In this work we study the dynamics of free three-dimensional relativistic Gaussian wave packets with different spin polarizations. We analyze the connection between the symmetry of initial state and the dynamical characteristics of moving particle. The corresponding solutions of the Dirac equation having different types of symmetry were evaluated analytically and numerically and after that the electron probability densities, as well as the spin densities were visualized. The average values of velocity of the packet center and the average spin were calculated analytically, and the parameters of transient Zitterbewegung in different directions were obtained. These results can be useful for the interpretation of future experiments with trapped ions.

We investigate the symmetry breaking role of noise in adiabatic quantum computing using the example of the controlled-not gate. In particular, we analyze situations where the choice of initial Hamiltonian produces symmetries in the Hamiltonian and degeneracies in the spectrum. We show that, in these situations, the conventional stipulation that the initial and problem Hamiltonians do not commute is unnecessary, as noise will inherently play the role of a universal symmetry-breaking perturbation and split any level crossings that may impede or obstruct the computation. The effects of an artificial noise source with a tailored time-dependent amplitude are also explored and it is found that such a scheme could offer a considerable performance enhancement. These results are found using a generalized version of the Pechukas-Yukawa model of eigenvalue dynamics.

We consider the input-output process with low-$Q$ cavities confining atoms for quantum-information processing, based on a general expression for reflection coefficient of the single photon. Focusing on the qubit encoding in decoherence-free subspace (DFS), we propose entanglement generation, universal quantum computing, and multiqubit controlled phase flip, using individual photon input and output from the cavities. Because of the DFS and no requirement for high-$Q$ cavities, our schemes are not only immune to dephasing but also feasible with currently available technology.

We present a phenomenon of an asymptotic revival of bipartite entanglement between two stable solid-state qubits interacting via a single-mode cavity subject to dissipation. This effect is achievable in cavity quantum electrodynamics systems, assisted with strong classical pumping detuned from the cavity eigenmode, under the assumption of short system-bosonic reservoir correlation times. Moreover, we prove that this effect is independent of the initial cavity state and that all initially prepared Bell states experience the same qualitative effects. We present a method that can be used to generalize an arbitrary number of solid-state qubits.

The line center of a resonance is affected by the presence of neighboring resonances due to quantum interference between the two resonant processes. Such shifts must be accounted for in high-precision measurements but are easily overlooked. In the present work, we develop an analytic formulation for the effect in the simplest case of a three-level atom. The shifts in this model system are large enough to be of concern for precision measurements.

We construct the most general Hamiltonian for the electromagnetic interaction of the finite-size particle-like nucleus with arbitrary spin, magnetic dipole, and electric quadrupole moments. It includes all the terms, which are important for obtaining atomic energy levels up to the order ${\alpha }^6$. The result is verified against spin $s=0$, $1/2$, and $1$ cases, where the Foldy-Wouthuysen transformation is performed of the corresponding relativistic equation.

The parameter $W_a$, which characterizes nuclear-spin-dependent parity violation (PV) in the molecular spin-rotational Hamiltonian, was computed with a quasirelativistic Hartree-Fock approach for radium fluoride (RaF) and found to be one of the largest absolute values predicted so far. The peculiar electronic structure of RaF leads to highly diagonal Franck-Condon matrices between the energetically lowest two electronic states, which qualifies RaF for direct laser cooling. A subset of diatomic molecules with a wide range of internal structures suitable for this cooling technique is also indicated. As trapped cold molecules offer superior coherence times, RaF can be considered promising for high-precision experiments aimed at molecular PV.

Potential barriers in the effective radial potential experienced by a photoexcited electron are shown to result in dramatic, resonancelike effects in two-photon ionization processes. In a two-photon ionization process, such potential barriers may affect not only the final state of the electron (as in ordinary photoionization), but also the intermediate-state electron wave packet corresponding to the absorption of one photon. We illustrate these effects for the generalized two-photon cross sections for ionization of Ar and Xe within a single-active-electron, central-potential model.

We study the ground-state phases for a mixture of two atomic spin-1 Bose-Einstein condensates in the presence of a weak magnetic ($B$) field. The ground state is found to contain a broken-axisymmetry (BA) phase due to competitions among intraspecies and interspecies spin-exchange interactions and the linear Zeeman shifts. This is in contrast to the case of a single-species spin-1 condensate, where the axisymmetry breaking results from competitions among the linear and quadratic Zeeman shifts and the intraspecies ferromagnetic interaction. All other remaining ground-state phases for the mixture are found to preserve axisymmetry. We further elaborate on the ground-state phase diagram and calculate the Bogoliubov excitation spectra of the phases. For the BA phase, there exist three Goldstone modes that attempt to restore the broken U(1) and SO(2) symmetries.

We study vortex formation in a Bose-Einstein condensate in a rotating double-well potential. In addition to the ordinary quantized vortices and elusive ghost vortices, “hidden” vortices are found distributed along the central barrier. These hidden vortices are invisible like ghost vortices but carry angular momentum. Moreover, their core size is not given by the healing length, but is strongly influenced by the external potential. We find that the Feynman rule can be well satisfied only after including the hidden vortices. There is no critical rotation frequency for the formation of hidden vortices while there is one for the formation of ordinary visible vortices. Hidden vortices can be revealed in the free expansion of Bose-Einstein condensates. In addition, the hidden vortices in a Bose-Einstein condensate can appear in other external potentials, such as a rotating anisotropic toroidal trap.

