We discuss the ground state of the two-dimensional Bose-Hubbard (BH) Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral that includes a summation over U(1) topological charge. We derive an effective quantum action for the BH model, which enables a nonperturbative treatment of the zero-temperature phase transition. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter $f=0$, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattices, which improves upon previous theoretical treatments. The ground state of the rotating Bose-Einstein condensates on a triangular lattice appears to be most stable against the effects of rotation. Performed calculations revealed strong dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, which separates the global coherent from the insulating state, on topology of the lattice.

We study dynamics of a two-level system driven by a strong off-resonant electromagnetic field. We derive an analytical solution for arbitrary pulse shape. We discuss possible applications and presented experimental demonstration of the results obtained.

Electromagnetic negative refraction in metamaterials has attracted increasingly great interest since its first experimental verification in 2001. It potentially leads to the applications superior to conventional devices including compact antennas for mobile stations, imaging beyond the diffraction limit, and high-resolution radars, not to mention the anomalous wave propagation in fundamental optics. Here, we report how metamaterials could be used to simulate the “negative refraction of spin-zero particles interacting with a strong potential barrier,” which gives rise to the Klein paradox—a counterintuitive relativistic process. We address the underlying physics of analogous wave propagation behaviors in those two entirely different domains of quantum and classical.

We put forward through both analytical and numerical methods the advantage of using non–slowly-varying envelope-approximation model equations for describing the propagation of few-optical-cycle pulses in transparent media. It is proven that the dynamical model based on the generic modified Korteweg–de Vries sine-Gordon equation retrieves the results reported so far in the literature, and so demonstrating its remarkable mathematical capabilities in describing the physics of few-cycle-pulse optical solitons.

We address the pair of conjugated field modes obtained from parametric down-conversion as a convenient system to analyze the quantum-classical transition in the continuous variable regime. We explicitly evaluate intensity correlations, two-mode antibunching, and entanglement for the system initially in a thermal state and show that a hierarchy of nonclassicality thresholds naturally emerges in terms of thermal and down-conversion photon number. We show that the transition from quantum to classical regime may be tuned by controlling the intensities of the seeds and detected by intensity measurements, even in the case of the transition between separability and entanglement. Besides, we show that the thresholds are not affected by losses, which only modify the amount of nonclassicality. The multimode case is also analyzed in some detail.

Electrodynamics of rotating systems is expected to exhibit novel nonlocal features that come about when acceleration-induced nonlocality is introduced into the special relativity theory in conformity with the Bohr-Rosenfeld principle. The implications of nonlocality for the amplitude and frequency of electromagnetic radiation received by uniformly rotating observers are investigated.

We investigate which non-Gaussian resources are needed, in addition to Gaussian operations and measurements, for implementation of arbitrary quantum gates on multimode quantum states of light. We show that an arbitrary set of pure non-Gaussian states with finite expansion in Fock basis is sufficient for this task. As an illustration we present an explicit scheme for probabilistic implementation of the nonlinear sign gate using resource non-Gaussian states and Gaussian operations.

We quantify the effect of phase fluctuations on atom chip interferometry of Bose-Einstein condensates. At very low temperatures, we observe small phase fluctuations, created by mean-field depletion, and a resonant production of vortices when the two clouds are initially in antiphase. At higher temperatures, we show that the thermal occupation of Bogoliubov modes makes vortex production vary smoothly with the initial relative phase difference between the two atom clouds. We also propose a technique to observe vortex formation directly by creating a weak link between the two clouds. The position and direction of circulation of the vortices are subsequently revealed by kinks in the interference fringes produced when the two clouds expand into one another. This procedure may be exploited for precise force measurement or motion detection.

We present a theoretical study of vortices within a harmonically trapped Bose-Einstein condensate in a rotating optical lattice. Due to the competition between vortex-vortex interactions and pinning to the optical lattice, we find a very complicated energy landscape, which leads to hysteretic evolution. The qualitative structure of the vortex configurations depends on the commensurability between the vortex density and the site density—with regular lattices when these are commensurate and the appearance of ringlike structures when they are not. We model the imaging of these structures by calculating time-of-flight column densities. As in the absence of the optical lattice, the vortices are much more easily observed in a time-of-flight image than in situ.

We analyze families of localized solutions of a nonlinear Schrödinger equation in the presence of a disordered potential modeling a waveguide array. A coupled mode theory approximation reveals that the families of disordered lattice solitons follow a cascade of Hopf-like bifurcations. Using a perturbation method, we analyze the origins of this bifurcation structure. We find that each family of solutions is characterized by a constant number of nodes. These predictions are in agreement with the numerical results of the nonlinear Schrödinger equation with a disordered potential.

We observe overtone signal generation of a near-resonant bichromatic light field interacting with ${}^{85}\text{R}\text{b}$ on the Zeeman split $F=2\leftrightarrow F^{\prime }=1,2,3$ hyperfine transitions of the $D_2$ line at 780 nm. A nonperturbative theoretical model for electromagnetically induced transparency is developed in order to explain this phenomenon. Assuming a $\Lambda$ system, an explicit and convenient expression for the atomic coherence is derived from the Lindblad equation assuming a phase-damping channel. The light field state is parametrically varied through one beat note of the bichromatic field and the spatial properties are studied by numerically solving the coupled-wave equation. The polarization characteristics is analyzed on the Poincaré sphere, which together with field intensity analysis offers a simple explanation of the harmonic beating signal due to Stokes vector rotation around the Poincaré sphere and decoherence effects. The experimental data and theoretical analysis focus on the first and second harmonics, although many higher harmonics are present. A distinct and narrow minimum of the second-harmonic generation is measured on two-photon resonance.

