced by earlier calculations. We also find evidence of a Ramsauer-Townsend minimum, which our calculation places at about $0.2\mathrm{eV}$.

We discuss exact solutions of the Schrödinger equation for the system of two ultracold atoms confined in an axially symmetric harmonic potential. We investigate different geometries of the trapping potential, in particular we study the properties of eigenenergies and eigenfunctions for quasi-one-dimensional and quasi-two-dimensional traps. We show that the quasi-one-dimensional and the quasi-two-dimensional regimes for two atoms can be already realized in the traps with moderately large (or small) ratios of the trapping frequencies in the axial and the transverse directions. Finally, we apply our theory to Feshbach resonances for trapped atoms. Introducing in our description an energy-dependent scattering length we calculate analytically the eigenenergies for two trapped atoms in the presence of a Feshbach resonance.

We present ab initio quantum and classical investigations on the production and control of a single attosecond pulse by using few-cycle intense laser pulses as the driving field. The high-harmonic-generation power spectrum is calculated by accurately and efficiently solving the time-dependent Schrödinger equation using the time-dependent generalized pseudospectral method. The time-frequency characteristics of the attosecond xuv pulse are analyzed in detail by means of the wavelet transform of the time-dependent induced dipole. To better understand the physical processes, we also perform classical trajectory simulation of the strong-field electron dynamics and electron returning energy map. We found that the quantum and classical results provide complementary and consistent information regarding the underlying mechanisms responsible for the production of the coherent attosecond pulse. For few-cycle $\left(5\mathrm{fs}\right)$ driving pulses, it is shown that the emission of the consecutive harmonics in the supercontinuum cutoff regime can be synchronized and locked in phase resulting in the production of a coherent attosecond pulse. Moreover, the time profile of the attosecond pulses can be controlled by tuning the carrier envelope phase.

A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the nonperturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin’s minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum $Z$ gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significantly is a multicomponent low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.

Many papers have proven the security of quantum key distribution (QKD) systems in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any implemented QKD system required, it is needed to evaluate a protocol with a finite coding length. For this purpose, we derive a tight upper bound of the eavesdropper’s information. This bound is better than existing bounds. We also obtain the exponential rate of the eavesdropper’s information. Further, we approximate our bound by using the normal distribution.

We construct a class of quantum bipartite $d\otimes d$ states which are positive under partial transposition (PPT states). This class is invariant under the maximal commutative subgroup of $\mathrm{U}\left(d\right)$ and contains as special cases many well-known examples of PPT states. States from our class provide criteria for testing the indecomposability of positive maps. Such maps are crucial for constructing entanglement witnesses.

Analytic expressions for the width and shift of a photoassociative resonance or an optically induced Feshbach resonance in ultracold collisions are derived using the quasi-classical stationary phase approximation. This approach for the width is applicable over a wider range of cases than the reflection approximation. Possible applications for optical Feshbach resonances between ultracold alkaline-earth-metal atoms, such as Ca and Sr, are discussed. Our approach also applies to photoassociation in gases of heteronuclear alkali-metal atoms.

We use a Sagnac interferometer to measure the dispersive and absorptive properties of room temperature Rubidium vapor on the $D_2$ line at $780.2\mathrm{nm}$. We apply a pump beam such that the resulting $\Lambda$ system exhibits electromagnetically induced transparency. Using a “biased alignment” technique we demonstrate a direct and robust method of measuring the rapid variation in the refractive index. Such a “slow-light” Sagnac interferometer is ideally suited to precision measurement applications such as magnetometry and inertial sensing.

We study a temporal version of Young’s interference experiment by attosecond soft-x-ray pulses. The photoelectron energy spectra by attosecond double pulses exhibit an interference pattern, since we have no information on which pulse has generated the electron. We can re-establish the “which-way” information and control the interference visibility by changing the electron’s momentum with phase-stabilized laser pulses, by an amount depending on the time of ionization. Moreover, if we use a triple pulse, we can realize a situation where the electron passes through a single and a double slit simultaneously to the same direction and is observed by the same detector.

The ground state energies and the one-body densities of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of one molecule from $3\text{to}50\text{molecules}$. These calculations show that parahydrogen clusters exhibit a clear geometrical order which excludes any liquidlike structure. A definite confirmation of the magic size for the cluster with $13\text{molecules}$ is also obtained.

We propose a more general method for detecting a set of entanglement measures, i.e., negativities, in an arbitrary tripartite quantum state by local operations and classical communication. To accomplish the detection task using this method, three observers do not need to perform partial transposition maps by the structural physical approximation; instead, they only need to collectively measure some functions via three local networks supplemented by a classical communication. With these functions, they are able to determine the set of negativities related to the tripartite quantum state.

