We study temporal incoherent solitons in noninstantaneous response nonlinear media. Contrarily to the usual temporal soliton, which is known to require a focusing nonlinearity with anomalous dispersion, we show that a highly noninstantaneous nonlinear response leads to incoherent soliton structures which require the inverted situation: In the focusing regime (and anomalous dispersion) the incoherent wave packet experiences an unlimited spreading, whereas in the defocusing regime (still with anomalous dispersion) the incoherent wave packet exhibits a self-trapping. These counterintuitive results are explained in detail by a long-range Vlasov formulation of the problem.

The dynamics of two correlated bosons hopping on a one-dimensional lattice and driven by a sinusoidal force is analytically investigated by means of a multiple-time-scale asymptotic analysis of the driven Bose-Hubbard Hamiltonian. By assuming the ratio $\epsilon =J/\omega$ between the tunneling rate $J$ and modulation frequency $\omega$ of the driving field as a small parameter, the perturbative analysis shows that, under appropriate driving conditions, coherent destruction of tunneling can be simultaneously realized for both paired and unpaired states up to the long time scale $\sim$$1/\left(\omega {\epsilon }^2\right)$ in the regime corresponding to an energy quantum $\hslash \omega$ of the driving field of the same order of magnitude as the particle interaction energy $\hslash U_0$. The predictions of the perturbative analysis are confirmed by direct numerical simulations of the two-particle Bose-Hubbard Hamiltonian and by direct quasienergy-band computation.

The losses in a bosonic channel are the primary source of errors in current optic quantum communications. Astonishingly, by combining the noiseless attenuation and noiseless linear amplification, Mičuda et al. showed that the unavoidable losses in optic links can be compensated in a nondeterministically but heralded way (M. Micuda, I. Straka, M. Mikova, M. Dusek, N. J. Cerf, J. Fiurasek, and M. Jezek, arXiv:1206.2852). Here we analyze their noiseless loss suppression scheme in a more realistic scenario in which conventional on-off photon detectors as well as the heralded single photon are involved. We use the Wigner function method and investigate the performance of loss suppression in all Fock state space. The noiseless loss suppression for transmitting a weak coherent and single-mode squeezing state are investigated. All these results show that the noiseless attenuation and noiseless linear amplification, if combined, could help to eliminate the channel loss and could be beneficial in future quantum communication.

We consider an array of three optomechanical cavities coupled either reversibly or irreversibly to each other and calculate the amount of entanglement between the different optical and mechanical modes. We show that the composite system exhibits intercavity photon-phonon entanglement.

We present highly accurate solutions of the Schrödinger equation for three fermions in two different spin states with zero-range $s$-wave interactions under harmonic confinement. Our approach covers spherically symmetric, strictly two-dimensional, strictly one-dimensional, cigar-shaped, and pancake-shaped traps. In particular, we discuss the transition from quasi-one-dimensional to strictly one-dimensional and from quasi-two-dimensional to strictly two-dimensional geometries. We determine and interpret the eigenenergies of the system as a function of the trap geometry and the strength of the zero-range interactions. The eigenenergies are used to investigate the dependence of the second- and third-order virial coefficients, which play an important role in the virial expansion of the thermodynamic potential, on the geometry of the trap. We show that the second- and third-order virial coefficients for anisotropic confinement geometries are, for experimentally relevant temperatures, very well approximated by those for the spherically symmetric confinement for all $s$-wave scattering lengths.

A theoretical study is presented on the orientation-dependent retarding force experienced by a slow homonuclear linear trimer moving at arbitrary alignment with the direction of its flight in a three-dimensional degenerate electron gas of metallic densities. We apply a standard multiple-scattering method for elastic scattering of independent electrons off a three-center system in a screening environment. These centers are modeled by short-range auxiliary potentials and thus they are characterized by an effective $s$-type phase shift $\eta$. Within this framework for the orientation-dependent retarding force, the interplay of wave interference and multiple scattering is analyzed in a comparative manner for a realistic set of the input parameters. By allowing a restricted variation in the polar angle between the linear multicenter orientation and its velocity direction, a reasonable agreement with data obtained by a slow carbon trimer is established.

Optical properties of ensembles of three-level quantum emitters coupled to plasmonic systems are investigated employing a self-consistent model. It is shown that the stimulated Raman adiabatic passage (STIRAP) technique can be successfully adopted to control optical properties of hybrid materials with collective effects present and playing an important role in light-matter interactions. We consider a core-shell nanowire composed of a silver core and a shell of coupled quantum emitters and utilize a STIRAP scheme to control the scattering efficiency of such a system in a frequency and spatially dependent manner. After the STIRAP-induced population transfer to the final state takes place, the core-shell nanowire exhibits two sets of Rabi splittings with Fano line shapes, indicating strong interactions between two different atomic transitions driven by plasmon near-fields.

