We investigate the number fluctuations in small cells of quantum gases pointing out important deviations from the thermodynamic limit fixed by the isothermal compressibility. Both quantum and thermal fluctuations in weakly as well as highly compressible fluids are considered. For the two-dimensional (2D) superfluid Bose gas we find a significant quenching of fluctuations with respect to the thermodynamic limit, in agreement with recent experimental findings. An enhancement of the thermal fluctuations is instead predicted for the 2D dipolar superfluid Bose gas, which becomes dramatic when the size of the sample cell is of the order of the wavelength of the rotonic excitation induced by the interaction.

Within the Bose-Hubbard model, we theoretically determine the stationary states of two distinguishable atoms in a one-dimensional optical lattice and compare with the case of two identical bosons. A heterodimer has odd-parity dissociated states that do not depend on the interactions between the atoms, and the lattice momenta of the two atomic species may have different averages even for a bound state of the dimer. We discuss methods to detect the dimer. The different distributions of the quasimomenta of the two species may be observed in suitable time-of-flight experiments. Also, an asymmetry in the lineshape as a function of the modulation frequency may reveal the presence of the odd-parity dissociated states when a heterodimer is dissociated by modulating the depth of the optical lattice.

We propose a scheme to generate stable ultraslow three-dimensional spatiotemporal optical solitons, or ultraslow optical bullets, at very low light levels via atomic coherence. The system we consider is an ensemble of resonant, lifetime-broadened $N$-type four-level atoms, working in a regime of electromagnetically induced transparency. Due to the quantum interference effect induced by a control field, the absorption of a probe field is largely suppressed. Moreover, the Kerr nonlinearity is greatly enhanced, and the dispersion property of the probe field is drastically changed. Using a method of multiple scales, we derive two coupled nonlinear envelope equations controlling the evolution of the envelopes of the probe field and an assisted field. We show that under certain conditions the envelope of the probe field satisfies a three-dimensional nonlinear Schrödinger equation and the envelope of the assisted field obeys a linear Helmholtz equation. We obtain various optical bullet solutions for the probe-field envelope and demonstrate that such optical bullets have many novel features, including very slow propagating velocity and very low generation power. In addition, they can be actively controlled and manipulated by adjusting system parameters. The stabilization of the optical bullets obtained can be easily realized by the trapping potential contributed by the assisted field, which is also investigated in detail.

We study the coherent cooperative phenomena of the system composed of two interacting atomic ensembles in the thermodynamic limit. Remarkably, the system exhibits the Dicke-like quantum phase transition and entanglement behavior although the governing Hamiltonian is fundamentally different from the spin-boson Dicke Hamiltonian, offering the opportunity for investigating collective matter-light dynamics with pure matter waves. The model can be realized with two Bose-Einstein condensates or atomic ensembles trapped in two optical cavities coupled to each other. The interaction between the two separate samples is induced by virtual photon exchange.

A theoretical investigation of solitary wave refraction in nematic liquid crystals is undertaken. A modulation theory based on a Lagrangian formulation of the governing optical solitary wave equations is developed. The resulting low-dimensional equations are found to give solutions in excellent agreement with full numerical solutions of the governing equations, as well as with previous experimental studies. The analysis deals with a number of types of refraction from a more to a less optically dense medium, the most famous being the Goos-Hänchen shift upon total internal reflection.

We show theoretically that accelerating light beams can be used to manipulate nonlinear optical processes through spatiotemporal quasi-phase-matching, allowing for unprecedented temporal and spectral shaping of the generated light. As a proof of principle, we demonstrate exquisite control over the high-order harmonic frequency conversion process, showing efficient enhancement of an extremely broad range of harmonics emitted during a selected quarter-cycle of the driving laser pulse.

Recently Yampol’skii et al. [Phys. Rev. A 82, 032511 (2010)] advocated that Lifshitz theory is not applicable when the characteristic wavelength of the fluctuating electromagnetic field, responsible for the thermal correction to the Casimir force, is larger than the size of the metal test bodies. It was claimed that this is the case in experiments which exclude Lifshitz theory combined with the Drude model. We calculate the wavelengths of the evanescent waves making the dominant contribution to the thermal correction and we find that they are much smaller than the sizes of the test bodies. The opposite conclusion obtained by the authors arose from confusion between propagating and evanescent waves.

