The communication capacity of Gaussian bosonic channels with memory has recently attracted much interest. Here, we investigate a method to prepare the multimode entangled input symbol states for encoding classical information into these channels. In particular, we study the usefulness of a Gaussian matrix-product state (GMPS) as an input symbol state, which can be sequentially generated although it remains heavily entangled for an arbitrary number of modes. We show that the GMPS can achieve more than 99.9$\%$ of the Gaussian capacity for Gaussian bosonic memory channels with a Markovian or non-Markovian correlated noise model in a large range of noise correlation strengths. Furthermore, we present a noise class for which the GMPS is the exact optimal input symbol state of the corresponding channel. Since GMPS are ground states of particular quadratic Hamiltonians, our results suggest a possible link between the theory of quantum communication channels and quantum many-body physics.

A method to systematically construct the $XX$ quantum spin chains with nearest-neighbor interactions that allow perfect state transfer (PST) is shown. Sets of orthogonal polynomials (OPs) are in correspondence with such systems. The key observation is that for any admissible one-excitation energy spectrum, the weight function of the associated OPs is uniquely prescribed. This entails the complete characterization of these PST models with the mirror-symmetry property arising as a corollary. A simple and efficient algorithm to obtain the corresponding Hamiltonians is presented. A model connected to a special case of the symmetric $q$-Racah polynomials is offered. An explanation of how additional models with PST can be derived from a parent system by removing energy levels from the one-excitation spectrum of the latter is given. This is achieved through Christoffel transformations and is also completely constructive in regards to the Hamiltonians.

In recent years it has been found that quantum systems can posses entanglement in equilibrium thermal states provided temperature is low enough. In the present work we explore a possibility of having entanglement in nonequilibrium stationary states. We show analytically that, in a simple one-dimensional spin chain, there is entanglement even at the highest attainable energies; that is, starting from an equilibrium state at infinite temperature, a sufficiently strong driving can induce entanglement, even in the thermodynamic limit. We also show that dissipative dephasing, on the other hand, destroys entanglement.

The system of four identical bosons with a large two-boson scattering length is described using momentum-space integral equations for the four-particle transition operators. The creation of Efimov trimers via ultracold four-boson recombination is studied. The universal behavior of the recombination rate is demonstrated.

We propose a one-dimensional model of spinor bosons with SU(2) symmetry and a two-body finite-range Gaussian interaction potential. We show that the model is exactly solvable when the width of the interaction potential is much smaller than the interparticle separation. This model is then solved via the asymptotic Bethe-ansatz technique. The ferromagnetic ground-state energy and chemical potential are derived analytically. We also investigate the effects of a finite-range potential on the density profiles through the local-density approximation. Finite-range potentials are more likely to lead to quasi-Bose-Einstein condensation than zero-range potentials.

We consider a two-component Bose-Einstein condensate in a quasi-one-dimensional harmonic trap, where the immiscible components are pressed against each other by an external magnetic force. The zero-temperature nonstationary Gross-Pitaevskii equations are solved numerically; analytical models are developed for the key steps in the process. We demonstrate that if the magnetic force is strong enough, then the condensates may swap their places in the trap due to dynamic quantum interpenetration of the nonlinear matter waves. The swapping is accompanied by development of a modulational instability leading to quasiturbulent excitations. Unlike the multidimensional Rayleigh-Taylor instability in a similar geometry of two-component quantum fluid systems, quantum interpenetration has no classical analog. In a two-dimensional geometry a crossover between the Rayleigh-Taylor instability and the dynamic quantum interpenetration is investigated.

A mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate is considered in which $s$-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction long-range and anisotropic in nature and tunable by the dipolar interaction. It is shown that such an interaction can significantly increase the prospect of realizing a superfluid with a gap parameter characterized with a coherent superposition of all odd partial waves. In the spirit of the Hartree-Fock-Bogoliubov mean-field approach, a theory is formulated that allows the estimation of the critical temperature when the anisotropic Fock potential is taken into consideration and the determination of the system parameters that optimize the critical temperature at which such a superfluid emerges before the system begins to phase separate.

We report on the theoretical observation of optical rogue waves in a dissipative system, namely, a mode-locked fiber laser. These rogue waves are pulses of huge peak power which may chaotically appear in the laser. They exist in the normal dispersion regime and exhibit peak powers exceeding those of stable dissipative solitons by a factor of 13. Their height exceeds the so-called significant wave height by a factor of 6. The peak power of the rogue waves can be changed by varying the laser gain. These rogue waves arise from noise by a peculiar nonlinear focusing process of the intracavity light in this dissipative system without requiring any specific initial conditions. Moreover, we identify the crucial effect of gain saturation on the focusing process and, consequently, on the peak amplitude of rogue waves. Similar to rogue events in the ocean, the laser rogue pulses are also accompanied by holes which are moving dark solitons.

The optical properties of three-dimensionally-ordered self-assembled photonic crystals are studied in the Bragg wave coupling regime. Angle-resolved photonic stop gap measurements show the Bragg wave coupling extending over an angular range of 18°. The new diffraction peak originating at the Bragg wave coupling regime is due to the ($\overline{1}11$) stop gap. The Bragg wave coupling regime is analyzed for photonic crystals with different lattice constants and refractive index contrasts. For lower-index-contrast photonic crystals, Bragg wave coupling occurs at a lower angle of incidence as compared to higher-index-contrast photonic crystals of similar lattice constants. The exchange of energy between the diffraction peaks in the coupling regime is discussed. Experimental results are compared with theoretical calculations and they are in good agreement. Furthermore, we demonstrate tunable stop gap with high reflectance and photonic strength in the fiber-optic communication wavelength range.