We present experimental evidence supporting the postulation that the secondary effects of light-assisted collisions are the main reason that the superradiant light scattering efficiency in condensates is asymmetric with respect to the sign of the pump-laser detuning. Contrary to recent experimental study, however, we observe severe and comparable heating with all three pump-laser polarizations. We also perform two-color, double-pulse measurements to directly study the degradation of condensate coherence and the resulting impact on the superradiant scattering efficiency.

We describe a surface structure that possesses a different transmissivity for a surface plasmon polariton incident on it from one side of it than it has for a surface plasmon polariton incident on it from the opposite side. This asymmetric transmission of a surface plasmon polariton does not require either electrical nonlinearity or the presence of a magnetic field but is a consequence solely of the geometry of the structure. This property of the structure is demonstrated by the results of computer simulation calculations.

We numerically analyze the quantum efficiency and dark noise of a cavity-based single-atom detector, with particular emphasis on the ability to measure number squeezing in an atom-laser beam. We consider the influence of the electric-dipole force on an atom in a red-detuned detection beam and discuss the much improved detection efficiency for detuned probe beams, with respect to resonant probes, resulting from this influence. Cavities allow real-time monitoring of atomic flux, with single-atom resolution, but they are much slower than their analog in photonics (the avalanche photodiode), so flux limits must be imposed. The proposed detector operates at a maximum flux of 5000 atoms/second, but with a shot-noise clearance of up to 23 dB, allowing the full advantage afforded by number squeezing to be observed.

Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy and one of the most fundamental and simplest measure of the quantum fluctuations, the Heisenberg uncertainty principle. Then, we show that the latter represents a sensitive probe of superradiant quantum phase transitions in standard models of photons such as the Dicke Hamiltonian, which embodies an ensemble of two-level systems interacting with one quadrature of a single and uniform bosonic field. We derive exact results in the thermodynamic limit and for a finite number $N$ of two-level systems: as a reminiscence of the entanglement properties between light and the two-level systems, the product $\Delta x\Delta p$ diverges at the quantum critical point as $N^{1/6}$. We generalize our results to the double quadrature Dicke model where the two quadratures of the bosonic field are now coupled to two independent sets of two-level systems. Our findings, which show that the entanglement properties between light and matter can be accessed through the Heisenberg uncertainty principle, can be tested using Bose-Einstein condensates in optical cavities and circuit quantum electrodynamics.

The Bethe logarithm is calculated for the lowest rotational-vibrational states of H${}_2{}^{+}$ and HD${}^{+}$ hydrogen molecular ions in a wide range of vibrational ($v=0$–4) and total orbital momentum ($L=0$–4) quantum numbers. Numerical results with eight to nine significant digits are obtained for all the states within this range. This allows us to reduce an error in the leading-order radiative contribution, which results eventually in the relative uncertainty of rovibrational frequency intervals at a level lower than ${10}^{-11}$. This high precision is important for the rovibrational spectroscopy experiments of hydrogen molecular ions aiming to determine the electron-to-proton mass ratio.

In this paper we explore the low-dimension long-range superfluid order in the trapped Bose-Einstein condensate driven by spin-orbit coupling at any finite temperature. With the help of the Bogoliubov inequality we give rigorous proofs in both one and two dimensions. For one dimension, no long-range superfluid order can be found, even if spin-orbit coupling exists. For two dimensions, we find that the long-range superfluid order cannot be ruled out in the presence of the unequal Rashba-Dresselhaus-type spin-orbit coupling. However, this long-range superfluid order disappears for the equal case, which has been achieved in recent experiments.

We present an almost fully analytical technique for computing Casimir interactions between periodic lamellar gratings based on a modal approach. Our method improves on previous work on Casimir modal approaches for nanostructures [Phys. Rev. A 82, 062111 (2010)] by using the exact form of the eigenvectors of such structures, and computing eigenvalues by solving numerically a simple transcendental equation. In some cases eigenvalues can be solved for exactly, such as the zero-frequency limit of gratings modeled by a Drude permittivity. Our technique also allows us to predict analytically the behavior of the Casimir interaction in limiting cases, such as the large-separation asymptotics. The method can be generalized to more complex grating structures and may provide a deeper understanding of the geometry-composition-temperature interplay in Casimir forces between nanostructures.

