We show the influence of stable and unstable periodic orbits on the energy eigenstates of the HOCl molecule, both below and above dissociation. The energy range considered is low enough to hold the HO bond fixed, allowing a two-dimensional model of the molecule. Above dissociation unstable periodic orbits, in a chaotic sea, anchor quasibound states of the molecule. Quasibound states are calculated using reaction matrix theory and are found to have lifetimes ranging over five orders of magnitude.

We present improved measurements of the static polarizability of the $8s\hspace{0.5em}{}^2{S}_{1/2}$ state of atomic cesium. Measured separately on two hyperfine components of the $6s\hspace{0.5em}{}^2{S}_{1/2}\to 8s\hspace{0.5em}{}^2{S}_{1/2}$ transition, we determine an average polarizability of ${\alpha }_{8s}=9.490\pm 0.012\hspace{0.5em}\mathrm{MHz}\mathrm{\hspace{0.5em}}(\mathrm{kV}/\mathrm{cm}{)}^{-2}$, and a difference of only $\Delta {\alpha }_{8s}=0.014\pm 0.016\hspace{0.5em}\mathrm{MHz}\mathrm{\hspace{0.5em}}(\mathrm{kV}/\mathrm{cm}{)}^{-2}$. ${\alpha }_{8s}$ is consistent with, but of higher precision ($<0.15\%$) than, the previous measurement and theory. The difference $\Delta {\alpha }_{8s}$ is smaller than our previous determination, and within 1 $\sigma$ of zero. Our new technique is insensitive to the frequency calibration of the laser.

The major task in quantum control theory is to find an external field that transforms the system from one state to another or executes a predetermined unitary transformation. We investigate the difficulty of computing the control field as the size of the Hilbert space is increased. In the models studied the controls form a small closed subalgebra of operators. Complete controllability is obtained by the commutators of the controls with the stationary Hamiltonian. We investigate the scaling of the computation effort required to converge a solution for the quantum control task with respect to the size of the Hilbert space. The models studied include the double-well Bose Hubbard model with the SU(2) control subalgebra and the Morse oscillator with the Heisenberg-Weil algebra. We find that for initial and target states that are classified as generalized coherent states (GCSs) of the control subalgebra the control field is easily found independent of the size of the Hilbert space. For such problems, a control field generated for a small system can serve as a pilot for finding the field for larger systems. Attempting to employ pilot fields that generate superpositions of GCSs or cat states failed. No relation was found between control solutions of different Hilbert space sizes. In addition the task of finding such a field scales unfavorably with Hilbert space sizes. We demonstrate the use of symmetry to obtain quantum transitions between states without phase information. Implications to quantum computing are discussed.

We have numerically explored the asymmetry in the branching ratio of the photofragments in the photodissociation of HD${}^{+}$ (neutral D and neutral H), leading to the possibility of localization of the electron on a chosen nucleus by careful tuning of the laser parameters. For two different frequencies we show that, starting from an initial stationary wave function, proper tuning of the pulse duration (2σ) and peak intensities ($I^0$) of the laser pulses can lead to very different branching ratios of the two reaction channels. The results are interpreted in terms of the propagation of the nonstationary wave packet through regions having dominant radiative or nonradiative interactions at different times. We also investigate what effect the choice of initial vibrational state has on the overall asymmetry in the branching ratio of the dissociation products.

In this contribution, we investigate the relativistic ionization characteristics of highly charged hydrogenlike ions in short intense laser pulses as a function of the laser pulse parameters by means of the numerical solution of the time-dependent Dirac equation and the time-dependent Klein-Gordon equation as well as by the classical phase-space averaging method. For this purpose, we generalize the phase-space averaging method such that it is applicable to relativistically driven particles in arbitrary central potentials. If the ionization probability is not too small, quantum mechanical and classical methods give similar results for laser wavelengths in the range from the near-infrared to soft x-ray radiation. We find that ionization in few-cycle intense laser pulses depends sensitively on the pulses’ peak intensity but little on the pulse tails and on the pulse energy. The ionization probability is shown to be strongly linked to the peak intensity allowing for an estimation of the laser intensity via ionization yields.

The spin-wave (SW) $N$-particle path-entangled $|N,0\rangle +|0,N\rangle$ (NOON) state is an $N$-particle Fock state with two atomic spin-wave modes maximally entangled. Attributed to the property that the phase is sensitive to collective atomic motion, the SW NOON state can be utilized as an atomic interferometer and has promising application in quantum enhanced measurement. In this paper we propose an efficient protocol to deterministically produce the atomic SW NOON state by employing the Rydberg blockade. Possible errors in practical manipulations are analyzed. A feasible experimental scheme is suggested. Our scheme is far more efficient than the recent experimentally demonstrated one, which only creates a heralded second-order SW NOON state.

We consider a small $F=1$ spinor condensate inside an optical cavity driven by an optical probe field, and subject the output of the probe to a homodyne detection, with the goal of investigating the effect of measurement backaction on the spin dynamics of the condensate. Using the stochastic master equation approach, we show that the effect of backaction is sensitive to not only the measurement strength but also the quantum fluctuation of the spinor condensate. The same method is also used to estimate the atom numbers below which the effect of backaction becomes so prominent that extracting spin dynamics from this cavity-based detection scheme is no longer practical.

We formulate the time-dependent Bogoliubov dynamics of colliding Bose-Einstein condensates in terms of a positive-$P$ representation of the Bogoliubov field. We obtain stochastic evolution equations for the field which converge to the full Bogoliubov description as the number of realizations grows. The numerical effort grows linearly with the size of the computational lattice. We benchmark the efficiency and accuracy of our description against Wigner distribution and exact positive-$P$ methods. We consider its regime of applicability, and show that it is the most efficient method in the common situation when the total particle number in the system is insufficient for a truncated Wigner treatment.

Motivated by the recent experiment on $p$-orbital-band bosons in optical lattices, we study theoretically the quantum phases of Mott insulator and superfluidity in two dimensions. The system features a superfluid phase with transversely staggered orbital current at weak interaction and a Mott insulator phase with antiferro-orbital order at strong coupling and commensurate filling. We go beyond mean-field theory and derive from a microscopic model an effective action that is capable of describing both the $p$-band Mott insulating and superfluid phases in strong coupling. We further calculate the excitation spectra near the quantum critical point and find two gapless modes away from the tip of the Mott lobe but four gapless modes at the tip. Our effective theory reveals how the phase coherence peak builds up in the Mott regime when approaching the critical point. We also discuss the finite-temperature phase transition of $p$-band superfluidity.

We study the possibility of changing the topological charge of incident beams by layered helical structures consisting of planar layers. We show that such structures can effectively change the topological charge of the incoming beam by unity. The problem of the fundamental mode and optical vortex passage through such a layered helical waveguide of a finite length is solved. The spectral characteristics of these processes are obtained. It is shown that such a waveguide can operate as a broadband compact generator of optical vortices from both regular and singular beams.

We consider the problem of coherent resonant scattering of electromagnetic waves by a spherical medium of two-level atoms. The frequency dependence of the scattering amplitudes and cross sections reveals a complex structure of narrow peaks and dips. We relate these scattering resonances to the cooperative emission resonances characteristic of a sphere. We find the scattering to show considerable interference between the electric and magnetic multipole contributions, particularly in the lower multipole orders. This interference tends to enhance anisotropies in the differential scattering cross section even for small spheres. For such spheres, the peak values of the resonant contributions of the low-order multipoles to the total scattering cross section can increase with multipole order, in contrast to the usual decrease seen in nonresonant scattering.

We introduce discrete vortex solitons and vortex breathers in circular arrays of nonlinear waveguides. The simplest vortex breather in a four-waveguide coupler is a nonlinear dynamic state changing its topological charge between $+1$ and $-1$ periodically during propagation. We find the stability domain for this solution and suggest an all-optical vortex switching scheme.

