We give a general definition for the transition time in the Landau-Zener model. This definition allows us to compute numerically the Landau-Zener transition time at any sweeping rate without ambiguity in both diabatic and adiabatic bases. With this new definition, analytical results are obtained in both the adiabatic limit and the sudden limit.

We present a simple, analytic model for pump-probe spectroscopy in dilute atomic gases. Our model treats multilevel atoms, takes several broadening mechanisms into account and, with no free parameters, shows excellent agreement with experimentally observed spectra.

We investigate a repumping scheme for magneto-optically trapped calcium atoms. It is based on excitation of the $4s3d^1{D}_2$–$4s5p^1{P}_1$ transition at $672$ nm with an extended cavity diode laser. The effect of the repumping is approximately a factor of three increase in trap lifetime and a doubling of the trapping efficiency from a Zeeman slowed thermal beam. Added to this, the 672-nm laser repumps atoms from an otherwise dark state to yield an overall increase in detected fluorescence signal from the magneto-optic trap (MOT) of more than an order of magnitude. Furthermore, we report isotope shift measurements of the $672$-nm transition, for the first time, for four naturally occurring even isotopes. Using available charge radii data, the observed shifts, extending up to $4.3$ GHz, display the expected linear dependence in a King plot analysis. The measured shifts are used to determine the isotope shifts of the remaining ${}^{41,43,46}\mathrm{Ca}$ isotopes. These might be of interest where less abundant isotopes are used enabling isotope selective repumping, resulting in enhanced trapping and detection efficiencies.

We study the rich properties of the imbalanced antiferromagnet in an optical lattice. We present its phase diagram, discuss spin waves, and explore the emergence of topological excitations in two dimensions, known as merons, which are responsible for a Kosterlitz-Thouless transition that has never unambiguously been observed.

We present a numerical study of the one-dimensional BCS-BEC crossover of a spin-imbalanced Fermi gas. The crossover is described by the Bose-Fermi resonance model in a real space representation. Our main interest is in the behavior of the pair correlations, which, in the BCS limit, are of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type, while in the Bose-Einstein condensate limit, a superfluid of diatomic molecules forms that exhibits quasi-condensation at zero momentum. We use the density matrix renormalization group method to compute the phase diagram as a function of the detuning of the molecular level and the polarization. As a main result, we show that FFLO-like correlations disappear well below full polarization close to the resonance. The critical polarization depends on both the detuning and the filling.

The decay of a vortex from a nonrotating high temperature Bose-Einstein condensate is modeled using the stochastic projected Gross-Pitaevskii equation (SPGPE). In order to exploit the tunability of temperature in SPGPE theory while maintaining the total atom number constant, we develop a simple and accurate Hartree-Fock method to estimate the SPGPE parameters for systems close to thermal equilibrium. We then calculate the lifetime of a vortex using three classical field theories that describe vortex decay in different levels of approximation. The SPGPE theory is shown to give the most complete description of the decay process, predicting significantly shorter vortex lifetimes than the alternative theories. Using the SPGPE theory to simulate vortex decay for a trapped gas of $5\times {10}^5$ ${}^{87}\mathrm{Rb}$ atoms, we calculate a vortex lifetime $\mathrm{t̄}$ that decreases linearly with temperature, falling in the range $20\mathrm{s}>\mathrm{t̄}>1.5\mathrm{s}$ corresponding to the temperature range $0.78T_c⩽T⩽0.93T_c$. The vortex lifetimes calculated provide a lower bound for the lifetime of a persistent current with unit winding number in our chosen trap geometry in the limit of vanishing vortex pinning potential.

In this article we report on the production of a Bose-Einstein condensate (BEC) of ${}^{23}\mathrm{Na}$ using light-induced desorption as an atomic source. We load about $2\times {10}^7$ atoms in a magneto-optical trap (MOT) from this source with a $~6$ s loading time constant. The MOT lifetime can be kept around $27$ s by turning off the desorbing light after loading. We show that the pressure drops down by a factor of 40 in less than $100$ ms after the extinction of the desorbing light, restoring the low background pressure for evaporation. Using this technique, a BEC with ${10}^4$ atoms is produced after a $6$ s evaporation in an optical dipole trap.

We have analyzed the transmission properties of pulses through one-dimensional periodic structures in order to systematically explore the best conditions to achieve the maximum delay with the minimum possible distortion. In the absence of absorption and no layer variation, the transmission coefficient $t_N$ can be well approximated by a sum of Lorentzian resonances. The ratio between their width ${\Gamma }_{\mathrm{r}}$ and their separation $\Delta {\omega }_{\mathrm{r}}$ is a crucial parameter to characterize the distortion of the transmitted pulse. For typical values of the parameters used in telecommunications and high index of refraction contrasts $n_2/n_1$, the distortion of the transmitted pulse is unacceptably large for frequencies near the edge of the transmission window. We estimate fractional delays achievables in terms of the central frequency used and the pulse bandwidth.

Interference effects of photon pairs propagating through two-dimensional lattices of evanescently coupled waveguides are theoretically analyzed for input states of independent and path-entangled photons. Their correlation unveils characteristic Hong-Ou-Mandel interferences as well as more complex phenomena unique to these structures. Furthermore, purely classical states of light are used to simulate these quantum interferences in intensity correlation experiments. The results suggest that waveguide arrays can be employed as convenient devices for manipulating quantum states of light.

The propagation of polarization-entangled states of light through fluctuating loss channels in the turbulent atmosphere is studied, including the situation of strong losses. We consider violations of Bell inequalities by light, emitted by a parametric down-conversion source, after transmission through the turbulent atmosphere. It is shown by analytical calculations that, in the presence of background radiation and dark counts, fluctuating loss channels may preserve entanglement properties of light even better than standard loss channels, when postselected measurements are applied.

We consider the generation and propagation of ($2+1$)-dimensional beams in a nonlinear waveguide with the linear gain. Simple self-similar evolution of the beams is achieved at the asymptotic stage if the input beams represent the fundamental mode. On the contrary, if they carry vorticity or amplitude nodes (or phase slips), vortex tori and ring dark solitons (RDSs) are generated, featuring another type of the self-similar evolution, with an exponentially shrinking vortex core or notch of the RDS. Numerical and analytical considerations reveal that these self-similar structures are robust entities in amplifying waveguides, being stable against azimuthal perturbations.

In this report, we show explicitly that the tangles of an arbitrary pure state in a $2\otimes 2\otimes 4$ system satisfy the monogamy relation. This relation is also generalized to mixed states. As the tangle is always larger than the square of the concurrence, our result implies that the monogamy relation holds for concurrence too. It also supports the idea that the tangle could qualify as an elementary bipartite entanglement measure.

The transmission of electrons of energies 300–1000 eV through a single glass macrocapillary has been investigated. Falloff of the transmission intensity with respect to sample tilt angle relative to the beam direction has two regions, direct and indirect, for all investigated energies. The rate of transmission falloff in the direct region is independent of incident electron energy, whereas a maximum in the falloff rate for 500 eV was observed for the indirect. Rutherford scattering seems to dominate at lower energies, while Coulombic repulsion takes over at the higher energies.

A basic assumption behind the inequalities used for testing noncontextual hidden variable models is that the observables measured on the same individual system are perfectly compatible. However, compatibility is not perfect in actual experiments using sequential measurements. We discuss the resulting “compatibility loophole” and present several methods to rule out certain hidden variable models that obey a kind of extended noncontextuality. Finally, we present a detailed analysis of experimental imperfections in a recent trapped-ion experiment and apply our analysis to that case.

A detailed analysis of electron-positron–pair creation from vacuum in counterpropagating laser pulses is presented. Our particular interest lies in the nonperturbative multiphoton regime of interaction in different frequency domains. The pair creation may proceed both resonantly and nonresonantly where characteristic Rabi oscillations are shown for the near-resonance. By means of a quasiclassical method we obtain intuitive physical insight into the process. An independent numerical approach confirms and extends the analytical results by providing rich information on momentum spectra, resonance widths, and the time dependence of the creation probability, both on and off the resonance.

The first stage of the hybrid quantum repeaters is entanglement generation based on transmission of pulses in coherent states over a lossy channel. Protocols to make entanglement with only one type of error are favorable for rendering subsequent entanglement distillation efficient. Here we provide the tight upper bound on performances of these protocols that is determined only by the channel loss. In addition, we show that this bound is achievable by utilizing a proposed protocol [K. Azuma, N. Sota, R. Namiki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, Phys. Rev. A 80, 060303(R) (2009)] composed of a simple combination of linear optical elements and photon-number-resolving detectors.

We propose and work out a scheme to generate the entangled $W$ states for a chain of $N$ four-level atoms which are transported through an optical cavity by means of an optical lattice. This scheme is based on the combined laser-cavity mediated interaction between distant and equally separated atoms and works in a completely deterministic way for qubits encoded by two hyperfine levels of the atoms. Only two parameters, namely the distance between the atoms and the velocity of the chain, determine the effective interaction among the atoms and, therefore, the degree of entanglement that is obtained for the overall chain of $N$ qubits. In particular, we work out the parameter regions for which the $W_N$ states are generated most reliably for chains of $N=2,3,4$ and $5$ atoms. In addition, we analyze the sensitivity in the formation of entanglement for such chains of qubits due to uncertainties produced by the oscillations of atoms in optical lattices.

It is shown that while entanglement ensures difficulty in discriminating a set of mutually orthogonal states perfectly by local operations and classical communication (LOCC), entanglement content does not. In particular, for a class of entangled multiqubit states, the maximum number of perfectly LOCC distinguishable orthogonal states is shown to be independent of the average entanglement of the states, and the spatial configuration with respect to which LOCC operations may be carried out. It is also pointed out that for this class, the makeup of an ensemble, that is whether it consists only of entangled states or not, determines the maximum number of perfectly distinguishable states.

Presented is a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a superbraid. The crossing of world lines can be quantum-mechanical in nature, most conveniently expressed analytically with ladder-operator-based quantum gates. At a crossing, independent world lines can become entangled. Complicated superbraids are systematically reduced by recursively applying quantum skein relations. If the superbraid is closed (e.g., representing quantum circuits with closed-loop feedback, quantum lattice gas algorithms, loop or vacuum diagrams in quantum field theory), then one can decompose the resulting superlink into an entangled superposition of classical links. Thus, one can compute a superlink invariant, for example, the Jones polynomial for the square root of a classical knot.

The finite-element discrete variable representation is proposed to express the nonequilibrium Green’s function for strongly inhomogeneous quantum systems. This method is highly favorable against a general basis approach with regard to numerical complexity, memory resources, and computation time. Its flexibility also allows for an accurate representation of spatially extended Hamiltonians and thus opens the way toward a direct solution of the two-time Schwinger-Keldysh-Kadanoff-Baym equations on spatial grids, including, for example, the description of highly excited states in atoms. As benchmarks, we compute and characterize, in Hartree-Fock and second Born approximations, the ground states of the He atom, the ${\mathrm{H}}_2$ molecule, and the LiH molecule in one spatial dimension. Thereby, the ground-state and binding energies, densities, and bond lengths are compared with the direct solution of the time-dependent Schrödinger equation.