We propose experimental schemes for realizing frequency up- and down-conversion in two-mode cavity QED by considering the atom-cavity interaction in the presence of a strong driving classical field. In contrast to the recent paper based on dispersive atom-cavity interaction [Serra et al., Phys. Rev. A 71, 045802 (2005)], our scheme is based on resonant interaction of the cavity modes with a single driven three-level atom, so that the quantum dynamics operates at a high speed, which is important in view of decoherence. It is shown that, with the help of a strong driving classical field, frequency up- and down-conversion operations can be realized by initially preparing the atom in a certain state.

We propose a scheme for a viable and highly flexible all-optical atomic cooling and trapping using twisted light. In particular, we explain how one-dimensional twisted optical molasses should lead to a microscale atomic ring or a picoampere ionic current. Two-dimensional and three-dimensional molasses lead, respectively, to the creation of atom or ion loops and discrete atom clusters positioned at the eight corners of a microcube. These features at the microscale should find applications in physics and in quantum information processing using optically trapped atoms and ions.

Bell’s theorem states that no local realistic explanation of quantum mechanical predictions is possible, in which the experimenter has a freedom to choose between different measurement settings. Within a local realistic picture the violation of Bell’s inequalities can only be understood if this freedom is denied. We determine the minimal degree to which the experimenter’s freedom has to be abandoned, if one wants to keep such a picture and be in agreement with the experiment. Furthermore, the freedom in choosing experimental arrangements may be considered as a resource, since its lacking can be used by an eavesdropper to harm the security of quantum communication. We analyze the security of quantum key distribution as a function of the (partial) knowledge the eavesdropper has about the future choices of measurement settings which are made by the authorized parties (e.g., on the basis of some quasi-random generator). We show that the equivalence between the violation of Bell’s inequality and the efficient extraction of a secure key—which exists for the case of complete freedom (no setting knowledge)—is lost unless one adapts the bound of the inequality according to this lack of freedom.

We present two strategies to enhance the dynamical entanglement transfer from continuous-variable (CV) to finite-dimensional systems by employing multiple qubits. First, we consider the entanglement transfer to a composite finite-dimensional system of many qubits simultaneously interacting with a bipartite CV field. We show that, considering realistic conditions in the generation of CV entanglement, a small number of qubits resonantly coupled to the CV system are sufficient for an almost complete dynamical transfer of the entanglement. Our analysis also sheds further light on the transition between the microscopic and macroscopic behaviors of composite finite-dimensional systems coupled to bosonic fields (like atomic clouds interacting with light). Furthermore, we present a protocol based on sequential interactions of the CV system with some ancillary qubit systems and on subsequent measurements, allowing us to probabilistically convert CV entanglement into “almost-perfect” Bell pairs of two qubits. Our proposals are suited for realizations in various experimental settings, ranging from cavity-QED to cavity-integrated superconducting devices.

We study the effect of pure dephasing on the entanglement of a pair of two-level subsystems (qubits). We show that partial dephasing induced by a super-Ohmic reservoir, corresponding to well-established properties of confined charge states and phonons in semiconductors, may lead to complete disentanglement. We show also that the disentanglement effect increases with growing distance between the two subsystems.

Highly accurate nonrelativistic ground-state wave function and energy of the lithium atom are obtained in the Hylleraas basis set. The leading relativistic corrections, as represented by the Breit-Pauli Hamiltonian, are obtained in fair agreement with the former results. The calculational method is based on analytical evaluation of Hylleraas integrals with the help of recursion relations.

The bound vibrational levels for $J=0$ have been computed for the series of alkali-metal hydride molecules from LiH to RbH, including NaH and KH. For all four molecules the corresponding potential-energy curves have been obtained for each isolated species and for its positron-bound complex $\left(e^{+}X\mathrm{H}\right)$. It is found that the calculated positron affinity values strongly depend on the molecular vibrational state for which they are obtained and invariably increase as the molecular vibrational energy content increases. The consequences of our findings on the likelihood of possibly detecting such weakly bound species are briefly discussed.