The chained Bell inequalities of Braunstein and Caves involving $N$ settings per observer have some interesting applications. Here we obtain the minimum detection efficiency required for a loophole-free violation of the Braunstein-Caves inequalities for any $N\ge 2$. We discuss both the case in which both particles are detected with the same efficiency and the case in which the particles are detected with different efficiencies.

We investigate the effects of acceleration on the energy-level shifts of a hydrogen atom interacting with the electromagnetic field and in the presence of an infinite perfectly conducting plate. We consider the contributions of vacuum fluctuations and of the radiation reaction field to the Lamb shift, and we discuss their dependence from the acceleration of the atom. We show that, because of the presence of the boundary, both vacuum field fluctuations and radiation reaction field contributions are affected by atomic acceleration. In particular, the effect of the vacuum field fluctuations on the energy-level shifts is not equivalent to that of a thermal field. We also discuss the dependence of the Lamb shift from the orientations of the atomic dipole. We show that, for specific orientations of the atomic dipole, the atomic level shifts contain an extra contribution, as compared with the case of an atom at rest, suggesting the possibility to detect the effects of the acceleration for atoms with anisotropic polarizability.

We compute the coefficients of bulk viscosity for a nonrelativistic superfluid corresponding to a fermionic system close to the unitarity limit. We consider the low temperature regime assuming that the transport properties of the system are dominated by phonons. To compute the coefficients of bulk viscosity we use kinetic theory in the relaxation time approximation and the low energy effective field theory of the corresponding system. We show that the three independent bulk viscosity coefficients, ${\zeta }_1,{\zeta }_2,{\zeta }_3$, associated with irreversible flows vanish for phonons with a linear dispersion law. Considering a phonon dispersion law with a cubic term in momentum we find that in the conformal limit ${\zeta }_1={\zeta }_2=0$, while ${\zeta }_3$ is nonzero. Including a conformal breaking term that arises for a large but finite $s$-wave scattering length, $a$, at the leading order in $1/a$ we obtain that ${\zeta }_1\propto 1/a$ and ${\zeta }_2\propto 1/a^2$.

We characterize and control the harmonic emission in the spectral and spatial domains in order to define in which conditions the harmonic radiation can be a high-quality seed for soft x-ray and x-ray free-electron lasers. The length of the gas cell, where harmonics are generated, was optimized and the energy per pulse was determined in absolute value with a calibrated x-ray photodiode. The beam spatial profile was measured and, in some conditions, a very collimated beam with a half-angle divergence below 1 mrad could be obtained. We also show that increasing the intensity of the fundamental laser field leads to a considerable broadening of the bandwidth of the harmonic radiation, allowing us to cover a large spectral range. This effect is due to fundamental reshaping leading to an efficient phase matching of both short- and long-trajectory contributions.

We have previously shown that the quantum Zeno effect can be used to implement quantum logic gates for quantum computing applications, where the Zeno effect was produced using a strong two-photon absorbing medium. Here we show that the Zeno effect can also be used to implement classical logic gates whose inputs and outputs are high-intensity fields (coherent states). The operation of the devices can be understood using a quasistatic analysis, and their switching times are calculated using a dynamic approach. The two-photon absorption coefficient of rubidium vapor is shown to allow operation of these devices at relatively low power levels.

We demonstrate runaway evaporative cooling directly with a tightly confining optical-dipole trap and achieve fast production of condensates of $1.5\times {10}^5$ ${}^{87}\text{R}\text{b}$ atoms. Our scheme uses a misaligned crossed-beam far off-resonance optical-dipole trap (MACRO-FORT). It is characterized by independent control of the trap confinement and depth allowing forced all-optical evaporation in the runaway regime. Although our configuration is particularly well suited to the case of ${}^{87}\text{R}\text{b}$ atoms in a 1565 nm optical trap, where an efficient initial loading is possible, our scheme is general and will allow all-optical evaporative cooling at constant stiffness for every optically trappable atomic or even molecular species.

A method for decelerating a continuous beam of neutral polar molecules is theoretically demonstrated. This method utilizes nonuniform static electric fields and regions of adiabatic population transfer to generate a mechanical force that opposes the molecular beam’s velocity. By coupling this technique with dissipative trap-loading molecular densities $\ge {10}^{11}{\text{cm}}^{-3}$ are possible.

We study polarization effects of two-component atomic Fermi gases loaded on three-leg triangular optical lattice by using the density-matrix renormalization-group method. Concentrating on a case in which a Mott phase coexists with metallic ones, we observe plateulike structures in the Mott phase polarization as a function of the input population imbalance. The structures are clearly analogous to the magnetization plateau states studied in the triangular Heisenberg lattice model under the magnetic field. In fact, we find that spin patterns peculiar to the plateau states emerge inside the Mott phase. This result suggests that the Mott phase is an excellent stage in systematically investigating frustrated spin systems.

We show that thermalization and the breakdown of integrability in the one-dimensional Lieb-Liniger model caused by local three-body elastic interactions is suppressed by pairwise quantum correlations when approaching the strongly correlated regime. If the relative momentum $k$ is small compared to the two-body coupling constant $c$ the three-particle scattering state is suppressed by a factor of ${\left(k/c\right)}^{12}$. This demonstrates that in one-dimensional quantum systems it is not the freeze out of two body collisions but the strong quantum correlations which ensures integrability.