The present work is devoted to the description of a nonperturbative treatment of anharmonic effect and mode-mode coupling taking place in molecular vibrational systems. The information is obtained from the four-wave-mixing signal detected in the usual photon-echo phase-matched direction, termed 4WM photon-echo, using heterodyne detection to test separately the real and the imaginary parts of the third-order polarization. This approach allows a complete redistribution of the relaxation, dephasing, and transition constants on account of the magnitude of the coupling strength. In addition, our analytical approach accounts for the contributions provided by the various possible chronological orderings of the field interactions. The high sensitivity of the signal with both the energy shifts induced by the internal couplings and off-resonant energy parameter of the laser excitation is properly analyzed in the framework of our analytical description.

We study superfluidity of supersolid phases of dipolar Bose gases in two-dimensional optical lattices. We perform linear stability analyses for the corresponding dipolar Bose-Hubbard model in the hard-core boson limit to show that a supersolid can have stable superflow until the flow velocity reaches a certain critical value. The critical velocity for the supersolid is found to be significantly smaller than that for a conventional superfluid phase. We propose that the critical velocity can be used as a signature to identify the superfluidity of the supersolid phase in experiment.

In the present work, we offer a unifying perspective between the dark soliton stripe and the vortex multipole (dipole, tripole, aligned quadrupole, quintopole, etc.) states that emerge in the context of quasi-two-dimensional Bose-Einstein condensates. In particular, we illustrate that the multivortex states with the vortices aligned along the (former) dark soliton stripe sequentially bifurcate from the latter state in a supercritical pitchfork manner. Each additional bifurcation adds an extra mode to the dark soliton instability and an extra vortex to the configuration; moreover, the bifurcating states inherit the stability properties of the soliton prior to the bifurcation. The critical points of this bifurcation are computed analytically via a few-mode truncation of the system, which clearly showcases the symmetry-breaking nature of the corresponding bifurcation. We complement this small(-er) amplitude, few mode bifurcation picture, with a larger amplitude, particle-based description of the ensuing vortices. The latter enables us to characterize the equilibrium position of the vortices, as well as their intrinsic dynamics and anomalous modes, thus providing a qualitative description of the nonequilibrium multivortex dynamics.

A two-component Bose-Einstein condensate rotating in a toroidal trap is investigated. The topological constraint depends on the density distribution of each component along the circumference of the torus, and therefore the quantization condition on the circulation can be controlled by changing the miscibility using the Feshbach resonance. We find that the system exhibits a variety of dynamics depending on the initial angular momentum when the miscibility is changed.

The possibility of direct observation of the nonlinear Landau-Zener tunneling effect with a device consisting of two waveguide arrays connected to a tilted reduced refractive index barrier is discussed. Numerical simulations on this realistic setup are interpreted via a simplified double-well system and different asymmetric tunneling scenarios are predicted varying just the injected beam intensity.

Wave propagation in two-dimensional generalized honeycomb lattices is studied. By employing the tight-binding (TB) approximation, the linear dispersion relation and associated discrete envelope equations are derived for the lowest band. In the TB limit, the Bloch modes are localized at the minima of the potential wells and can analytically be constructed in terms of local orbitals. Bloch-mode relations are converted into integrals over orbitals. With this methodology, the linear dispersion relation is derived analytically in the TB limit. The nonlinear envelope dynamics are found to be governed by a unified nonlinear discrete wave system. The lowest Bloch band has two branches that touch at the Dirac points. In the neighborhood of these points, the unified system leads to a coupled nonlinear discrete Dirac system. In the continuous limit, the leading-order evolution is governed by a continuous nonlinear Dirac system. This system exhibits conical diffraction, a phenomenon observed in experiments. Coupled nonlinear Dirac systems are also obtained. Away from the Dirac points, the continuous limit of the discrete equation leads to coupled nonlinear Schrödinger equations when the underlying group velocities are nearly zero. With semiclassical approximations, all the parameters are estimated analytically.

