We investigate theoretically the stationary states of two bosons in a one-dimensional optical lattice within the Bose-Hubbard model. Starting from a finite lattice with periodic boundary conditions, we effect a partial separation of the center-of-mass and relative motions of the two-atom lattice dimer in the lattice momentum representation, and carefully analyze the eigenstates of the relative motion. In the limit when the lattice becomes infinitely long, we find closed-form analytic expressions for both the bound state and the dissociated states of the lattice dimer. We outline the corresponding analysis in the position representation. The results are used to discuss three ways to detect the dimer: by measuring the momentum distribution of the atoms, by finding the size of the molecule with measurements of atom number correlations at two lattice sites, and by dissociating a bound state of the lattice dimer with a modulation of the lattice depth.

We develop a quasianalytical theory for the quantum reflection amplitude of Bose-Einstein condensates. We derive and calculate the decay width of a Bose-Einstein condensate (BEC). A general relation between the time-dependent decay law of the system and its quantum reflection amplitude allows us to explain the quantum reflection anomaly of Bose-Einstein condensates present in BEC-surface systems as a direct consequence of the repulsive particle interaction.

Both Landau instability and dynamical instability of Bose-Einstein condensates in moving two-dimensional optical lattices are investigated numerically and analytically. Phase diagrams for both instabilities are obtained numerically for different system parameters. These phase diagrams show that the Landau instability does not depend on direction for weak lattices while the dynamic instability is direction dependent. These features are explained analytically.

Using a generalized version of double optical gating, we produced single isolated attosecond pulses with 2-mJ, 25-fs driving lasers. Temporal characterization revealed that the 160-as pulses are accompanied with very weak pre- and postpulses. The dependence of the extreme-ultraviolet spectrum on the carrier-envelope phase of the 25-fs laser exhibited a unique $2\pi$ periodicity, indicating the robustness of the subcycle gating.

We study experimentally and numerically the spatiotemporal dynamics of the multiple filament arrays excited by self-focusing of intense elliptical laser beams in fused silica. Our results demonstrate that although multiple filament arrays emerge as apparently regular patterns in the space domain, the spatiotemporal dynamics of the individual filaments is governed by the input-beam power and the input-beam ellipticity. In the case of moderate input-beam ellipticity, the individual filaments propagate in curved trajectories arising from skewed (spatiotemporal) coherence. The spatiotemporal propagation dynamics is regularized by increasing the input-beam ellipticity, and in part due to permanent modifications of fused silica that occur under intense irradiation. In this case, strong pulse reshaping and shock-front generation are observed, which yields a regular array of very short ($<5$ fs) superluminally propagating localized peaks in the leading front, followed by the subpulses centered on the input-pulse top, and trailed by subluminally propagating pulses with rather complex transverse intensity distribution.

We study the finite-element method analysis of the Dicke effect using numerical simulations in an all-optical system of an optical waveguide side-coupled to two interacting ring resonators in a liquid crystal environment. The system is shown to exhibit all the signatures of the Dicke effect under active and reversible control by an applied voltage.

A detailed study of the photophysical properties of several chromium-related color centers produced within chemical vapor deposition diamond is presented. These emitters show narrow luminescence lines in the range of $740-770$ nm. Single-photon emission was verified with continuous and pulsed excitation with detected emission rates at saturation in the range of ($2-3$) $\times$ ${10}^6$ counts/s, while direct lifetime measurements reveal excited state lifetimes for the distinct centers ranging $1-14$ ns. In addition, a number of quantum emitters demonstrate two-level behavior with no bunching present in the second-order correlation function. The three-level systems revealed typically photoluminescence lines with width half-maximum of $~4$ nm while the two-level emitters have full width half-maximum of $~10$ nm at room temperature. In addition, the quantum efficiency of the two-level system was measured to be four times higher than that of the three-level system.

We investigate how the polarization correlations of entangled photons described by wave packets are modified when measured by moving detectors. For this purpose, we analyze the Clauser-Horne-Shimony-Holt Bell inequality as a function of the apparatus velocity. Our analysis is motivated by future experiments with entangled photons designed to use satellites. This is a first step toward the implementation of quantum information protocols in a global scale.

