We study the quantum dynamics of a model for a vortex in a Bose gas with repulsive interactions in an anisotropic, harmonic trap. By solving the Schrödinger equation numerically, we show that the circulation of the vortex can undergo periodic reversals by quantum-mechanical tunneling. With increasing interaction strength or particle number, vortices become increasingly stable, and the period for reversals increases. Tunneling between vortex and antivortex states is shown to be described to a good approximation by a superposition of vortex and antivortex states (Schrödinger cat state), rather than the mean-field state, and we derive an analytical expression for the oscillation period. The problem is shown to be equivalent to that of the two-site Bose-Hubbard model with attractive interactions.

We report the experimental manifestation in optical physics of wave propagation involving self-steepening without concomitant self-phase-modulation. The conditions are realized through the interplay of quadratic and cubic nonlinearities in a frequency-doubling crystal. The experiment constitutes the physical realization of the Chen-Lee-Liu equation, a derivative nonlinear Schrödinger equation that governs pulse propagation.

An analogy is found between Wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field. Whereas in the process of Wigner tunneling an electron encounters a classically allowed region where a discrete energy level coincides with its energy, in the magnetic field the potential barrier is constant in the direction of tunneling. Along the tunneling path, certain regions are formed where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. These regions play the role of potential wells, where a discrete energy level can coincide with the electron energy. This phenomenon, which occurs at a certain magnetic field, is called Euclidean resonance and substantially depends on the shape of the potential forces in the direction perpendicular to tunneling. Under conditions of Euclidean resonance, a long-distance underbarrier motion is possible, which can be observed in experiments.

Recently we predicted a random blinking, i.e., macroscopic quantum jumps, in the fluorescence of a laser-driven atom-cavity system [Metz et al., Phys. Rev. Lett. 97, 040503 (2006)]. Here we analyze the dynamics underlying this effect in detail and show its robustness against parameter fluctuations. Whenever the fluorescence of the system stops, a macroscopic dark period occurs and the atoms are shelved in a maximally entangled ground state. The described setup can therefore be used for the controlled generation of entanglement. Finite photon detector efficiencies do not affect the success rate of the state preparation, which is triggered upon the observation of a macroscopic fluorescence signal. High fidelities are achieved even in the vicinity of the bad cavity limit due to the inherent role of dissipation in the jump process.

We propose an upper bound for the eavesdropper’s information in the direct and reverse reconciliated coherent states quantum key distribution protocols with heterodyne detection. This bound is derived by maximizing the leaked information over the symplectic group of transformations that spans every physical Gaussian attack on individual pulses. We exhibit four different attacks that reach this bound, which shows that this bound is tight. Finally, we compare the secret key rate obtained with this bound to the homodyne rate.

Rules for quantizing the walker-coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical walk (QOW) is introduced by means of a rule that treats the quantum or classical noise affecting the coin’s state as a source of quantization. The long-term asymptotic statistics of the QO walker’s position, which shows enhanced diffusion rates as compared to the classical case, is exactly solved. A quantum optical implementation of the walk provides a physical framework for quantum simulation of its asymptotic statistics. The simulation utilizes interacting two-level atoms and/or randomly pulsating laser fields with fluctuating parameters.

We suggest a way to use strong Rydberg dipole-dipole interactions in order to induce nontrivial conditional dynamics in individual-atom systems and mesoscopic ensembles. Contrary to previous works, we suggest exciting atoms into different Rydberg states, which results in a potentially richer dynamical behavior. Specifically, we investigate systems of individual hydrogenlike atoms or mesoscopic ensembles excited into high-lying hydrogenlike $s$, $p$, or $d$ states, and show how to perform three-qubit conditional dynamics on the information they contain through a proper use of dipole-dipole-interaction-induced energy shifts.

The quantum resonances of an atom possessing a single valence electron which shows hyperfine interaction with the nucleus is investigated in the presence of a three-dimensional magnetic quadrupole field. Particular emphasis is put on the study of the interplay of the hyperfine and quadrupole forces. By analyzing the underlying Hamiltonian, a variety of symmetries are revealed, which give rise to a twofold degeneracy of the resonance energies. Our numerical approach employs the complex scaling method and a Sturmian basis set. Several regimes and classes of short- and long-lived resonances are identified. The energies and decay widths of the resonances are characterized by their electronic and nuclear spin properties.

We study an ultracold and dilute superfluid Bose-Fermi mixture confined in a strictly one-dimensional (1D) atomic waveguide by using a set of coupled nonlinear mean-field equations obtained from the Lieb-Liniger energy density for bosons and the Gaudin-Yang energy density for fermions. We consider a finite Bose-Fermi interatomic strength $g_{bf}$ and both periodic and open boundary conditions. We find that with periodic boundary conditions—i.e., in a quasi-1D ring—a uniform Bose-Fermi mixture is stable only with a large fermionic density. We predict that at small fermionic densities the ground state of the system displays demixing if $g_{bf}>0$ and may become a localized Bose-Fermi bright soliton for $g_{bf}<0$. Finally, we show, using variational and numerical solutions of the mean-field equations, that with open boundary conditions—i.e., in a quasi-1D cylinder—the Bose-Fermi bright soliton is the unique ground state of the system with a finite number of particles, which could exhibit a partial mixing-demixing transition. In this case the bright solitons are demonstrated to be dynamically stable. The experimental realization of these Bose-Fermi bright solitons seems possible with present setups.