We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: The master equation for the model, which takes into account both a coherent continuous drive and radiative as well as nonradiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between $0$ and $1$, and divides the diagram identified by the two energy scales of the system—the tunneling and the nonlinear Kerr interaction—into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities, and the emitted light is coherent. In the opposite limit, photon blockade sets in, and the system shows an insulatorlike state with photons locked on each cavity, identified by antibunching of emitted light.

We observe a convex subset of the set of all $M\otimes N$ separable states. On the basis of this observation, we give an alternative sufficient condition for separability of bipartite states. This criterion gives rise to a family of quantum channels which are entanglement breaking.

Beam dynamics in synthetic optical media with $\mathcal{PT}$ symmetries imposed by a balanced arrangement of gain or loss is investigated. We find that the beam power evolution is insensitive to microscopic details of the system and that it follows three distinct universal laws which depend only on the magnitude of the gain or loss parameter. Our theoretical calculations are confirmed numerically for the experimentally realizable case of a lattice consisting of coupled $\mathcal{PT}$-symmetric dimers.

Recent experiments aim at cooling nanomechanical resonators to the ground state by coupling them to nonequilibrium environments in order to observe quantum effects such as entanglement. This raises the general question of how such environments affect entanglement. Here we show that there is an optimal dissipation strength for which the entanglement between two coupled oscillators is maximized. Our results are established with the help of a general framework of exact quantum Langevin equations valid for arbitrary bath spectra, in and out of equilibrium. We point out why the commonly employed Lindblad approach fails to give even a qualitatively correct picture.

Quantum teleportation enables deterministic and faithful transmission of quantum states, provided a maximally entangled state is preshared between sender and receiver, and a one-way classical channel is available. Here, we prove that these resources are not only sufficient, but also necessary, for deterministically and faithfully sending quantum states through any fixed noisy channel of maximal rank, when a single use of the cannel is admitted. In other words, for this family of channels, there are no other protocols, based on different (and possibly cheaper) sets of resources, capable of replacing quantum teleportation.

A general theorem as a necessary condition for the separability of quantum states in both finite and infinite dimensional systems, based on concave-function uncertainty relations, is derived. Two special cases of the general theorem are stronger than two known entanglement criteria based on the Shannon entropic uncertainty relation and the Landau-Pollak uncertainty relation, respectively; other special cases are able to detect entanglement where some famous entanglement criteria fail.

The presence of shape resonances due to tunneling through the centrifugal barrier modifies strongly the dynamics of cold atom scattering. As shown on the example of the ground and lowest triplet electronic states of the ${}^{85}\mathrm{Rb}$${}^{133}\mathrm{Cs}$ molecule, the crucial parameter is, as usual for cold collisions, the scattering length. A general description of shape resonances of diatomic molecules is given from three simple single channel asymptotic models, whose respective performances are discussed. The first model, which consists of a $R^{-6}$ potential limited at short range by a repulsive wall, positioned to reproduce the $s$-wave scattering length, accounts satisfactorily for the main system-independent properties of shape resonances. Introduction in the model of energy- and angular-momentum-dependent nodal lines specific to the inner part of the potential greatly improves its efficiency. When the energy and angular momentum dependence of the nodal lines cannot be deduced from full potential calculations or from experiment, a rough, but universal, estimate of these properties is obtained by extending the $R^{-6}$ behavior of the potential up to the origin.

We compute the Casimir interaction between a plane and a sphere, the configuration employed in the most precise experiments. The scattering formula is developed by taking a suitably chosen plane-wave and multipole basis and is valid for arbitrary values of the sphere radius, interplate distance, temperature, and arbitrary dielectric functions for both sphere and plate. Our analytical and numerical results for metallic surfaces show a nontrivial interplay between the effects of curvature, temperature, finite conductivity, and dissipation.

We present a joint theoretical-experimental study on electron scattering by propane (C${}_3$H${}_8$) in the low- and intermediate-energy ranges. Calculated elastic differential, integral, and momentum transfer as well as total (elastic $+$ inelastic) and total absorption cross sections are reported for impact energies ranging from $2$ to $500$ eV. Also, experimental absolute elastic cross sections are reported in the $40$- to $500$-eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics. A theoretical method based on the single-center-expansion close-coupling framework and corrected by the Padé approximant is used to solve the scattering equations. The experimental angular distributions of the scattered electrons are converted to absolute cross sections using the relative flow technique. The comparison of our calculated with our measured results, as well as with other experimental and theoretical data available in the literature, is encouraging.