We present a theoretical investigation of a cavity-QED system controlled by bichromatic adiabatic passage in a dissipative environment. We analyze the production of a controlled Fock state in the cavity by a traveling atom simultaneously coupled by a laser field, and the leakage of the corresponding photons from the cavity.

We report the existence and stability of lattice solitons in parity-time ($\mathcal{PT}$)-symmetric mixed linear-nonlinear optical lattices in Kerr media. We focus on studying the characteristic effects on soliton propagation in the semi-infinite gap if we consider different amplitudes of real and imaginary parts of both the linear refractive index modulation profile and of periodic nonlinearity-modulation spatial distribution. It was found that the combination of $\mathcal{PT}$-symmetric linear and nonlinear lattices can stabilize lattice solitons and can provide unique soliton properties. It is revealed that the parameters of the linear lattice periodic potential play a significant role in controlling the extent of the stability domains and that the lattice solitons can stably propagate only in the low-power regime.

The third level has great influence on the time evolution of the spontaneous decay from the excited state, when the counter-rotating terms are taken into account. The influence in the cascade-type and $\mathsf{V}$-type three-level systems is investigated for two initial states, excited from the ground states of the whole system (atom plus vacuum modes) and from the bare atom. The third level results in the additional virtual photon processes, emitting a photon from one level and reabsorbing the same photon to another level and vice versa. The main influence of the third level is to accelerate the decay, which leads to or enhances the anti-Zeno effect, especially for the initial state excited from the ground state of the whole system. Therefore, the third level cannot be neglected, if the counter-rotating terms are taken into account.

We discuss the use of asymptotic-in and -out fields in a Hamiltonian treatment of nonlinear electromagnetic problems. Our approach allows a description of nonlinear phenomena in a number of geometries and is suitable to treat integrated photonic structures, particularly cavities. We present examples in which the nonlinear phenomena are weak enough for pump depletion to be neglected, and we report some results related to the description of second-order nonlinear processes in ring resonators and layered structures.

It is a familiar fact that, in an isolated sphere or ellipsoid of uniform polarization density, the electrostatic field also is uniform. Because of this, the state of uniform polarization in a spherical sample of uniformly distributed two-level atoms is an eigenmode of the coherent decay process in the limit of a small radius compared to the resonant wavelength of a single atom. Consequently, in this special geometry, the Dicke picture of uniform exponential decay should hold. In nonspheroidal geometries or in spherical geometries with nonuniform atomic density, the decay should be more complicated. Here, we find the characteristic equations that determine the eigenmodes of the Lienard-Wiechert interaction for a partly hollowed sphere of identical two-level atoms in two different radial configurations. We show that the Dicke picture for emission from a coherently prepared sample does not correctly describe the system's dynamics even when we take the radius of the sphere to be much smaller than the radiation wavelength.

We analyze the formation of the low-energy structure (LES) in above-threshold ionization spectra in strong-field ionization by midinfrared laser pulses by using both quasiclassical and quantum approaches. We show this structure to be largely classical in origin, resulting from a two-dimensional focusing in the energy–angular-momentum plane of the strong-field dynamics in the presence of the atomic potential. The latter is shown to cause the LES even in the absence of a long-range Coulomb tail. The peak at low energy is strongly correlated with high angular momenta of the photoelectrons. Quantum simulations confirm this scenario. We find the LES to be remarkably sensitive to the carrier-envelope phase of the laser field.

A thermodynamic theory is developed to describe the behavior of the entanglement between the coin and position degrees of freedom of the quantum walk on the line. It is shown that, in spite of the unitary evolution, a steady state is established after a Markovian transient stage. This study suggests that if a quantum dynamics develops in a composite Hilbert space (i.e., the tensor product of several subspaces), then the behavior of an operator that belongs only to one of the subspaces may camouflage the unitary character of the global evolution.

We give a systematic theoretical description of homodyne detection in the case where both the signal and the local oscillator pass through the turbulent atmosphere. Imperfect knowledge of the local-oscillator amplitude is effectively included in a noisy density operator, leading to postprocessing noise. Alternatively, we propose a technique with monitored transmission coefficient of the atmosphere, which is free of postprocessing noise.

We report an eight-element, linear-array, single-photon detector that uses multiple fibers of differing lengths coupled to a single detector, the timing information from which reveals the position in which the photon was measured. Using two such arrays and two detectors we measure the correlations of photons produced by parametric downconversion, without recourse to mechanical scanning. Spatial light modulators acting as variable focal length lenses positioned between the downconversion crystal and the arrays allow us to switch between measurement of position, transverse momentum, or intermediate bases. We observe the product of the variances of the conditional probabilities for position and momentum to be more than an order of magnitude below the classical limit, realizing a full-field demonstration of the Einstein-Podolsky-Rosen paradox. Such, multistate measurement technologies allow access to the higher information content of the photon based upon spatial modes.

The Hardy test of nonlocality can be seen as a particular case of the Bell tests based on the Clauser-Horne (CH) inequality. Here we stress this connection when we analyze the relation between the CH-inequality violation, its threshold detection efficiency, and the measurement settings adopted in the test. It is well known that the threshold efficiencies decrease when one considers partially entangled states and that the use of these states, unfortunately, generates a reduction in the CH violation. Nevertheless, these quantities are both dependent on the measurement settings considered, and in this paper we show that there are measurement bases which allow for an optimal situation in this trade-off relation. These bases are given as a generalization of the Hardy measurement bases, and they will be relevant for future Bell tests relying on pairs of entangled qubits.