Highly accurate quantum mechanical calculations are performed for the $1s^{2}2s^2$ (${}^1{S}_0$) $\to$ $1s^{2}2p^2$ (${}^1{S}_0$) transition energy in the isotopomers of ${\mathrm{C}}^{2+}$ ion to determine the isotope shifts. Explicitly correlated Gaussian functions and a variational approach that explicitly includes the nuclear motion are employed in the calculations. The leading relativistic and quantum electrodynamics corrections to the transition energy are also calculated using the perturbation theory with the nonrelativistic wave function as the zero-order approximation. It is determined that the ${}^{12}{\mathrm{C}}^{2+}$ transitions energy, which is obtained from the calculations to be 182 519.031 cm${}^{-1}$ (vs the experimental value of 182 519.88 cm${}^{-1}$, an excellent sub-wave-number agreement) up-shifts by 1.755 cm${}^{-1}$ for ${}^{13}{\mathrm{C}}^{2+}$ and by additional 1.498 cm${}^{-1}$ for ${}^{14}{\mathrm{C}}^{2+}$. Those shifts are sufficiently large to be measured experimentally.

We study resolved sideband laser cooling of a one-dimensional optical lattice with one atom per site, and in particular the effect of the dipole interaction between radiating atoms. For simplicity, we consider the case where only a single cooling laser is applied. We derive a master equation and solve it in the limit of a deep lattice and weak laser driving. We find that the dipole interaction significantly changes the final temperature of the particles, increasing it for some phonon wave vectors and decreasing it for others. The total phonon energy over all modes is typically higher than in the noninteracting case but can be made lower by the right choice of parameters.

Partial photoionization cross sections from the ${}^{1}S$ ground and the ${}^{3}P$ metastable states of the Be isoelectronic series to different final states, including a number of satellite (ionization plus excitation) channels are studied using the $R$-matrix method. As expected, the ratio of each satellite partial cross section to the dominant partial cross section is found to be a monotonic decreasing function of $Z$ for both the ground and the metastable states. The complicated patterns of these ratios as functions of photon energy are analyzed.

We investigate few-boson systems in finite one-dimensional multiwell traps covering the full interaction crossover from uncorrelated to fermionized particles. Our treatment of the ground-state properties is based on the numerically exact multiconfigurational time-dependent Hartree method. For commensurate filling, we trace the fingerprints of localization as the interaction strength increases, in several observables like reduced-density matrices, fluctuations, and momentum distribution. For a filling factor larger than 1 we observe on-site repulsion effects in the densities and fragmentation of particles beyond the validity of the Bose-Hubbard model upon approaching the Tonks-Girardeau limit. The presence of an incommensurate fraction of particles induces incomplete localization and spatial modulations of the density profiles, taking into account the finite size of the system.

We describe an experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a two-bit Boolean function in the framework of one-way quantum computation. For this purpose, a two-photon six-qubit cluster state was engineered. Its peculiar topological structure is the basis of the original measurement pattern allowing the algorithm realization. The good agreement of the experimental results with the theoretical predictions, obtained at $~1$ kHz success rate, demonstrates the correct implementation of the algorithm.

We show that the quantum dynamics of interacting and noninteracting quantum particles are fundamentally different in the context of solving a particular computational problem. Specifically, we consider the graph isomorphism problem, in which one wishes to determine whether two graphs are isomorphic (related to each other by a relabeling of the graph vertices), and focus on a class of graphs with particularly high symmetry called strongly regular graphs (SRGs). We study the Green’s functions that characterize the dynamical evolution single-particle and two-particle quantum walks on pairs of nonisomorphic SRGs and show that interacting particles can distinguish nonisomorphic graphs that noninteracting particles cannot. We obtain the following specific results. (1) We prove that quantum walks of two noninteracting particles, fermions or bosons, cannot distinguish certain pairs of nonisomorphic SRGs. (2) We demonstrate numerically that two interacting bosons are more powerful than single particles and two noninteracting particles, in that quantum walks of interacting bosons distinguish all nonisomorphic pairs of SRGs that we examined. By utilizing high-throughput computing to perform over 500 million direct comparisons between evolution operators, we checked all tabulated pairs of nonisomorphic SRGs, including graphs with up to 64 vertices. (3) By performing a short-time expansion of the evolution operator, we derive distinguishing operators that provide analytic insight into the power of the interacting two-particle quantum walk.