The statistical distributions of the number of simultaneously emitted secondary electrons (SEs) from a carbon foil have been measured with proton beams of $0.5-3.5$ MeV. In this experiment, the forward- and backward-emitted SEs have been measured simultaneously with foil-transmitted protons using a digitizer. As a method to examine how the forward and backward SE emissions correlate to each other, the forward (backward) SE yields ${\gamma }_{\mathrm{F}}$ (${\gamma }_{\mathrm{B}}$), that is, the mean number of the forward-emitted (backward-emitted) electrons per projectile, have been evaluated as a function of the number of the backward-emitted (forward-emitted) SEs, $n_{\mathrm{B}}$ ($n_{\mathrm{F}}$). At higher incident energies, ${\gamma }_{\mathrm{F}}$ (${\gamma }_{\mathrm{B}}$) increases with increasing $n_{\mathrm{B}}$ ($n_{\mathrm{F}}$). With decreasing incident energy, this so-called positive correlation becomes weaker and then changes to negative at the lowest incident energy. Although measurements using a slightly thicker foil exhibit just the same trend, the correlation changes from positive to negative at the higher incident energy. For a given foil thickness, the range of the produced binary electron and hence the incident proton energy seems to determine the sign of the correlation. A simple Monte Carlo simulation for the forward and backward SE emission in the present experimental condition can qualitatively reproduce the observed incident-energy dependence of the positive correlation but cannot reproduce the negative one observed at the lower incident energies.

We exploit the variation of the atomic interaction in order to move ultracold atoms with attractive interaction across an ac-driven periodic lattice. By breaking relevant symmetries, a gathering of atoms is achieved. Accurate control of the gathered atoms’ positions can be demonstrated via the control of the atomic localization process. The localization process is analyzed with the help of the nonlinear Floquet states where the Landau-Zener tunneling between states is observed and controlled. Transport effects in the presence of disorder are discussed.

We consider a uniform dipolar Fermi gas in two dimensions (2D) where the dipole moments of fermions are aligned by an orientable external field. We obtain the ground state of the gas in the Hartree-Fock approximation and investigate random-phase-approximation stability against density fluctuations of finite momentum. It is shown that the density-wave instability takes place in a broad region where the system is stable against collapse. We also find that the critical temperature can be a significant fraction of Fermi temperature for a realistic system of polar molecules.

We study how different many-body states appear in a quantum-gas microscope, such as the one developed at Harvard [Bakr et al., Nature 462, 74 (2009)], where the site-resolved parity of the atom number is imaged. We calculate the spatial correlations of the microscope images, corresponding to the correlation function of the parity of the number of atoms at each site. We produce analytic results for a number of well-known models: noninteracting bosons, the large-$U$ Bose-Hubbard model, and noninteracting fermions. We find that these parity correlations tend to be less strong than density-density correlations, but they carry similar information.

We present extensions to the theory of double-resonance laser pumping of ${}^4\mathrm{He}$ in the context of magnetometer instrumentation. This extended theory allows for arbitrary optical polarization, magnetic resonance ($H_1$) coil orientation, and overall instrument orientation relative to the ambient magnetic field. Steady-state solutions are presented for portions of the extended parameter space. These calculations are used to analyze the shot-noise-limited sensitivities for helium magnetometers for selected parameter values, and we find that linearly polarized light can have a relatively simple orientational dependence for a particular choice of angle between the $H_1$ coils and the light polarization vector. Calculations are also compared to experimentally measured magnetic resonance curves, and a shot-noise limit on sensitivity of $6\hspace{0.5em}\mathrm{fT}/\sqrt{\mathrm{Hz}}$ is determined for a particular magnetometer apparatus using a cell 2.4 cm in diameter and 7.5 cm in length. This extended theory can be utilized to select optimal operational parameter values and obtain ideal sensitivities for helium magnetometers.