We discuss a technique to probe the properties of an interacting cold atomic gas that can be viewed as a dynamical compressibility measurement. We apply this technique to the study of the superfluid-to-Mott-insulator quantum phase transition in one and three dimensions for a bosonic gas trapped in an optical lattice. Excitations of the system are detected by time-of-flight measurements. The experimental data for the one-dimensional case are in good agreement with the results of a time-dependent density-matrix-renormalization-group calculation.

The classical product state capacity of a noisy quantum channel with memory is investigated. A forgetful noise-memory channel is constructed by Markov switching between two depolarizing channels which introduces non-Markovian noise correlations between successive channel uses. The computation of the capacity is reduced to an entropy computation for a function of a Markov process. A reformulation in terms of algebraic measures then enables its calculation. The effects of the hidden-Markovian memory on the capacity are explored. An increase in noise correlations is found to increase the capacity.

A relativistic many-body perturbation calculation is applied to calculate the hyperfine constants on the low-lying states of the alkaline-earth-metal ion ${{}^{135}\text{B}\text{a}}^{+}$. Orbital energies and wave functions are calculated by solving Dirac equation. Zeroth-order hyperfine constants are calculated with Dirac wave functions. The finite basis sets of the Dirac equation are constructed by $B$ splines. With the finite basis sets, the core polarization and the correlation effect are calculated for the hyperfine constants. The final results for ${{}^{135}\text{B}\text{a}}^{+}$ are $a\left(6S_{1/2}\right)=3754.813\text{MHz}$, $a\left(6P_{1/2}\right)=658.042\text{MHz}$, $a\left(6P_{3/2}\right)=109.383\text{MHz}$, $b\left(6P_{3/2}\right)=61.220\text{MHz}$, $a\left(5D_{3/2}\right)=180.649\text{MHz}$, $b\left(5D_{3/2}\right)=31.729\text{MHz}$, $a\left(5D_{5/2}\right)=-19.104\text{MHz}$, and $b\left(5D_{5/2}\right)=42.251\text{MHz}$.

We consider the behavior of an interacting many-particle system under slow external driving—a many-body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single-particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are “nonadiabatic” in that even at very slow driving it is exceedingly difficult to push the center of the distribution toward the limit of full ground-state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.

In this work we investigate the collision-induced (CI) dipole moment $\Delta {\mu }_i\left(R\right)$, the CI polarizability tensor $\Delta {\alpha }_{ik}\left(R\right)$, and the first dipole-hyperpolarizability tensor $\Delta {\beta }_{ijk}\left(R\right)$ of the ${\text{H}}_2\text{-Ar}$ pair as a function of the intermolecular distance $R$, and the relative orientation of the intermolecular vector $\hat{\mathbf{R}}$ and the ${\text{H}}_2$ molecule. For each type of spectroscopy the induction operator should be given in the symmetry adapted form. In our case the components of the CI dipole hyperpolarizability are expressed in such a way that their rotational behavior is unambiguously defined. The above description is based on the spherical rotationally adapted method presented here. Spherical rotationally adapted components $\Delta {\beta }_{\lambda L}^{\left(s,K\right)}\left(R\right)$ of the vector $\left(K=1\right)$ and the septor $\left(K=3\right)$ parts of the first dipole-hyperpolarizability tensor $\Delta \mathit{\beta }\left(R\right)$ are computed and discussed. Results are applied to the case of ${\text{H}}_2\text{-Ar}$ pair. Asymptotic long-range analytical formulas are proposed for the multipole-induced spherical rotationally adapted components $\Delta {\beta }_{\lambda L}^{\left(s,K\right)}\left(R\right)$ of $\Delta \mathit{\beta }\left(R\right)$, respectively. Reasonable agreement is observed between the long-range analytical and ab initio numerical data.

We determine the ground-state properties of a gas of interacting bosonic atoms in a one-dimensional optical lattice. The system is modeled by the Bose-Hubbard Hamiltonian. We show how to apply the time-evolving block decimation method to systems with periodic boundary conditions and employ it as a reference to find the ground state of the Bose-Hubbard model. Results are compared with recently proposed approximate methods, such as Hartree-Fock-Bogoliubov (HFB) theories generalized for strong interactions and the variational Bijl-Dingle-Jastrow method. We find that all HFB methods do not bring any improvement to the Bogoliubov theory and therefore provide correct results only in the weakly interacting limit, where the system is deeply in the superfluid regime. On the other hand, the variational Bijl-Dingle-Jastrow method is applicable for much stronger interactions but is essentially limited to the superfluid regime as it reproduces the superfluid–Mott-insulator transition only qualitatively.

Condensed Fermi systems with an odd number of particles can be described by means of polarizing external fields having a time-odd character. We illustrate how this works for Fermi gases and atomic nuclei treated by density-functional theory or Hartree-Fock-Bogoliubov theory. We discuss the method based on introducing two chemical potentials for different superfluid components, whereby one may change the particle-number parity of the underlying quasiparticle vacuum. Formally, this method is a variant of noncollective cranking, and the procedure is equivalent to the so-called blocking. We present and exemplify relations between the two-chemical-potential method and the cranking approximation for Fermi gases and nuclei.

We experimentally analyze a Bessel beam produced with a conical mirror, paying particular attention to its superluminal and diffraction-free properties. We spatially characterized the beam in the radial and on-axis dimensions and verified that the central peak does not spread over a propagation distance of 73 cm. In addition, we measured the superluminal phase and group velocities of the beam in free space. Both spatial and temporal measurements show good agreement with the theoretical predictions.

We propose an alternative scheme for quantum repeater without phase stabilization and polarization calibration of photons transmitted over long-distance channel. We introduce time-bin photonic states and use a two-photon interference configuration to robustly generate entanglement between distant atomic-ensemble-based memory qubits. Our scheme can be performed with current experimental setups through making some simple adjustments.

We study the exact entanglement dynamics of two qubits in a common structured reservoir. We demonstrate that for certain classes of entangled states, entanglement sudden death occurs, while for certain initially factorized states, entanglement sudden birth takes place. The backaction of the non-Markovian reservoir is responsible for revivals of entanglement after sudden death has occurred, and also for periods of disentanglement following entanglement sudden birth.

Cross sections for dissociative electron attachment (DEA) to formic acid and glycine are calculated by the resonant $R$-matrix theory. A model with one effective reaction coordinate close to the O-H stretch motion is employed. The choice of the anion $R$-matrix pole and the surface amplitude as functions of the reaction coordinate for formic acid are based on scattering phase-shift calculations using the finite element discrete model. For glycine the input parameters are adjusted to reproduce experimental data. The results show that the mechanism of DEA in these molecules is similar to that for the hydrogen halides and involves electron capture into a ${\sigma }^{\ast }\left(\text{OH}\right)$ orbital so that no ${\sigma }^{\ast }/{\pi }^{\ast }$ coupling is required. Nonlocal effects play an important role for both molecules. In particular, pronounced steps and cusps are seen at the vibrational excitation thresholds. A sharp threshold peak in glycine is interpreted as a vibrational Feshbach resonance.

Experimental and theoretical studies of the electron-impact excitation of the $\left(4s4p\right){{}^{1,3}P}_1$, $\left(4s5s\right){{}^{3}S}_1$, and $\left(4s4d\right){}^{1,3}D$ states of zinc atoms are reported. Relative emission cross sections were measured from the excitation thresholds to 50 eV incident energy. Theoretical angle-integrated and emission cross sections were obtained using the convergent close-coupling and $B$-spline $R$-matrix methods. The measured data were normalized to theory and are discussed in terms of electron spin and correlation effects. The studies highlight the significance of both channel coupling to the continuum and the inner $3d$-shell electrons.