We emphasize and demonstrate that besides using the usual recursion relations involving successive layers, generalized Fresnel coefficients of a multilayer can equivalently be calculated using the recursion relations involving stacks of layers, as introduced some time ago [M. S. Tomaš, Phys. Rev. A 51, 2545 (1995)]. Moreover, since the definition of the generalized Fresnel coefficients employed does not imply properties of the stacks, these nonstandard recursion relations can be used to calculate Fresnel coefficients not only for a local but also for a general multilayer consisting of various types (local, nonlocal, inhomogeneous, etc.) of layers. Their utility is illustrated by deriving a few simple algorithms for calculating the reflectivity of a Bragg mirror and extending the formula for the Casimir force in a planar cavity to arbitrary media.

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this article, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called $X$ states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they are independent measures of correlation with no simple relative ordering between them.

Wave-function Monte Carlo methods are an important tool for simulating quantum systems, but the standard method cannot be used to simulate decoherence in continuously measured systems. Here I present a Monte Carlo method for such systems. This was used to perform the simulations of a continuously measured nanoresonator in [Phys. Rev. Lett. 102, 057208 (2009)].

We present high-resolution line-shape and line-intensity measurements of self-broadened ${\mathrm{O}}_2$ $b\hspace{0.5em}{}^1{\Sigma }_g^{+}(v=1)\leftarrow X\hspace{0.5em}{}^3{\Sigma }_g^{-}(v=0)$ band ($B$-band) transitions measured using the frequency-stabilized cavity ring-down spectroscopy technique under relatively low pressure conditions. We give line-shape parameters describing collisional broadening and shifting, and we treat line narrowing in terms of Dicke narrowing or the speed dependence of collisional broadening. We indicate the importance of the line-narrowing effect which, if neglected, changes the experimentally determined collisional broadening coefficients by up to $48\%$. We report measured line intensities with relative uncertainties below $0.7\%$ and compare these measurements to published data.

We present four kinds of sum rules for the exchange-correlation energy functional of the extended constrained-search theory. They are applicable even to the conventional density functional theory. As an application of these sum rules, we utilize them to check the validity of the vorticity expansion approximation (VEA) of the current-density functional theory (CDFT). The VEA formula fulfils three of them, though the local density approximation formula of the CDFT fulfills only one. The validity of the VEA formula is thus confirmed successfully from the viewpoint of the sum rules.

We present a theory for the calculation of the Casimir-Polder potential experienced by an atom near the surface of a nanostructure. The potential is found by means of the electrodynamic Green’s tensor based on a layer-multiple-scattering method. We calculate the distance law of the Casimir-Polder potential for a monolayer of metallic and dielectric nanospheres arranged periodically on a square lattice. We find, in particular, that the Casimir-Polder potential for a metallic nanostructure is practically independent of the type of the metal from which the nanostructure is made. Also, the Casimir-Polder potential shows an exponential decay close to the nanostructure and an inverse power-law decrease away from it wherein the exponent depends on the size of the spheres of the nanostructure.

The particularly weak isotropic spectrum of the recently reported [Verzhbitskiy et al., Phys. Rev. A 81, 012702 (2010)] nearly depolarized collision-induced Raman scattering band ${\mathrm{SF}}_6$(${\nu }_1$)$+{\mathrm{N}}_2$(${\nu }_1$) at room temperature was obtained and is presented here. The spectrum was extracted from high-quality measurements of two independent incident-field polarization scattering components. Its zero-order moment was found to be about 200 times smaller than that of its anisotropic counterpart. Agreement, both in spectral shape and in intensity, was found with predictions based on the dipole-induced dipole polarization model once corrected for the very substantial back-induction, dispersion, and dipole-induced quadrupole-induced dipole interaction mechanisms, all of which were considered within the model framework of two point-polarizable molecules. Quantum-mechanical calculations revealed a large contribution from bound and predissociating dimers that amounts to more than one-third of the total isotropic scattering intensity.

We investigate the behavior of the light pulse in $\Lambda$-type cold-atom gases with two counter-propagating control lights with equal strength by directly simulating the dynamic equations and exploring the dispersion relation. Our analysis shows that, depending on the length $L_0$ of the stored wave packet and the decay rate $\gamma$ of ground-spin coherence, the recreated light can behave differently. For long $L_0$ and/or large $\gamma$, a stationary light pulse is produced, while two propagating light pulses appear for short $L_0$ and/or small $\gamma$. In the $\gamma \to 0$ limit, the light always splits into two propagating pulses for a sufficiently long time. This scenario agrees with a recent experiment [Y.-W. Lin et al., Phys. Rev. Lett. 102, 213601 (2009)] where two propagating light pulses are generated in laser-cooled cold-atom ensembles.

