Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. Although this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.

We theoretically study the internal Josephson effect, which is driven by spin-exchange interactions and magnetic dipole-dipole interactions, in a three-level system for spin-1 Bose–Einstein condensates, obtaining novel spin dynamics. We introduce single spatial mode approximations into the Gross–Pitaevskii equations and derive the Josephson-type equations, which are analogous to tunneling currents through three junctions between three superconductors. From an analogy with two interacting nonrigid pendulums, we identify unique varied oscillational modes, called the $0–\pi$, $0–\mathit{running}$, $\mathit{running}–\mathit{running}$, $2n\pi \hspace{0.5em}\&\hspace{0.5em}\mathit{running}–2\pi$, $\mathit{single nonrigid pendulum}$, and $\mathit{two rigid pendulums}$ phase modes. These Josephson modes in the three states are expected to be found in real atomic Bose gas systems.

We show that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states. We identify such solutions with Lieb’s type II excitations from weak to strong interactions, clarifying a long-standing question of the physical meaning of this excitation branch. We demonstrate that the metastable quantum phase transition previously found in mean-field analysis of the weakly interacting Lieb-Liniger Hamiltonian [Phys. Rev. A 79, 063616 (2009)] extends into the medium- to strongly interacting regime of a periodic one-dimensional Bose gas. Our methods are exact diagonalization, finite-size Bethe ansatz, and the boson-fermion mapping in the Tonks-Girardeau limit.

Spontaneous emission (SE) from a two-level atom in an anisotropic photonic crystal (PC) is investigated by the fractional calculus. Physical phenomena of the SE are studied analytically by solving the fractional kinetic equations of the SE. There is a dynamical discrepancy between the SE of anisotropic and isotropic PCs. We find that, contrary to the SE phenomenon of the isotropic PC, the SE near the band edge of an anisotropic PC shows no photon-atom bound state. It is consistent with the experimental results of Barth, Schuster, Gruber, and Cichos [Phys. Rev. Lett. 96, 243902 (2006)] that the anisotropic property of the system enhances the SE. We also study effects of dispersion curvatures on the changes of the photonic density of states and the appearance of the diffusion fields in the SE.

We study the existence and properties of vortex solitons supported by an interface between two distinct optical lattices imprinted in nonlinear quadratic media. We analyze the impact of guiding parameters of lattices and phase mismatching conditions on the existence and stability of two-color interface vortex solitons. The salient point is that interface vortex solitons feature highly asymmetric profiles, and are stable throughout almost the entire existence domain.

We present a systematic investigation of ultrashort electromagnetic pulse propagation in metamaterials (MMs) with simultaneous cubic electric and magnetic nonlinearity. We predict that spatiotemporal electromagnetic solitons may exist in the positive-index region of a MM with focusing nonlinearity and anomalous group velocity dispersion (GVD), as well as in the negative-index region of the MM with defocusing nonlinearity and normal GVD. The experimental circumstances for generating and manipulating spatiotemporal electromagnetic solitons can be created by elaborating appropriate MMs. In addition, we find that, in the negative-index region of a MM, a spatial ring may be formed as the electromagnetic pulse propagates for focusing nonlinearity and anomalous GVD; while the phenomenon of temporal splitting of the electromagnetic pulse may appear for the same case except for the defocusing nonlinearity. Finally, we demonstrate that the nonlinear magnetization makes the sign of effective electric nonlinear effect switchable due to the combined action of electric and magnetic nonlinearity, exerting a significant influence on the propagation of electromagnetic pulses.

We identify a process in which we can control the behavior of an atomic medium to switch between transparent and enhanced-absorption at multiple frequencies. The process relies on the quantum interference between multiple dark states, which can be constructive or destructive at different frequencies and can be altered dramatically by changing the phase difference between the two circularly polarized components of a single coherent field. This phase-controlled switching behavior is obtainable without altering the powers or frequency detunings of the beams. We demonstrate the process experimentally by using two coherent fields and atomic rubidium vapor. Such selective switching between multiple frequency channels could also have applications in optical communication and quantum information processing.