A general approach for ab initio calculations of electronic continuum processes is described in which the many-electron wave function is expanded using a combination of orbitals at short range and the finite-element discrete-variable representation (FEM-DVR) at larger distances. The orbital portion of the basis allows efficient construction of many-electron configurations in which some of the electrons are bound, but because the orbitals are constructed from an underlying FEM-DVR grid, the calculation of two-electron integrals retains the efficiency of the primitive FEM-DVR approach. As an example, double photoionization of beryllium is treated in a calculation in which the $1s^2$ core is frozen. This approach extends the use of exterior complex scaling (ECS), successfully applied to helium and ${\mathrm{H}}_2$, to calculations with two active electrons on more complicated targets. Integrated, energy-differential and triply-differential cross sections are exhibited, and the results agree well with other theoretical investigations.

Details of the pathway for the dissociative ionization process of the ground electronic state of aligned ${\mathrm{D}}_2{}^{+}$ produced from the first ionization of ${\mathrm{D}}_2$ in a short ($~100$ fs) and intense ($4.0\times {10}^{14}$ W cm${}^{-2}$) 480 nm laser pulse are analyzed and visualized. The initial vibrational state of ${\mathrm{D}}_2{}^{+}$ comes from the vertical transformation of the ground state of ${\mathrm{D}}_2$. The initial wave packet in the ground electronic state of ${\mathrm{D}}_2{}^{+}$ is outgoing through a dissociation-ionization channel accompanied by a strong coupling between the $1s{\sigma }_g$ and $2p{\sigma }_u$ electronic states. We show explicitly that the transition from the coupling states $1s{\sigma }_g$ and $2p{\sigma }_u$ to the ionization state is not a direct transition, but takes place through other intermediate states having some dissociative energy that results in a relatively wide internuclear distribution of the ionization state.

A detailed description of the Monte Carlo wave packet technique applied to dissociative multiple ionization of diatomic molecules in short intense laser pulses is presented. The Monte Carlo wave packet technique relies on the Born-Oppenheimer separation of electronic and nuclear dynamics and provides a consistent theoretical framework for treating simultaneously both ionization and dissociation. By simulating the detection of continuum electrons and collapsing the system onto either the neutral, singly ionized or doubly ionized states in every time step the nuclear dynamics can be solved separately for each molecular charge state. Our model circumvents the solution of a multiparticle Schrödinger equation and makes it possible to extract the kinetic energy release spectrum via the Coulomb explosion channel as well as the physical origin of the different structures in the spectrum. The computational effort is restricted and the model is applicable to any molecular system where electronic Born-Oppenheimer curves, dipole moment functions, and ionization rates as a function of nuclear coordinates can be determined.

Theoretical calculations on dissociative double ionization of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ in short intense laser pulses using the Monte Carlo wave packet technique are presented for several different field intensities, wavelengths, and pulse durations. We find convincing agreement between theory and experimental results for the kinetic energy release spectra of the nuclei. Besides the correctly predicted spectra the Monte Carlo wave packet method offers insight into the nuclear dynamics during the pulse and makes it possible to address the origin of different structures observed in the spectra. Three-photon resonances in the singly ionized molecule and charge-resonance-enhanced ionization are shown to be the main processes responsible for the observed nuclear energy distributions.

We report on the spin textures produced by cooling unmagnetized ${}^{87}\mathrm{Rb}$ $F=1$ spinor gases into the regime of quantum degeneracy. At low temperatures, magnetized textures form that break translational symmetry and display short-range periodic magnetic order characterized by one- or two-dimensional spatial modulations with wavelengths much smaller than the extent of the quasi-two-dimensional degenerate gas. Spin textures produced upon cooling spin mixtures with a nonzero initial magnetic quadrupole moment also show ferromagnetic order that, at low temperature, coexists with the spatially modulated structure.