Here, we present an estimate of the characteristic wavelengths of the evanescent modes, which define the main contribution to the thermal part of the Casimir force. This estimate is more precise than the one in the preceding Comment by Bimonte et al. [Phys. Rev. A 84, 036501 (2011)]. The wavelengths we derive are indeed smaller than the sizes of the interacting bodies. We also discuss the results of several experiments on the thermal effects in the Casimir force.

Quantum cryptographic protocols based on complementarity are not secure against attacks in which complementarity is imitated with classical resources. The Kochen-Specker (KS) theorem provides protection against these attacks, without requiring entanglement or spatially separated composite systems. We analyze the maximum tolerated noise to guarantee the security of a KS-protected cryptographic scheme against these attacks and describe a photonic realization of this scheme using hybrid ququarts defined by the polarization and orbital angular momentum of single photons.

We study a driven-dissipative system of atoms in the presence of laser excitation to a Rydberg state and spontaneous emission. The atoms interact via the blockade effect, whereby an atom in the Rydberg state shifts the Rydberg level of neighboring atoms. We use mean-field theory to study how the Rydberg population varies in space. As the laser frequency changes, there is a continuous transition between the uniform and antiferromagnetic phases. The nonequilibrium nature also leads to a novel oscillatory phase and bistability between the uniform and antiferromagnetic phases.

The passage of ultracold three-level atoms through the potential induced by the vacuum cavity mode is discussed using cascade atomic configuration. We study the tunneling or traversal time of the ultracold atoms via a bimodal high-$Q$ cavity. It is found that the phase time, which may be considered as a measure for the time required to traverse the cavity, exhibits superclassical and subclassical behaviors. Further, the dark states and interference effects in cascade atomic configuration may influence the passage time of the atom through the cavity.

An alternative one-parameter measure of divergence is proposed, quantifying the discrepancy among general probability densities. Its main mathematical properties include (i) comparison among an arbitrary number of functions, (ii) the possibility of assigning different weights to each function according to its relevance on the comparative procedure, and (iii) ability to modify the relative contribution of different regions within the domain. Applications to the study of atomic density functions, in both conjugated spaces, show the versatility and universality of this divergence.

The $J$-matrix approach to electron-atom scattering is revised by merging it with the Fano's multiconfiguration interaction matrix elements [U. Fano, Phys. Rev. 140, A67 (1965)]. The revised method is then applied to the $S$-wave model of the $e$-He scattering problem demonstrating remarkable computational efficiency and accuracy. In particular, the method is in complete agreement with the convergent-close-coupling elastic, $2^{1,3}S$ excitation and single ionization cross sections for impact energies in the range 0.1–1000 eV. The $S$-wave resonance structures in the elastic and $2^{1,3}S$ excitation cross sections are highlighted.

The cross sections of spin-orbit energy exchange between the cesium $6{}^2{P}_{1/2}\leftrightarrow 6{}^2{P}_{3/2}$ states induced by collisions with N${}_2$, H${}_2$, HD, D${}_2$, CH${}_4$, C${}_2$H${}_6$, CF${}_4$, and C${}_2$F${}_6$ were obtained for pressures less than 100 Torr at room temperature by means of steady-state laser-induced fluorescence techniques. The spin-orbit energy exchange rate with N${}_2$, H${}_2$, HD, D${}_2$, CH${}_4$, C${}_2$H${}_6$, CF${}_4$, and C${}_2$F${}_6$, have been measured as ${\sigma }_{21}(6{}^2{P}_{3/2}\to 6{}^2{P}_{1/2})=$ 16.3, 34.1, 30.0, 22.7, 21.4, 65.6, 64.8, and 137 ${\AA }^2$ and ${\sigma }_{12}(6{}^2{P}_{1/2}\to 6{}^2{P}_{3/2})=$ 1.8, 4.4, 4.1, 3.0, 2.9, 13.3, 9.7, and 16.3 ${\AA }^2$, respectively. Correlations of the spin-orbit transfer probabilities with rotational-energy defect and vibrational-energy defect have been shown.