The effect of spin-orbit interaction activated interchannel coupling in dipole and quadrupole photoionization of the $4p$ and $4d$ subshells of Xe and the $5p$ and $5d$ subshells of Rn using the relativistic random phase approximation (RRPA) is studied. Interference between channels arising from spin-orbit split components is found to influence the dipole cross sections of $\text{Xe}4d$ and $\text{Rn}5d$ subshells, and also the quadrupole cross sections of $\text{Xe}4p$ and $\text{Rn}5p$ subshells. The photoelectron angular distribution parameters are also affected, but to a lesser extent. Using the understanding gained, the conditions required for large spin-orbit interaction activated interchannel coupling effects are delineated.

We treat the interaction of an atom with a short intense few-cycle laser pulse by the use of the Magnus expansion of the time-evolution operator. Terms of the Magnus expansion up to the third order in the pulse duration are evaluated explicitly, and expressions for the transition probability between atomic eigenstates are given. The transition operators up to this order are particularly simple, involving only momentum and position shifts arising from the laser field alone. The connection to other existing approaches is established. For a variety of generic short-pulse forms the results of the Magnus approximation are in excellent agreement with time-dependent transition probabilities obtained from accurate ab initio numerical calculations. However, the limitation of the Magnus expansion for pulses having both vanishing momentum and position shifts is demonstrated also.

We present a feasibility study for loading cold atomic clouds into magnetic traps created by single-wall carbon nanotubes grown directly onto dielectric surfaces. We show that atoms may be captured for experimentally sustainable nanotube currents, generating trapped clouds whose densities and lifetimes are sufficient to enable detection by simple imaging methods. This opens the way for a different type of conductor to be used in atomchips, enabling atom trapping at submicron distances, with implications for both fundamental studies and for technological applications.

The dynamics of recombination in an ultrastrong laser field is studied by numerical simulations performed for one-dimensional (1D), two-dimensional, and three-dimensional atomic systems modeled by the hydrogen atom Coulomb potential as well as by a model potential with a smoothed core. A nonmonotonic behavior of the total bound-states' final population is studied as a function of the laser field amplitude. The dependence of the results on the used atomic potential is demonstrated. It is shown that the recombination probabilities calculated in these two cases may differ even qualitatively. Even eigenstates of the 1D hydrogen atom are shown to play a significant role in the time evolution.

When an incident light beam is scattered off a sample of ultracold atoms trapped in a double-well potential, the statistical properties of the retroreflected field contain information about the quantum state of the atoms, and permit, for example, to distinguish between atoms in a superfluid state and a product of Fock states for each well (Mott-insulator-like state). This paper extends our previous analysis of this problem to include the effects of cavity damping. We use a Monte Carlo wave-function method to determine the two-time correlation function and time-dependent physical spectrum of the retroreflected field. We also analyze quantitatively the entanglement between the atoms and the light field for atoms in these two states.

We investigate the coherent two-color photoassociation (PA) process in a spinor-1 atomic Bose-Einstein condensate by comparing the single-spin and mixed-spin cases. We find that, by tuning the PA light applied on different spin components, one can observe quite different features for the atomic spin-mixing dynamics (with weak PA field) or coherent atom-molecule conversion (with strong PA field), indicating a research field of so-called superchemistry or coherent PA in a spinor gas.

We apply a Bayesian data analysis scheme known as the Markov chain Monte Carlo to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical information concerning all reconstruction parameters including their statistical correlations with no a priori assumptions as to the form of the distribution from which it has been obtained. From this vector we can derive, e.g., the marginal distributions and uncertainties of all model parameters, and also of other quantities such as the purity of the reconstructed state. We demonstrate the utility of this scheme by reconstructing the Wigner function of phase-diffused squeezed states. These states possess non-Gaussian statistics and therefore represent a nontrivial case of tomographic reconstruction. We compare our results to those obtained through pure maximum-likelihood and Fisher information approaches.

By studying sets of operators having constant weight, we present an analytical upper bound on the pure quantum stabilizer codes whose underlying quantum system can be of arbitrary dimension, which outperforms the well-known quantum Hamming bound, the optimal analytical upper bound so far for small code length.