We have investigated the quantum phase transition employing the quantum renormalization-group method while, in most of the previous literature, entanglement (concurrence) has been barely demonstrated. However, it is now well known that entanglement is not the only signature of quantum correlations and a variety of computable measures have been developed to characterize quantum correlations in the composite systems. As an illustration, two cases are elaborated: a one-dimensional anisotropic (i) $XXZ$ model and (ii) an $XY$ model, with various measures of quantum correlations, including quantum discord, geometric discord, measurement-induced disturbance, measurement-induced nonlocality, and violation of Bell inequalities [e.g., Clauser-Horne-Shimony-Holt (CHSH) inequality]. We have proved that all of these correlation measures can effectively detect the quantum critical points associated with quantum phase transitions after several iterations of the renormalization in both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar with entanglement and, even when concurrence vanishes, there still exists some kind of quantum correlation which is not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iteration procedure, which indicates that block-block entanglement cannot revealed by the CHSH inequality. Moreover, the nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a by-product, we verify that measurement-induced disturbance is exactly equal to the quantum discord measured by ${\sigma }_z$ for general $\mathsf{X}$-structured states.

We propose a theoretical and practical framework for the study of light-matter interactions and the angular momentum of light. Our proposal is based on helicity, total angular momentum, and the use of symmetries. We compare the framework to the current treatment, which is based on separately considering spin angular momentum and orbital angular momentum and using the transfer between the two in physical explanations. In our proposal, the fundamental problem of spin and orbital angular momentum separability is avoided, predictions are made based on the symmetries of the systems, and the practical application of the concepts is straightforward. Finally, the framework is used to show that the concept of spin to orbit transfer applied to focusing and scattering is masking two completely different physical phenomena related to the breaking of different fundamental symmetries: transverse translational symmetry in focusing and electromagnetic duality symmetry in scattering.

We propose a scheme to distribute graph states over quantum networks in the presence of noise in the channels and in the operations. The protocol can be implemented efficiently for large graph sates of arbitrary (complex) topology. We benchmark our scheme with two protocols where each connected component is prepared in a node belonging to the component and subsequently distributed via quantum repeaters to the remaining connected nodes. We show that the fidelity of the generated graphs can be written as the partition function of a classical Ising-type Hamiltonian. We give exact expressions of the fidelity of the linear cluster and results for its decay rate in random graphs with arbitrary (uncorrelated) degree distributions.

The Hohenberg-Kohn theorem is generalized to the case of a finite system of $N$ electrons in external electrostatic $\mathcal{E}\left(\mathbf{r}\right)=-\nabla v\left(\mathbf{r}\right)$ and magnetostatic $\mathbf{B}\left(\mathbf{r}\right)=\nabla \times \mathbf{A}\left(\mathbf{r}\right)$ fields in which the interaction of the latter with both the orbital and spin angular momentum is considered. For a nondegenerate ground state a bijective relationship is proved between the gauge invariant density $\rho \left(\mathbf{r}\right)$ and physical current density $\mathbf{j}\left(\mathbf{r}\right)$ and the potentials $\left\{v\right(\mathbf{r}),\mathbf{A}(\mathbf{r}\left)\right\}$. The possible many-to-one relationship between the potentials $\left\{v\right(\mathbf{r}),\mathbf{A}(\mathbf{r}\left)\right\}$ and the wave function is explicitly accounted for in the proof. With the knowledge that the basic variables are $\left\{\rho \right(\mathbf{r}),\mathbf{j}(\mathbf{r}\left)\right\}$, and explicitly employing the bijectivity between $\left\{\rho \right(\mathbf{r}),\mathbf{j}(\mathbf{r}\left)\right\}$ and $\left\{v\right(\mathbf{r}),\mathbf{A}(\mathbf{r}\left)\right\}$, the further extension to $N$-representable densities and degenerate states is achieved via a Percus-Levy-Lieb constrained-search proof. A $\left\{\rho \right(\mathbf{r}),\mathbf{j}(\mathbf{r}\left)\right\}$-functional theory is developed. Finally, a Slater determinant of equidensity orbitals which reproduces a given $\left\{\rho \right(\mathbf{r}),\mathbf{j}(\mathbf{r}\left)\right\}$ is constructed.

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second-order perturbation theory. The relativistic atomic states used for the calculations are obtained by making use of the finite basis set method and are expressed in terms of ${\displaystyle B}$ splines and ${\displaystyle B}$ polynomials. We introduce two experimental scenarios in which the light is circularly and linearly polarized, respectively. For each of these scenarios, the polarization-dependent angular distribution and the degrees of circular and linear polarization of the scattered light are investigated as a function of scattering angle and photon energy. Analytical expressions are derived for the polarization-dependent angular distribution which can be used for scattering by both hydrogenic as well as many-electron systems. Detailed computations are performed for Rayleigh scattering by atomic hydrogen within the incident photon energy range 0.5 to 5 keV. Particular attention is paid to the effects that arise from higher (nondipole) terms in the expansion of the electron-photon interaction.

We systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing-wave phase or plane-wave phase when the strength of the Zeeman field is below a critical value related to the strength of spin-orbit coupling. The Zeeman field can induce a phase transition between standing-wave and plane-wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner: the linear Zeeman effect magnetizes the standing-wave phase along the direction of the magnetic field, but the quadratic Zeeman effect demagnetizes the plane-wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum.