We present numerical studies of Bose-Einstein condensates in an optical box trap. The box trap is modeled by using Gaussian-wall or hard-wall trapping potentials along the boundary of the box to mimic a recent experimental setup. In order to study a quasi-one-dimensional system, the Gaussian walls are separated differently along the axial and radial directions. Furthermore, the two-body interaction is described by a hard-sphere potential, whose radius equals the $s$-wave scattering length. Using a finite-temperature path integral Monte Carlo method, we have calculated the density profiles of the system as a function of the temperature, the strength of the two-body interaction, and the number of particles. Our numerical results show clearly the Tonks-gas–like behavior in the strong interaction limit. In addition, we have compared our numerical data with the experimental data and theoretical results, and found that our simulation data agree with them quantitatively.

We present numerical solutions in the form of spatially localized nonrotating and rotating (azimuthon) multisolitons in the two-dimensional (“pancake-shaped configuration”) Bose-Einstein condensate (BEC) confined by a parabolic trap. The numerical relaxation procedure with a stabilizing factor is used.

In this paper, we generate the Lax pair for the one-dimensional Gross-Pitaevskii equation with time-dependent scattering length in the presence of a confining or expulsive harmonic time-dependent trap. We then exploit the Lax pair profitably to construct multisoliton solutions using gauge transformation from a trivial input solution. In particular, we have investigated the effect of both expulsive and confining traps on soliton interaction. Even though we find that the amplitude of the bright soliton relies upon the time-dependent scattering length and the external time-dependent trap with the velocity being dictated by the external trap alone, the observation of interdependence of the scattering length on the trap shows that the bright solitons not only can be compressed into a desirable width and amplitude but also can be remote controlled and driven anywhere in the plane by suitably maneuvering the external time-dependent trap alone.

A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes.

The entanglement between two modes of free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated. It is found that the same initial entanglement for an initial state parameter $\alpha$ and its “normalized partner” $\sqrt{1-{\alpha }^2}$ will be degraded by the Unruh effect along two different trajectories except for the maximally entangled state, which just shows the inequivalence of the quantization for a free field in Minkowski and Rindler coordinates. In the infinite-acceleration limit, the state does not have distillable entanglement for any $\alpha$ for the scalar field, but always remains entangled to a degree that is dependent on $\alpha$ for the Dirac field. It is also interesting to note that in this limit the mutual information equals just half of the initial mutual information; this result is independent of $\alpha$ and the type of field.

We calculate the frequencies of the Tkachenko oscillations of a vortex lattice in a harmonically trapped superfluid Fermi gas. We use the elastohydrodynamic theory and properly account for the elastic constants, the Thomas-Fermi density profile of the atomic cloud, and the boundary conditions. Thanks to the Fermi pressure, which is responsible for larger cloud radii with respect to the case of dilute Bose-Einstein condensed gases, large vortex lattices are achievable in the unitary limit of infinite scattering length, even at relatively small angular velocities. This opens the possibility of experimentally observing vortex oscillations in the regime where the dispersion relation approaches the Tkachenko law for incompressible fluids and the mode frequency is almost comparable to the trapping frequencies.

Quantum-state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in ${\mathrm{Pr}}^{3+}$ ions, doped into a ${\mathrm{Y}}_2\mathrm{Si}{\mathrm{O}}_5$ crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-Mølmer dark-state scheme [Roos and Mølmer, Phys. Rev. A 69, 022321 (2004)] Fidelities above $>90\%$, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-Mølmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.

We investigate entanglement distribution in pure-state quantum networks. We consider the case when nonmaximally entangled two-qubit pure states are shared by neighboring nodes of the network. For a given pair of nodes, we investigate how to generate the maximal entanglement between them by performing local measurements, assisted by classical communication, on the other nodes. We find optimal measurement protocols for both small and large one-dimensional networks. Quite surprisingly, we prove that Bell measurements are not always the optimal ones to perform in such networks. We generalize then the results to simple small two-dimensional (2D) networks, finding again counterintuitive optimal measurement strategies. Finally, we consider large networks with hierarchical lattice geometries and 2D networks. We prove that perfect entanglement can be established on large distances with probability one in a finite number of steps, provided the initial entanglement shared by neighboring nodes is large enough. We discuss also various protocols of entanglement distribution in 2D networks employing classical and quantum percolation strategies.

The theoretical and experimental values of the $5f$, $6f$, $7f$, and $8f$ radiative lifetimes $\tau$ of neutral potassium are reported. The reduced matrix elements for all allowed electric-dipole $n{f}_{5∕2}\text{−}{n}^{\prime }{d}_{5∕2}$, $n{f}_{5∕2}\text{−}{n}^{\prime }{d}_{3∕2}$, and $n{f}_{7∕2}\text{−}{n}^{\prime }{d}_{5∕2}$ transitions with $n=5–8$ in K are calculated using the relativistic linearized coupled-cluster method with single and double excitations of Dirac-Fock wave functions included to all orders in many-body perturbation theory. The resulting electric-dipole matrix elements are used to evaluate the lifetimes of the $5f$, $6f$, $7f$, and $8f$ states in neutral K and their uncertainties. The contributions from the $n{f}_{5∕2}\text{−}{n}^{\prime }{g}_{7∕2}$, $n{f}_{7∕2}\text{−}{n}^{\prime }{g}_{7∕2}$, and $n{f}_{7∕2}\text{−}{n}^{\prime }{g}_{9∕2}$ transitions to the lifetimes of the $6f$, $7f$, and $8f$ states are evaluated using the third-order many-body perturbation theory and are found to be very small. The theoretical results are ${\tau }_{5f}=117\left(4\right)\mathrm{ns}$, ${\tau }_{6f}=195\left(4\right)\mathrm{ns}$, ${\tau }_{7f}=301\left(6\right)\mathrm{ns}$, and ${\tau }_{8f}=441\left(9\right)\mathrm{ns}$. The experiment is performed in a cell using time-resolved fluorescence spectroscopy. The $nf$ states are excited stepwise, $4s\to 4p\to nf$, using two pulsed synchronous dye lasers for the dipole and quadrupole transitions, respectively. The measured values ${\tau }_{5f}=117\left(3\right)\mathrm{ns}$, ${\tau }_{6f}=190\left(6\right)\mathrm{ns}$, ${\tau }_{7f}=309\left(8\right)\mathrm{ns}$, and ${\tau }_{8f}=428\left(10\right)\mathrm{ns}$ are in excellent agreement with the present theoretical calculations.

Quantum control of a system with coherent laser fields involves not only a time-domain component but also a space-domain component. Here we used phase-controlled laser fields to achieve quantum control of tunneling ionization in the space domain and the resultant selective ionization of oriented molecules in the gas phase. The directionally asymmetric tunneling ionization induced by intense $(5.0\times {10}^{12}\mathrm{W}∕{\mathrm{cm}}^2)$ nanosecond phase-controlled fields consisting of a fundamental light and second-harmonic light led to selective ionization of oriented molecules, which reflects the geometric nature of the highest occupied molecular orbital in the ground state. High selectivity was achieved with a single control variable. Quantum control was robust, being free of both laser wavelength and pulse-duration constraints, and thus can be applied to a wide range of molecules. Moreover, the combination of a conventional laser source and an adjustment-free simple optical system provided robust quantum control with high reproducibility.

We extend a recently developed Hamiltonian formalism for nonlinear wave interaction processes in spatially periodic dielectric structures to the far-off-resonant regime and investigate numerically the three-wave resonance conditions in a one-dimensional optical medium with ${\chi }^{\left(2\right)}$ nonlinearity. In particular, we demonstrate that the cascading of nonresonant wave interaction processes generates an effective ${\chi }^{\left(3\right)}$ nonlinear response in these systems. We obtain the corresponding coupling coefficients through appropriate normal form transformations that formally lead to the Zakharov equation for spatially periodic optical media.

We use the two-atom concurrence and the visibility of interference fringes of photons to characterize a quantum phase transition for a hybrid system consisting of an array of coupled cavities and each cavity doped with a two-level atom. We compare them with the total excitation number fluctuation. Analytical and numerical simulation results show quantum critical phenomena similar to the Mott insulator to superfluid transition. Here, the contour lines of the atomic concurrence, the visibility of interference fringes of photons, and the excitation number fluctuation in the phase diagram are consistent in the vicinity of the nonanalytic locus of the atomic concurrence.

We first consider stimulated Raman adiabatic passages in a closed four-level tripod system. In this case, the adiabatic eigenstates of the system acquire real geometric phases. When the system is open and subject to decoherence they acquire complex geometric phases that we determine by a Monte Carlo wave function approach. We calculate the geometric phases and the state evolution in the closed as well as in the open system cases and describe the deviation between these in terms of the phases acquired. When the system is closed, the adiabatic evolution implements a Hadamard gate. The open system implements an imperfect gate and hence has a fidelity below unity. We express this fidelity in terms of the acquired geometric phases.

We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsäcker functional, instead of the more traditional approach where the nonlocal terms have the structure of the Thomas-Fermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionals means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved.

The dissociative recombination of the ozone cation has been studied at the heavy-ion storage ring CRYRING. The total cross section and branching fractions have been measured. The cross section from $\approx 0\text{eV}$ to 0.2 eV follows a nearly $E^{-1}$ dependence, which was theoretically predicted to be a characteristic of the direct dissociative recombination mechanism. The thermal rate coefficient has been deduced from the cross section to be $7.37\times {10}^{-7}{\left(T/300\right)}^{-0.55}{\text{cm}}^3{\text{s}}^{-1}$. The branching fraction analysis carried out at $\approx 0\text{eV}$ interaction energy has shown a strong propensity $\left(94\%\right)$ to dissociate through the three-body channel. Due to the overwhelming dominance of this channel it has been investigated in more detail. Of the six energetically available three-body pathways only three are significantly populated, such that the production of $\text{O}\left({}^{1}S\right)$ is highly unfavored and all atomic oxygen fragments are predominantly formed in ${}^{3}P$ and ${}^{1}D$ states. Analysis of the breakup geometries has been performed by means of the Dalitz plot. It is observed that the molecules dissociating through the $\text{O}\left({}^{3}P\right)+\text{O}\left({}^{3}P\right)+\text{O}\left({}^{3}P\right)$ and $\text{O}\left({}^{3}P\right)+\text{O}\left({}^{3}P\right)+\text{O}\left({}^{1}D\right)$ channels have an open linear geometry where the cleavage of two valence bonds occurs preferentially in unison, while the $\text{O}\left({}^{3}P\right)+\text{O}\left({}^{1}D\right)+\text{O}\left({}^{1}D\right)$ breakup might proceed partly through a sequential mechanism.

We analyze the control of molecular orientation by nonresonant and quasiresonant two-color laser pulses ($2+1$ process). The laser pulses are assumed to be short with respect to the rotational period. In the nonresonant case, we show that the efficiency of this strategy crucially depends on the polarizability and the hyperpolarizability of the molecule. In the quasiresonant case, i.e., if the $2\omega$ frequency is in quasiresonance with a vibrational frequency, one can improve the orientation by adjusting the detuning. The best orientation is obtained for an optimal value of the detuning, which is different from zero.

We investigate the properties of trapped Bose-Fermi mixtures for experimentally relevant parameters in one dimension. The effect of the attractive Bose-Fermi interaction onto the bosons is to deepen the parabolic trapping potential, and to reduce the bosonic repulsion in higher order. This leads for many situations to an increase in bosonic coherence. The opposite effect was observed in ${}^{87}\text{R}\text{b-}{}^{40}\text{K}$ experiments, most likely due to a sharp rise in temperature. We also discuss low-temperature features, such as a bosonic Mott insulator transition driven by the fermion concentration, and the formation of composite particles such as polarons and molecules.

We present an analytic theory of the diffraction of (matter) waves by a lattice in the “quasi-Bragg" regime, by which we mean the transition region between the long-interaction Bragg and “channeling” regimes and the short-interaction Raman-Nath regime. The Schrödinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and reinserting the result into the Schrödinger equation to yield a second-order correction. Closed expressions for arbitrary pulse shapes and diffraction orders are obtained and the losses of the population to output states otherwise forbidden by the Bragg condition are derived. We consider the phase shift due to couplings of the desired output to these states that depends on the interaction strength and duration and show how these can be kept negligible by a choice of smooth (e.g., Gaussian) envelope functions even in situations that substantially violate the adiabaticity condition. We also give an efficient method for calculating the effective Rabi frequency (which is related to the eigenvalues of Mathieu functions) in the quasi-Bragg regime.

We present a detailed analysis of the dynamics of Bloch oscillations of Bose-Einstein condensates in disordered lattice potentials. Due to the disorder and the interparticle interactions these oscillations undergo a dephasing, reflected in a damping of the center of mass oscillations, which should be observable under realistic experimental conditions. The interplay between interactions and disorder is far from trivial, ranging from an interaction-enhanced damping due to modulational instability for strong interactions, to an interaction-reduced damping due to a dynamical screening of the disorder potential.