Single- and double-charge-transfer cross sections of ${}^3\mathrm{He}^{2+}$ ions in collisions with ${\mathrm{N}}_2,{\mathrm{O}}_2$, CO, and $\mathrm{C}{\mathrm{O}}_2$ molecules have been measured in the energy range of 0.20 to $2.7\mathrm{keV}∕\mathrm{u}$. In addition, the same type of measurements for ${\mathrm{H}}_2$ molecules has been also carried out again for energies in the range from 0.13 to $0.40\mathrm{keV}∕\mathrm{u}$. For all molecules except for $\mathrm{C}{\mathrm{O}}_2$, the present single-charge-transfer cross sections are found to be generally larger than, or at least comparable to, double-charge-transfer cross sections in the energy region studied. This is a marked difference in comparison to experimental results reported earlier where a sharp increase for double charge transfer was observed below $0.3\mathrm{keV}∕\mathrm{u}$. The double-charge-transfer cross sections are found to be apparently larger than single-charge-transfer cross sections only for $\mathrm{C}{\mathrm{O}}_2$ molecules at energies below $0.8\mathrm{keV}∕\mathrm{u}$. A theoretical analysis based on a close-coupling method within a molecular representation has also been carried out for ${\mathrm{H}}_2$ and CO targets to provide some insights.

Collisions of polar ${}^1\Sigma$ state molecules at ultralow energies are considered, within a model that accounts for long-range dipole-dipole interactions, plus rotation of the molecules. We predict a substantial suppression of dipole-driven inelastic collisions at high values of the applied electric field, namely, field values of several times $B_0∕\mu$. Here $B_0$ is the rotational constant, and $\mu$ is the electric dipole moment of molecules. The sudden large drop in the inelastic cross section is attributed to the onset of degeneracy between molecular rotational levels, which dramatically alters the scattering Hamiltonian. This capability could, in principle, be used to stabilize ultracold gases against collisional losses.

The phase of an electronic wave function is shown to play an important role in coherent control experiments. By using a pulse shaping system with a femtosecond laser, we explore the phase relationships among resonant and off-resonant Raman transitions in ${\mathrm{Li}}_2$ by measuring the phases of the resulting wave packets, or quantum beats. Specific pixels in a liquid-crystal spatial light modulator are used to isolate the resonant and off-resonant portions of the Raman transitions in ${\mathrm{Li}}_2$. The off-resonant Raman transitions have an approximately 90° phase shift with respect to the resonant Raman transition, and there is an approximately 180° phase shift between the blue-detuned and the red-detuned off-resonant Raman transitions. Calculations using second-order time-dependent perturbation theory for the electronic transitions agree with the experimental results for the laser pulse intensities used here. Interferences between the off-resonant Raman transitions as a function of detuning are used to demonstrate coherent control of the Raman quantum wave packet.

We study the static and dynamic responses of an $F=1$ dipolar spinor condensate with magnetic dipole moment under external magnetic fields, focusing on the effects induced by the magnetic dipolar interactions between atoms. A rich set of phenomena are investigated such as the ground state quantum phases, the magnetization steps, spin squeezing, and macroscopic entanglement generation.

Using a model many-body wave function I analyze the standard criterion for Bose-Einstein condensation and its relation to coherence properties of the system. I pay special attention to an attractive condensate under such a condition that a characteristic length scale of the spatial extension of its center of mass differs significantly from length scales of relative coordinates. I show that although no interference fringes are produced in the two-slit Young interference experiment performed on this system, fringes of a high visibility can be observed in a conditional simultaneous detection of two particles.

We show how sub-Planck phase-space structures in the Wigner function [W. H. Zurek, Nature (London) 412, 712 (2001)] can be used to achieve Heisenberg-limited sensitivity in weak-force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent states, are shown to be useful for the measurement of weak forces that cause translations or rotations in phase space, which is done by entangling the quantum oscillator with a two-level system. Implementations of this strategy in cavity QED and ion traps are described.