Spectral excitations of ultracold gases of bosonic atoms trapped in one-dimensional optical lattices with disorder are investigated by means of the variational cluster approach applied to the Bose-Hubbard model. Qualitatively different disorder distributions typically employed in experiments are considered. The computed spectra exhibit a strong dependence on the shape of the disorder distribution and the disorder strength. We compare alternative results for the Mott gap obtained from its formal definition and from the minimum peak distance, which is the quantity available from experiments.

We present a study of phase transition to macroscopic superfluidity for an ultracold bosonic gas confined in a combined trap formed by a one-dimensional optical lattice and a harmonic potential, focusing on the critical temperature of this system and the interference patterns of the Bose gas released from the combined trap. Based on a semiclassical energy spectrum, we develop an analytic approximation for the critical temperature $T_c$, and compare the analytic results with that obtained by numerical computations. For finite temperatures below $T_c$, we calculate the interference patterns for both the normal gas and the superfluid gas. The total interference pattern shows a feature of “peak on a peak.” As a comparison, we also present the experimentally observed interference patterns of ${}^{87}\mathrm{Rb}$ atoms released from a one-dimensional optical lattice system in accord with our theoretical model. Our observations are consistent with the theoretical results.

We consider a spin-1 Bose-Einstein condensate trapped in a harmonic potential under the influence of a homogeneous magnetic field. We investigate spatial and spin structure of the mean-field ground states under constraints on the number of atoms and the total magnetization. We show that the trapping potential can make the antiferromagnetic condensate separate into three distinct phases and ferromagnetic condensate into two distinct phases. In the ferromagnetic case, the magnetization is located in the center of the harmonic trap, while in the antiferromagnetic case magnetized phases appear in the outer regions. We describe how the transition from the Thomas-Fermi regime to the single-mode approximation regime with decreasing number of atoms results in the disappearance of the domains. We suggest that the ground states can be created in experiment by adiabatically changing the magnetic-field strength.

We study dynamics of two interacting ultracold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the $\delta$-like potential, we study the time evolution of an initially separable state of two particles. The corresponding time-dependent single-particle density matrix is obtained and diagonalized, and single-particle orbitals are found. This allows us to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled, then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit.

After almost half a century since the work of Anderson [Phys. Rev. 109, 1492 (1958)], at present there is no well-established theoretical framework for understanding the dynamics of interacting particles in the presence of disorder. Here, we address this problem for interacting bosons near $T=0$, a situation that has been realized in trapped atomic experiments with an optical-speckle disorder. We develop a theoretical model for understanding the hydrodynamic transport of finite-sized Bose-Einstein condensates through disorder potentials. The goal has been to set up a simple model that will retain all the richness of the system yet provide analytic expressions, allowing deeper insight into the physical mechanism. Comparison of our theoretical predictions with the experimental data on large-amplitude dipole oscillations of a condensate in an optical-speckle disorder shows striking agreement. We are able to quantify various dissipative regimes of slow and fast damping. Our calculations provide clear evidence of a reduction in disorder strength due to interactions. The analytic treatment presented here allows us to predict the power law governing the interaction dependence of damping. The corresponding exponents are found to depend sensitively on the dimensionality and are in excellent agreement with experimental observations. Thus, the adeptness of our model in correctly capturing the essential physics of dissipation in such transport experiments is established.

In lossless periodic media, the concept of group velocity is fundamental to the study of propagation dynamics. When spatially averaged, the group velocity is numerically equivalent to energy velocity, defined as the ratio of energy flux to energy density of modal fields. However, in lossy media, energy velocity diverges from group velocity. Here, we define a modal field velocity which remains equal to the complex modal group velocity in homogeneous and periodic media. The definition extends to the more general situation of modal fields that exhibit spatial or temporal decay due to lossy elements or Bragg reflection effects. Our simple expression relies on a generalization of the concepts of energy flux and density. Numerical examples, such as a two-dimensional square array of silver rods in vacuum, are provided to confirm the result. Examples demonstrate how the dispersion relation of the periodic structure, the properties of its modes, and their group velocities change markedly in lossy media.

We examine the feasibility of generating continuous-variable multipartite entanglement in an intracavity concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci et al. [Phys. Rev. Lett. 101, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster state formation.

We present a procedure to generate parametrically shaped pulses after propagation through a microstructured hollow-core photonic crystal fiber. The properties of the fiber are characterized and employed to analytically design sequences of subpulses which are available after the fiber. In these sequences, each subpulse can be individually controlled in its physically intuitive parameters: position in time, energy, phase, and chirp as well as the polarization state with orientation, ellipticity, and helicity. Various endoscopic applications may arise from this approach.

We report the prediction of fully localized two-dimensional embedded solitons. These solitons are obtained in a quasi-one-dimensional waveguide array which is periodic along one spatial direction and localized along the orthogonal direction. Under appropriate nonlinearity, these solitons are found to exist inside the Bloch bands (continuous spectrum) of the waveguide and thus are embedded solitons. These embedded solitons are fully localized along both spatial directions. In addition, they are fully stable under perturbations.

We demonstrate the existence of shape-preserving self-localized nonlinear modes in a two-dimensional photonic lattice with a flat-topped defect that covers several lattice sites. The balance of diffraction, defocusing nonlinearity, and optical potential induced by lattices with various forms of defects results in novel families of solitons featuring salient properties. We show that the soliton shape can be controlled by varying the shape of lattice defects. The existence domains of fundamental and vortex solitons in the semi-infinite gap expand with the defect amplitude. Vortex solitons in the semi-infinite gap with rectangular intensity distributions will break into dipole solitons when the propagation constant exceeds a critical value. In the semi-infinite and first-finite gaps, we find that lattices with rectangular defects can support stable vortex solitons which exhibit noncanonical phase structure.