We consider collective emission of a single photon from a cloud of $N$ two-level atoms (one excited, $N-1$ ground state). For a dense cloud the problem is reduced to finding eigenfunctions and eigenvalues of an integral equation. We discuss an exact analytical solution of this many-atom problem for a spherically symmetric atomic cloud. Some eigenstates decay much faster then the single atom decay rate, while the others undergo very slow decay. We show that virtual processes yield a small effect on the evolution of rapidly decaying states. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important yielding additional decay channels which results in a slow decay of the otherwise trapped states. We also show that quantum mechanical treatment of spontaneous emission of weakly excited atomic ensemble is analogous to emission of $N$ classical harmonic oscillators.

We propose the use of a phase-diversity technique to estimate the orbital angular momentum (OAM) superposition state of an ensemble of photons that passes through an optical system, proceeding from an extended object. The phase-diversity technique permits the estimation of the optical transfer function (OTF) of an imaging optical system. As the OTF is derived directly from the wave-front characteristics of the observed light, we redefine the phase-diversity technique in terms of a superposition of OAM states. We test this new technique experimentally and find coherent results among different tests, which gives us confidence in the estimation of the photon ensemble state. We find that this technique not only allows us to estimate the square of the amplitude of each OAM state, but also the relative phases among all states, thus providing complete information about the quantum state of the photons. This technique could be used to measure the OAM spectrum of extended objects in astronomy or in an optical communication scheme using OAM states. In this sense, the use of extended images could lead to new techniques in which the communication is further multiplexed along the field.

We consider a number-operator–annihilation-operator uncertainty as a well-behaved alternative to the number-phase uncertainty relation, and examine its properties. We find a formulation in which the bound on the product of uncertainties depends on the expectation value of the particle number. Thus, while the bound is not a constant, it is a quantity that can easily be controlled in many systems. The uncertainty relation is approximately saturated by number-phase intelligent states. This allows us to define amplitude squeezing, connecting coherent states to Fock states, without a reference to a phase operator. We propose several setups for an experimental verification.

A large family of potentials related to the Maxwell fish-eye model is derived with the help of conformal mappings. It is shown that the whole family admits square-integrable $E=0$ solutions of the Schrödinger equation for discrete values of the coupling constant. A corresponding supersymmetric family of partner potentials to the preceding ones is derived as well. Some applications of the considered potentials are also discussed.

This paper deals with the entanglement, as quantified by the negativity, of pure quantum states chosen at random from the invariant Haar measure. We show that it is a constant ($0.72037$) multiple of the maximum possible entanglement. In line with the results based on the concentration of measure, we find evidence that the convergence to the final value is exponentially fast. We compare the analytically calculated mean and standard deviation with those calculated numerically for pure states generated via pseudorandom unitary matrices proposed by Emerson et al. [Science 302, 2098 (2003)]. Finally, we draw some conclusions about the geometry of quantum states based on our result.

We study the dynamics of wave packets in cesium dimers using a femtosecond-controlled pump-probe technique. We implement configurations with one pulse (pump) or two pulses (pump and control) to produce vibrational wave packets on the electronic excited state. The transmission of an additional, variable-delay probe pulse is measured to monitor the time evolution of the wave packets. In the case of the pump-control-probe configuration, a superposition of two independent wave packets is observed. In order to elucidate the observed experimental data, we develop a theory based on the Liouville equation for the density matrix associated with the Franck-Condon factors. Both the numerical and analytical calculations are in good agreement with our experimental results.

We investigate the excitation dynamics of Rydberg atoms in ultracold atomic samples by expanding the excitation probability and the correlation function between excited atoms in powers of the isolated atom Rabi frequency $\Omega$. In the Heisenberg picture, we give recurrence relations to calculate any order of these expansions, which are expected to be well behaved for arbitrarily strong interactions. For large homogeneous samples, the explicit terms of the expansions, up to ${\Omega }^4$, are given and then averaged over all possible random spatial distributions of atoms for the most important cases of excitation pulses and interactions.

We show that controlled dissipation can be used as a tool for exploring fundamental phenomena and managing mesoscopic systems of cold atoms and Bose-Einstein condensates. Even the simplest boson-Josephson junction, that is, a Bose-Einstein condensate in a double-well trap, subjected to removal of atoms from one of the two potential minima allows one to observe such phenomena as the suppression of losses and the nonlinear Zeno effect. In such a system the controlled dissipation can be used to create desired macroscopic states and implement controlled switching among different quantum regimes.