Using a three-dimensional quasiclassical technique, we explore double ionization in N${}_2$ when driven by a linearly polarized, infrared (800 nm) long (27 fs) laser pulse. For intensities ranging from the tunneling to the over-the-barrier regime, we identify the double-ionization pathways in a unified way as a function of total final electron energy. Moreover, for intermediate intensities in the over-the-barrier regime we find that the correlated electron momenta have a prevailing square pattern. This square pattern is mainly due to the delayed (one electron is ejected with a delay after recollision) pathway’s contribution to double ionization. For intermediate intensities the delayed pathway is dominated by “soft” recollisions [identified in Phys. Rev. A 80, 053415 (2009)], with the first electron tunneling at large field phases. We expect this square pattern to be absent for high intensities.

The efficiency of cavity sideband cooling of trapped molecules is theoretically investigated for the case in which the infrared transition between two rovibrational states is used as a cycling transition. The molecules are assumed to be trapped either by a radiofrequency or optical trapping potential, depending on whether they are charged or neutral, and confined inside a high-finesse optical resonator that enhances radiative emission into the cavity mode. Using realistic experimental parameters and COS as a representative molecular example, we show that in this setup, cooling to the trap ground state is feasible.

We present an efficient and accurate method to study electron detachment from negative ions by a few-cycle linearly polarized laser pulse. The adiabatic saddle-point method of Gribakin and Kuchiev [Phys. Rev. A 55, 3760 (1997)] is adapted to calculate the transition amplitude for a short laser pulse. Its application to a pulse with $N$ optical cycles produces $2(N+1)$ saddle points in complex time, which form a characteristic “smile.” Numerical calculations are performed for H${}^{-}$ in a 5-cycle pulse with frequency 0.0043 a.u. and intensities of 10${}^{10}$, $5\times {10}^{10}$, and 10${}^{11}$ W/cm${}^2$, and for various carrier-envelope phases. We determine the spectrum of the photoelectrons as a function of both energy and emission angle, as well as the angle-integrated energy spectra and total detachment probabilities. Our calculations show that the dominant contribution to the transition amplitude is given by 5–6 central saddle points, which correspond to the strongest part of the pulse. We examine the dependence of the photoelectron angular distributions on the carrier-envelope phase and show that measuring such distributions can provide a way of determining this phase.

We classify the ground states and topological defects of a rotating two-component condensate when varying several parameters: the intracomponent coupling strengths, the intercomponent coupling strength, and the particle numbers. No restriction is placed on the masses or trapping frequencies of the individual components. We present numerical phase diagrams which show the boundaries between the regions of coexistence, spatial separation, and symmetry breaking. Defects such as triangular coreless vortex lattices, square coreless vortex lattices, and giant skyrmions are classified. Various aspects of the phase diagrams are analytically justified thanks to a nonlinear $\sigma$ model that describes the condensate in terms of the total density and a pseudo-spin representation.

We examine several retro-reflecting optical elements, each involving two reflections. In the case of a hollow metallic cone having an apex angle of 90°, a circularly polarized incident beam acquires, upon reflection, the opposite spin angular momentum. However, no angular momentum is transferred to the cone, because the reflected beam picks up an orbital angular momentum that is twice as large but opposite in direction to that of its spin. A 90° cone made of a transparent material in which the incident light suffers two total internal reflections before returning may be designed to endow the retro-reflected beam with different mixtures of orbital and spin angular momenta. Under no circumstances, however, is it possible to transfer angular momentum from the light beam to the cone without either allowing absorption or breaking the axial symmetry of the cone. A simple example of broken symmetry is provided by a wedge-shaped metallic reflector having an apex angle of 90°, which picks up angular momentum upon reflecting a circularly polarized incident beam.

We study the quantum dynamics of the cavity optomechanical system formed by a Fabry-Perot cavity with a thin vibrating membrane at its center. We determine in particular to what extent optical absorption by the membrane hinders reaching a quantum regime for the cavity-membrane system. We show that even though membrane absorption may significantly lower the cavity finesse and also heat the membrane, one can still simultaneously achieve ground state cooling of a vibrational mode of the membrane and stationary optomechanical entanglement with state-of-the-art apparatuses.