We study the modification of a traditional electromagnetically induced transparency (EIT) stored-light technique that includes both EIT and four-wave mixing (FWM) in an ensemble of hot Rb atoms. The standard treatment of light storage involves the coherent and reversible mapping of one photonic mode onto a collective spin coherence. It has been shown that unwanted, competing processes such as four-wave mixing are enhanced by EIT and can significantly modify the signal optical pulse propagation. We present theoretical and experimental evidence to indicate that, while a Stokes field is indeed detected upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics of the fields and the impact of FWM on the spin wave.

We have theoretically and experimentally investigated coherent pump-probe spectra for the $3S_{1/2}$-$3P_{1/2}$ $D1$ transition of sodium atomic vapor. Probe transmission spectra in the presence of a coupling beam exhibit dramatic changes depending on experimental conditions. In the weak-excitation, low-atomic-density limit, the spectra are mainly characterized by electromagnetically induced transparency (EIT) and saturated absorption, but for the strong-excitation, high-density case, parametric amplification (PA) is dominant, featuring high probe gain and Stokes-wave generation. We have developed a theory that can explain these two seemingly totally different phenomena (EIT and PA) within the same theoretical framework by manipulating a few experimentally controllable parameters, and have successfully reproduced the observed spectra. Other than the main spectral features, many other interesting physical processes have been predicted and observed.

By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of parallel linearly coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give rise to three species of stable semidiscrete complexes (which are continuous in the longitudinal direction) with embedded vorticity $S$: triangular modes with $S=1$, hexagonal ones with $S=2$, both centered around an empty central core, and compact triangles with $S=1$, which do not not include the empty site. Collisions between stable triangular vortices are studied too. These waveguiding lattices can be realized in optics and Bose-Einstein condensate.

The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct—such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is not its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.

We study under which conditions it is possible to assert that a joint measurement cannot be simulated by local operations and classical communication. More concretely, we consider a scenario where two parties, Alice and Bob, send each a state selected from a labeled set of unknown states to a third party, Charlie, who in turn interacts with the states in some undisclosed way and then announces an outcome. We show that, under the assumption that Alice and Bob know the dimensionality of their systems, there exist situations where the statistics of the outcomes reveals the nature of Charlie’s measurement.

We study the quench dynamics of the topological quantum phase transition in the two-dimensional transverse Wen-plaquette model, which has a phase transition from a $Z_2$ topologically ordered to a spin-polarized state. By mapping the Wen-plaquette model onto a one-dimensional quantum Ising model, we calculate the expectation value of the plaquette operator $F_i$ during a slowly quenching process from a topologically ordered state. A logarithmic scaling law of quench dynamics near the quantum phase transition is found, which is analogous to the well-known static critical behavior of the specific heat in the one-dimensional quantum Ising model.

We have carried out a comprehensive study of electron impact on the open-chain ${\mathrm{S}}_3$ isomer by using the $R$-matrix method. Elastic (integrated and differential), momentum-transfer, excitation, and ionization cross sections, along with effective collision frequency over a wide electron temperature range (500–30 000 K) have been presented. The target states are represented by including correlations via a configuration interaction technique. The results of the static-exchange, correlated 1-state, and 24-state close-coupling approximations are presented. Our study has detected a shape resonance, six core-excited shape resonances, and one Feshbach resonance in the $24$-state model. We detect a stable bound state of ${\mathrm{S}}_3^{-}$ of ${}^2{B}_1$ symmetry having a configuration $\dots 11a_1^2,\dots 3b_1^{2}4b_1,\dots 8b_2^2,\dots 2a_2^2$, with a vertical electronic affinity value of 2.15 eV, and a ionization potential value of 9.77 eV, which are in good agreement with the experimental values of $2.093\pm 0.025$ and $9.68\pm 0.03$ eV, respectively. The ionization cross sections are calculated using the binary-encounter-Bethe model in which Hartree-Fock molecular orbitals at a self-consistent level are used to calculate kinetic and binding energies of the occupied molecular orbitals. We have used partial waves up to $l=4$ to represent continuum electron in our $R$-matrix method. A Born top-up procedure is invoked to account for the contribution of partial waves higher than $l=4$ to obtain converged cross sections.