We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. Sørensen et al., Phys. Rev. Lett. 94, 086803 (2005)]. Extending the previous work, we investigate conditions under which the FQH effect can be achieved for bosons on a lattice with an effective magnetic field and finite on-site interaction. Furthermore, we characterize the ground state in such systems by calculating Chern numbers which can provide direct signatures of topological order and explore regimes where the characterization in terms of wave-function overlap fails. We also discuss various issues which are relevant for the practical realization of such FQH states with ultracold atoms in an optical lattice, including the presence of a long-range dipole interaction which can improve the energy gap and stabilize the ground state. We also investigate a detection technique based on Bragg spectroscopy to probe these systems in an experimental realization.

In the strong-coupling Bose-Einstein condensation (BEC) region where a Feshbach resonance gives rise to tightly bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the BEC limit. In the low-density limit, we show how this dimer-fermion interaction gives the $s$-wave scattering length $a_{\mathit{BF}}=1.18a_F$ ($a_F$ is the $s$-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.

We present convergent-close-coupling (CCC) calculations of the angular anisotropy parameters ${\beta }_2,{\beta }_4$ and the recoil ion momentum distribution $d\sigma ∕d\mathit{p}$ in two-photon double ionization (TPDI) of helium. In a stark contrast to single-photon double ionization (SPDI), where the ${\beta }_2$ parameter varies widely changing the angular distribution from isotropic to nearly dipole for slow and fast photoelectrons, respectively, the $\beta$ parameters for TPDI show very little change. The angular distribution of the recoil ion is fairly isotropic in TPDI as opposed to a strong alignment with the polarization of light in SPDI.

The coherent states for the Kratzer-Fues potential, which are eigenstates of the annihilation operator and minimize the generalized position-momentum uncertainty relation, are constructed using the algebraic approach. The method is extended to include the rotating Kratzer-Fues oscillator. Construction of such states is important in the theory of molecular interactions with coherent electromagnetic fields, for example, in calculation of the dynamic alternation of the refractive index due to the interactions of the laser pulse with the coherent vibration-rotational states of the diatomic molecule.

A detailed study of the umbrellalike vibration in inner-shell spectroscopy is presented. The high-resolution x-ray absorption spectrum for the lowest lying core excitation of the $\mathrm{C}{\mathrm{H}}_3$ free radical was recorded. High quality potential energy surfaces (PES) for the initial and final states of the transition were calculated as a function of the symmetrical stretching and the umbrella deformation coordinates. The strong anharmonicity along the umbrella coordinate in the double-well region of the PES of the core excited state has a strong effect on the bending vibrational progressions. The excellent agreement between the experiment and theory allows an accurate spectroscopic characterization of the vibrational structure of the electronic transition, and the estimation of the umbrella inversion time of $149\mathrm{fs}$.

Electron detachment from negative ions by few-cycle laser pulses is considered. The results of a full numerical solution of the time-dependent Schrödinger equation are compared to those from several analytic approaches. A nonmonotonic dependence of the detachment probability on the pulse duration at small field amplitudes $(⪡1\mathrm{a.u.})$ is observed and explained. In addition, momentum distributions of detached electrons are presented and analyzed.

We investigate the effect of unequal masses of the Bose and Fermi particles on the collective oscillations of the degenerate boson-fermion mixtures. In particular, we consider the monopole and the quadrupole modes of the oscillations and study their characters and the frequencies by using variational-sum-rule approach. We find that for both the modes there exist critical values of the ratio of boson-fermion masses below and above which the character and frequency of the respective modes are significantly different.

We use coherent-mode representation of partially coherent fields to analyze correlated imaging with classical light sources. This formalism is very useful to study the imaging quality. By decomposing the unknown object as the superposition of different coherent modes, the components corresponding to small eigenvalues cannot be well imaged. The generated images depend crucially on the distribution of the eigenvalues of the coherent-mode representation of the source and the decomposition coefficients of the objects. Three kinds of correlated imaging schemes are analyzed numerically.

The electromagnetic interaction of a moving compound charged system with leading relativistic corrections is studied. An effective Hamiltonian is obtained by using a set of canonical transformations, and it is demonstrated that the coupling of the total motion to internal degrees of freedom is uniquely determined by Lorentz covariance. Several known results such as the Röntgen term and the interaction of the spin with the electric field are recovered, and new results for various relativistic and recoil corrections are obtained.

We introduce a feasible method of constructing the entanglement witness that detects genuine multiqubit entanglement in the vicinity of a given pure multiqubit state. We illustrate our method in the scenario of constructing the witnesses for the multiqubit states that are most often investigated theoretically and experimentally. It is shown that our method can construct the effective witnesses for experiments. We also investigate the entanglement detection of symmetric states and mixed states.

The interaction of orbital electrons with the charge and magnetic moment of the nucleus polarizes it, and the detailed description requires a careful treatment of the nuclear vector polarizability. We present a complete and closed-form expression for the resulting contribution to hyperfine splitting in light atomic systems.