The dynamics of a pair of atoms can significantly differ from the single-atom dynamics if the distance of the two atoms is small on a scale given by the relevant transition wavelengths. Here, we discuss two nearby three-level atoms in $\Lambda$ configuration, and focus on the dependence of the optical properties on the geometry of the setup. We find that in general transitions in the two atoms can be dipole-dipole coupled by interactions via the vacuum field even if their transition dipole moments are orthogonal. We give an interpretation of this effect and show that it may crucially influence the system dynamics. In particular, for a fixed setup of driving fields and detectors, the spatial orientation of the two-atom pair decides if the system reaches a true constant steady state or if it exhibits periodic oscillations in the long-time limit. As an example observable, we study the resonance fluorescence intensity, which is either constant or is modulated periodically in the long-time limit.

We present a semiconductor laser system tailored to exhibit unusual spectral broadband emission dynamics. We study the dynamics properties and its physical origin in detail and discuss the potential of this system as a high-power incoherent laser light source. Our semiconductor laser (SL) system comprises a particularly long edge-emitting laser of 1.6 mm length and a short external cavity of comparable length. We have adjusted for resonant coupling conditions between both cavities, such introducing strong modal coupling. By varying the pumping or the optical feedback phase, we obtain a characteristic cyclic scenario evolving from stable emission via a period-doubling cascade to chaos and back to stable emission. We find distinct differences to the short-cavity regime of conventional nonresonant SL systems reported so far. The most prominent difference is the onset of chaotic intensity dynamics in conjunction with pronounced multimode dynamics of high optical bandwidth exceeding $\sim 7\mathrm{nm}$, therefore comprising more than 100 lasing longitudinal modes. In that sense, the presented system represents an excellent nonlinear dynamical model system offering well-controllable generation of distinct multimode dynamics. Furthermore, we demonstrate that the nonlinear dynamics properties allow for controlled adjustment of the coherence length in a wide range between $\sim 130\mu \mathrm{m}$ and $\sim 8\mathrm{m}$. This property facilitates application in novel measurement technology in which (in)coherence properties are of importance.

Using the coarse-grain averaged hydrodynamic approach, we calculate all low energy transverse excitation spectrum of a rotating Fermi superfluid containing vortex lattices for all regimes along the Bose-Einstein condensate–Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. In the fast rotating regime, the molecular BEC enters into the lowest Landau level, but the superfluid in the unitarity and the BCS regimes occupies many low-lying Landau levels. The difference between the breathing mode frequencies at the BEC and unitarity limit shrinks to zero as the rotation speed approaches the radial trap frequency, in contrast to the finite difference in the nonrotating systems.

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size $N$ by using only $O\left(\sqrt{N}\right)$ queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either $M$ or $K$, our task is to determine which is the case. We show how to solve this problem with a high probability of success using iterations of Grover’s basic step only, and no other algorithm. Let $m$ be the required number of iterations; we prove that under certain restrictions on the sizes of $M$ and $K$ the estimation $m<2\sqrt{N}∕(\sqrt{K}-\sqrt{M})$ obtains. This bound reproduces previous results based on more elaborate algorithms, and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover’s algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.

We address the effects of natural three-qubit interactions on the computational power of one-way quantum computation. A benefit of using more sophisticated entanglement structures is the ability to construct compact and economic simulations of quantum algorithms with limited resources. We show that the features of our study are embodied by suitably prepared optical lattices, where effective three-spin interactions have been theoretically demonstrated. We use this to provide a compact construction for the Toffoli gate. Information flow and two-qubit interactions are also outlined, together with a brief analysis of relevant sources of imperfection.

We present a way to manipulate ultracold atoms where four atomic levels are trapped by appropriately tuned optical lattices. When employed to perform quantum computation via global control, this unique structure dramatically reduces the number of steps involved in the control procedures, either for the standard, network, model, or for one-way quantum computation. The use of a far-blue-detuned lattice and a magnetically insensitive computational basis makes the scheme robust against decoherence. The present scheme is a promising candidate for experimental implementation of quantum computation and for graph-state preparation in one, two, or three spatial dimensions.

We show that the classification of bipartite pure entangled states when local quantum operations are restricted yields a structure that is analogous in many respects to that of mixed-state entanglement. Specifically, we develop this analogy by restricting operations through local superselection rules, and show that such exotic phenomena as bound entanglement and activation arise using pure states in this setting. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. In particular, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed-state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.