An optical-trap method based on the illumination of a double-ring-shaped radially polarized beam (R-TEM${}_{11}^{*}$) is proposed. The numerical results based on the vector diffraction theory show that a highly focused R-TEM${}_{11}^{*}$ beam not only can produce a bright spot but also can form an optical cage in the focal region by changing the truncation parameter $\beta$, defined as the ratio of the radius of the aperture to the waist of the beam. The radiation forces acting on Rayleigh particles are calculated by using the Rayleigh scattering theory. The bright spot generated by the R-TEM${}_{11}^{*}$ beam with a $\beta$ value close to 2 can three-dimensionally trap a particle with a refractive index larger than that of the ambient. An optical cage or three-dimensional dark spot generated by the R-TEM${}_{11}^{*}$ beam with a $\beta$ value close to 1.3 can three-dimensionally trap a particle with refractive index smaller than that of the ambient. Because the adjustment of the truncation parameter can be actualized by simply changing the radius of a circular aperture inserted in the front of the lens, only one optical-trap system in the present method can be used to three-dimensionally trap two types of particles with different refractive indices.

We explore separability of bipartite divisions of mixed Gaussian states based on the positivity of the Abe-Rajagopal (AR) $q$-conditional entropy. The AR $q$-conditional entropic characterization provide more stringent restrictions on separability (in the limit $q\to \infty$) than that obtained from the corresponding von Neumann conditional entropy ($q=1$ case)—similar to the situation in finite dimensional states. Effectiveness of this approach, in relation to the results obtained by partial transpose criterion, is explicitly analyzed in three illustrative examples of two-mode Gaussian states of physical significance.

Two-photon double ionization (TPDI) of ${\mathrm{D}}_2$ is studied for $38$-eV photons at the Free Electron Laser in Hamburg (FLASH). Based on model calculations, instantaneous and sequential absorption pathways are identified as separated peaks in the measured ${\mathrm{D}}^{+}+{\mathrm{D}}^{+}$ fragment kinetic energy release (KER) spectra. The instantaneous process appears at high KER, corresponding to ionization at the molecule’s equilibrium distance, in contrast to sequential ionization mainly leading to low-KER contributions. Measured fragment angular distributions are in good agreement with theory.

We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.

Using the trace minimization algorithm, we carried out an exact calculation of entanglement in a 19-site two-dimensional transverse Ising model. This model consists of a set of localized spin-$\frac{1}{2}$ particles in a two-dimensional triangular lattice coupled through exchange interaction $J$ and subject to an external magnetic field of strength $h$. We demonstrate, for such a class of two-dimensional magnetic systems, that entanglement can be controlled and tuned by varying the parameter $\lambda =h/J$ in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of $\lambda$ shows that the system exhibits a quantum phase transition at about ${\lambda }_c=3.01$, a transition induced by quantum fluctuations at the absolute zero of temperature.

The inner-shell photoionization of highly charged ions is studied, together with their subsequent radiative decay, within the framework of the density matrix theory and the multiconfiguration Dirac-Fock (MCDF) approach. For the subsequent radiative decay of the ions, we investigate in particular how the linear polarization of characteristic radiation is affected if the incident light is itself polarized. Detailed calculations are performed for the $2p^{5}3s\to 2p^6$ radiative transitions following the production of a $2p$ vacancy in the sodiumlike ${\mathrm{Fe}}^{15+}$, ${\mathrm{W}}^{63+},$ and ${\mathrm{U}}^{81+}$ ions. From these calculations, it is shown that the (degree of) linear polarization of the characteristic radiation may be enhanced by a factor of $2$ due to the polarization transfer from the incident light.