In an experiment involving detection of a photoelectron and up to three photoions from $\mathrm{C}{\mathrm{O}}_2$ in coincidence, we observe the triple ion coincidence ${\mathrm{C}}^{+}:{\mathrm{O}}^{+}:{\mathrm{O}}^{+}$. Moreover, we observe double coincidences between doubly charged cations and singly charged cation pairs ${\mathrm{C}}^{2+}:{\mathrm{O}}^{+}$, ${\mathrm{O}}^{2+}:{\mathrm{C}}^{+}$, ${\mathrm{O}}^{2+}:{\mathrm{O}}^{+}$. These ion triplets and pairs arise from fragmentation of the triply charged molecular ion $\mathrm{C}\mathrm{O}_2{}^{3+}$. Other ion pairs—viz., ${\mathrm{C}}^{+}:{\mathrm{O}}^{+}$, ${\mathrm{O}}^{+}:{\mathrm{O}}^{+}$, ${\mathrm{O}}^{+}:\mathrm{C}{\mathrm{O}}^{+}$—arising from the doubly charged molecular ion $\mathrm{C}\mathrm{O}_2{}^{2+}$, are also observed. From an analysis of the coincidence pattern we postulate four decay modes of the $\mathrm{C}\mathrm{O}_2{}^{3+}$ ion. Kinetic energy release in the channel leading to ${\mathrm{C}}^{+}:{\mathrm{O}}^{+}:{\mathrm{O}}^{+}$ is measured, and its distribution is postulated to have four contributing precursor states.

Low-energy antiproton capture, $\overline{p}+{\mathrm{He}}^{+}\to \overline{p}{\mathrm{He}}^{2+}+e$, is investigated using a wave-packet-propagation full-quantum-mechanical method or a quantum-classical hybrid (i.e., semiclassical) approximation. If the adiabatic picture (i.e., Born-Oppenheinmer separation) is a good approximation, the antiproton capture, which is a typical nonadiabatic process, can rarely occur. It is found that the probability of the nonadiabatic transition is small (at most $\sim 0.1$). However, even in the zero energy limit $(E\to 0)$, the antiproton capture always occurs for the total angular momenta $J\lesssim 40$. Correspondingly, the cross section for the antiproton capture diverges as $E\to 0$. This happens due to the peculiarity that the Coulomb force range is longer than the centrifugal one. The importance of a Rydberg series of resonances in the capture process is emphasized. On the low-energy dynamical feature, some interesting similarities to the $e+\text{ion}$ system are also found.

The explosion dynamics of hydrogen clusters driven by an ultrashort intense laser pulse has been analyzed analytically and numerically by employing a simplified Coulomb explosion model. The dependence of average and maximum proton kinetic energy on cluster size, pulse duration, and laser intensity has been investigated respectively. The existence of an optimum cluster size allows the proton energy to reach the maximum when the cluster size matches with the intensity and the duration of the laser pulse. In order to explain our experimental results such as the measured proton energy spectrum and the saturation effect of proton energy, the effects of cluster size distribution as well as the laser intensity distribution on the focus spot should be considered. A good agreement between them is obtained.

We study stationary clusters of vortices and antivortices in dilute pancake-shaped Bose-Einstein condensates confined in nonrotating harmonic traps. Previous theoretical results on the stability properties of these topologically nontrivial excited states are seemingly contradicting. We clarify this situation by a systematic stability analysis. The energetic and dynamic stability of the clusters is determined from the corresponding elementary excitation spectra obtained by solving the Bogoliubov equations. Furthermore, we study the temporal evolution of the dynamically unstable clusters. The stability of the clusters and the characteristics of their destabilizing modes only depend on the effective strength of the interactions between particles and the trap anisotropy. For certain values of these parameters, there exist several dynamical instabilities, but we show that there are also regions in which some of the clusters are dynamically stable. Moreover, we observe that the dynamical instability of the clusters does not always imply their structural instability, and that for some dynamically unstable states annihilation of the vortices is followed by their regeneration, and revival of the cluster.

Optical-field-ionization collisional-excitation x-ray lasers in xenon and krypton clustered gas jets were experimentally investigated in detail. Dependence of x-ray lasing on atom density, laser focus position, and laser polarization ellipticity was mapped out to find the optimal lasing conditions, and a tomographic measurement technique was used to provide clear pictures of the x-ray amplification process.

We generalize the Greenberger-Horne-Zeilinger nonlocality without inequalities argument to cover the case of arbitrary mixed statistical operators associated to three-qubits quantum systems. More precisely, we determine the radius of a ball (in the trace distance topology) surrounding the pure GHZ state and containing arbitrary mixed statistical operators which cannot be described by any local and realistic hidden variable model and which are, as a consequence, noncompletely separable. As a practical application, we focus on certain one-parameter classes of mixed states which are commonly considered in the experimental realization of the original GHZ argument and which result from imperfect preparations of the pure GHZ state. In these cases we determine for which values of the parameter measuring the noise a nonlocality argument can still be exhibited, despite the mixedness of the considered states. Moreover, the effect of the imperfect nature of measurement processes is discussed.

We present a Bell-state analyzer for time-bin qubits allowing the detection of three out of four Bell states with linear optics, two detectors, and no auxiliary photons. The theoretical success rate of this scheme is 50%. A teleportation experiment was performed to demonstrate its functionality. We also present a teleportation experiment with a fidelity larger than the cloning limit of $F=\frac{5}{6}$.

When comparing quantum states to each other, it is possible to obtain an unambiguous answer, indicating that the states are definitely different, already after a single measurement. In this paper we investigate comparison of coherent states, which is the simplest example of quantum state comparison for continuous variables. The method we present has a high success probability, and is experimentally feasible to realize as the only required components are beam splitters and photon detectors. An easily realizable method for quantum state comparison could be important for real applications. As examples of such applications we present a “lock and key” scheme and a simple scheme for quantum public key distribution.