The nonrelativistic (nr) impulse approximation (NRIA) expression for Compton-scattering doubly differential cross sections (DDCS) for inelastic photon scattering is recovered from the corresponding relativistic expression (RIA) of Ribberfors [Phys. Rev. B 12, 2067 (1975)] in the limit of low momentum transfer ($q\to 0$), valid even at relativistic incident photon energies ${\omega }_1>m$ provided that the average initial momentum of the ejected electron $\langle p_i\rangle$ is not too high, that is, $\langle p_i\rangle$ $<m$. This corresponds to a binding energy $E_b<10$ keV. This $q\to 0$ nr limit is simultaneous with the approach of the scattering angle $\theta$ to $0^{°}$ ($\theta \to 0^{°}$) around the Compton peak maximum. This explains the observation that it is possible to obtain an accurate Compton peak (CP) even when ${\omega }_1>m$ using nr expressions when $\theta$ is small. For example, a $1\%$ accuracy can be obtained when ${\omega }_1=1\text{MeV}$ if $\theta <{20}^{°}$. However as ${\omega }_1$ increases into the MeV range, the maximum $\theta$ at which an accurate Compton peak can be obtained from nr expressions approaches closer to zero, because the $\theta$ at which the relativistic shift of CP to higher energy is greatest, which starts at ${180}^{°}$ when ${\omega }_1<300$ keV, begins to decrease, approaching zero even though the $\theta$ at which the relativistic increase in the CP magnitude remains greatest around $\theta ={180}^{°}$. The relativistic contribution to the prediction of Compton doubly differential cross sections (DDCS) is characterized in simple terms using Ribberfors further approximation to his full RIA expression. This factorable form is given by $\mathrm{DDCS}=\mathit{KJ}$, where $K$ is the kinematic factor and $J$ the Compton profile. This form makes it possible to account for the relativistic shift of CP to higher energy and the increase in the CP magnitude as being due to the dependence of $J(p_{\min },{\rho }_{\mathrm{rel}})$ (where $p_{\min }$ is the relativistic version of the $z$ component of the momentum of the initial electron and ${\rho }_{\mathrm{rel}}$ is the relativistic charge density) and $K(p_{\min })$ on $p_{\min }$. This characterization approach was used as a guide for making the nr QED $S$-matrix expression for the Compton peak kinematically relativistic. Such modified nr expressions can be more readily applied to large systems than the fully relativistic version.

We consider a rotationally hot diatomic molecule as an example of an open quantum system, where molecular vibrational wave packets are subject to dephasing due to rovibrational coupling. We report analytical and numerical results addressing whether the dephasing rate can be controlled by adjustment of the initial wave packet phases. It appears that over long time scales, phase-only control is not possible, but for earlier time scales the possibility of phase-only control of dephasing remains. In addition, we point out that the time dependence of the dephasing process depends significantly upon the degeneracy of the rotational environment states.

The rovibrational dynamics of stimulated Raman adiabatic passage (STIRAP) through permanent dipole moment transitions are investigated theoretically using a time-dependent quantum wave packet method for the ground electronic state of an HF molecule. The two basic STIRAP processes, $\Lambda$ and ladder systems, are simulated. The calculated results show that nearly $100\%$ of the population can be transferred to the target state. Besides the interested transitions, the pulses can induce other transitions which affect the dynamics of STIRAP. The final populations of the initial and target states depend on delay time.

Cold atoms, driven by a laser and simultaneously coupled to the quantum field of an optical resonator, may self-organize in periodic structures. These structures are supported by the optical lattice, which emerges from the laser light they scatter into the cavity mode and form when the laser intensity exceeds a threshold value. We study theoretically the quantum ground state of these structures above the pump threshold of self-organization by mapping the atomic dynamics of the self-organized crystal to a Bose-Hubbard model. We find that the quantum ground state of the self-organized structure can be the one of a Mott insulator, depending on the pump strength of the driving laser. For very large pump strengths, where the intracavity-field intensity is maximum and one would expect a Mott-insulator state, we find intervals of parameters where the phase is compressible. These states could be realized in existing experimental setups.