$J$-coupled nuclear magnetic resonance (NMR) spectroscopy in the strong coupling regime at low magnetic field ($10{}^{-7}$ T $<B<{10}^{-3}$ T) is more complex than at high field ($B>{10}^{-3}$ T) and at ultralow field ($B<{10}^{-7}$ T). We show that several upper and lower boundaries $B_i^{\mathrm{up}}$ and $B_i^{\mathrm{low}}$ of the magnetic field $B$ exist, where the complexity of $J$-coupled NMR spectra changes in terms of the number of lines. The index $i=1,2,\dots$ for $B_i^{\mathrm{up}}$ at high field specifies the perturbation order of the dominating Zeeman interaction and for $B_i^{\mathrm{low}}$ at ultralow field the perturbation order of the dominating $J$-coupling interaction. Mathematical expressions for these boundaries are derived for the case of a $J$-coupled $S$-$I$${}_N$ group where $S$ and $I$ are rare and abundant spins $\frac{1}{2}$ and $N$ counts the abundant spins $I$. The entire $B$-field range can further be delineated into two weak coupling regimes, one at high field with $B_2^{\mathrm{up}}<B<B_1^{\mathrm{up}}$ ($10{}^{-3}$ T $<B<{10}^2$ T), one at low field with $B_1^{\mathrm{low}}<B<B_2^{\mathrm{low}}({10}^{-8}$ T $<B<{10}^{-7}$ T), and a strong coupling regime with $B_2^{\mathrm{low}}<B<B_2^{\mathrm{up}}$ ($10{}^{-7}$ T $<B<{10}^{-3}$ T). The corresponding NMR spectra for the $S-I_N$ group are investigated by experiment and by simulation. In the strong coupling regime, the maximum number of lines is $(N+1){}^2$. In the weak coupling regime $B_1^{\mathrm{low}}<B<B_2^{\mathrm{low}}$ at low field, symmetric multiplet structures group around the frequencies $0$, $J$, ($3/2$)$J$, $2J$, ($5/2$)$J$, etc. These spectra determine the structure of the $S-I_N$ group unambiguously and are in dual correspondence to the weakly coupled spectra at high field. High-resolution NMR spectroscopy at ultralow field may open up new ways for chemical analysis by small and mobile instruments with many applications in science and technology.

Using only linear optics and projection measurement, we propose a simple multiphoton interference scheme for the demonstration of six-photon de Broglie wavelength, which leads to a $\cos 6\phi$ dependence on the single-photon phase $\phi$. Although the scheme does not reach the Heisenberg limit in sensitivity for phase measurement, it improves upon the standard quantum limit with super-resolved sensitivity in phase measurement. We discuss possible experimental implementation with three pairs of photons from parametric down-conversion.

Franson’s paradigm for nonlocal dispersion cancellation [J. D. Franson, Phys. Rev. A 45, 3126 (1992)] is studied using two kinds of jointly Gaussian-state signal and reference beams with phase-sensitive cross correlations. The first joint signal-reference state is nonclassical, with a phase-sensitive cross correlation that is at the ultimate quantum-mechanical limit. It models the outputs obtained from continuous-wave spontaneous parametric down-conversion. The second joint signal-reference state is classical—it has a proper $P$ representation—with a phase-sensitive cross correlation that is at the limit set by classical physics. Using these states we show that a version of Franson’s nonlocal dispersion cancellation configuration has essentially identical quantum and classical explanations except for the contrast obtained, which is much higher in the quantum case than it is in the classical case. This work bears on Franson’s recent article [J. D. Franson, Phys. Rev. A 80, 032119 (2009)], which asserts that there is no classical explanation for all the features seen in quantum nonlocal dispersion cancellation.

Shapiro recently argued that nonlocal dispersion cancellation using entangled pairs of photons is essentially classical in nature, based on a comparison with a classical model in which two stationary, chaotic beams of light have phases and frequencies that are anticorrelated, which he refers to as “phase-sensitive” light [J. H. Shapiro, Phys. Rev. A 81, 023824 (2010)]. It is shown here that there is no physical cancellation of dispersion for classical light of that kind and Shapiro’s results merely reflect the fact that identical dispersion occurs in both beams. The origin of the cross correlations between the intensities of the two beams is shown to be completely different in the classical and quantum mechanical cases.

We study the cooling of a dielectric nanoscale particle trapped in an optical cavity. We derive the frictional force for motion in the cavity field and show that the cooling rate is proportional to the square of oscillation amplitude and frequency. Both the radial and axial components of the center-of-mass motion of the trapped particle, which are coupled by the cavity field, are cooled. This motion is analogous to two coupled but damped pendulums. Our simulations show that the nanosphere can be cooled to $e^{-1}$ of its initial momentum over time scales of hundredths of milliseconds.

For systems described by the two-site Bose-Hubbard Hamiltonian, I show that a sinusoidal modulation of the tunneling matrix element assists higher-order cotunneling processes. Using this mechanism, I propose an efficient scheme for creating a coherent superposition of states in which all particles are either on one site or all on the other site, the so-called NOON state. This scheme yields an almost perfect NOON state periodically. For larger numbers of particles, further reduction of the time to create the state is possible if more than one modulation frequency is employed. With this scheme, NOON states with a larger number of particles could be realized with state-of-the-art techniques for cold Bose gases in a double-well potential.