We address one-dimensional soliton formation in a cubic nonlinear medium with two-photon absorption and transversally inhomogeneous gain landscape consisting of a single or several amplifying channels. Existence of the solitons requires certain threshold gain while the properties of solitons strongly depend on whether the number of the amplifying channels is odd or even. In the former case, an increase of the gain leads to symmetry breaking, which occurs through the pitchfork bifurcation, and to emergence of a single or several coexisting stable asymmetric modes. In the case of an even number of amplifying channels, we have found only asymmetric stable states.

Entangled qubit pairs can serve as a quantum memory or as a resource for quantum communication. The utility of such pairs is measured by how long they take to disentangle or decohere. To answer the question of whether qubit-qubit interactions can prolong entanglement, we calculate the dissipative dynamics of a pair of qubits coupled via the exchange interaction in the presence of random telegraph noise and $1/f$ noise. We show that for maximally entangled (Bell) states, the exchange interaction generally suppresses decoherence and disentanglement. This suppression is more apparent for random telegraph noise if the noise is non-Markovian, whereas for $1/f$ noise the exchange interaction should be comparable in magnitude to the strongest noise source. The entangled singlet-triplet superposition state of two qubits (${\psi }_{\pm }$ Bell state) can be protected by the interaction, while for the triplet-triplet state (${\varphi }_{\pm }$ Bell state), it is less effective. Thus the former is more suitable for encoding quantum information.

We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We give a highly intuitive geometric interpretation to entanglement via the Majorana representation, where these states correspond to points on a unit sphere. We use this to show how various entanglement properties are determined by the symmetry properties of the states. The geometric measure of entanglement is thus phrased entirely as a geometric optimization and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally, we see that different symmetries of the states correspond to different types of entanglement with respect to interconvertibility under stochastic local operations and classical communication.

Spectral changes of Na${}_2$ in liquid helium were studied using the sequential Monte Carlo–quantum mechanics method. Configurations composed by Na${}_2$ surrounded by explicit helium atoms sampled from the Monte Carlo simulation were submitted to time-dependent density-functional theory calculations of the electronic absorption spectrum using different functionals. Attention is given to both line shift and line broadening. The Perdew, Burke, and Ernzerhof (PBE1PBE, also known as PBE0) functional, with the PBE1PBE/6-311++G(2$d$,2$p$) basis set, gives the spectral shift, compared to gas phase, of 500 cm${}^{-1}$ for the allowed $X\hspace{0.5em}{}^1{\Sigma }_{\mathrm{g}}^{+}\to B\hspace{0.5em}{}^1{\Pi }_{\mathrm{u}}$ transition, in very good agreement with the experimental value (700 cm${}^{-1}$). For comparison, cluster calculations were also performed and the first $X\hspace{0.5em}{}^1{\Sigma }_{\mathrm{g}}^{+}\to A\hspace{0.5em}{}^1{\Sigma }_{\mathrm{u}}^{+}$ transition was also considered.

We study ultracold three-body collisions of bosons and fermions when the interatomic interaction is tuned near a narrow Feshbach resonance. We show that the width of the resonance has a substantial impact on the collisional properties of ultracold gases in the strongly interacting regime. From our numerical and analytical analyses, we identify universal features dependent on the resonance width. Remarkably, we find that all inelastic processes near narrow resonances leading to deeply bound states in bosonic systems are suppressed, while those for fermionic systems are enhanced. As a result, narrow resonances present a scenario that is the reverse of that found for broad resonances, opening up the possibility of creating stable samples of ultracold bosonic gases with large scattering lengths.

The collisional loss rates of 63$S_{1/2}$ Rydberg atoms in cesium magneto-optical trap are measured by using the state-selective pulse field ionization technique and used to investigate the interaction between Rydberg atoms. The collisional loss rate coefficients due to collisions with Rydberg atoms and ground-state atoms are obtained by fitting the experimental data. The results indicate that the large collisional loss mainly comes from the strong long-range interaction between ultracold Rydberg atoms, and the loss rate is significantly increased under a weak electric field.

High-intensity, extreme-ultraviolet (XUV) femtosecond interactions with large rare-gas clusters of xenon and argon have been studied at a wavelength of 38 nm. Pulses of XUV radiation with nJ energy are produced by high-order harmonic conversion from a 35-fs, near-infrared, terawatt laser. Mass resolved ion spectra show charge states up to Xe${}^{8+}$ and Ar${}^{4+}$. Kinetic-energy measurements of ions and electrons indicate that a nanoplasma is formed and a hydrodynamic cluster explosion ensues after heating by the short wavelength pulse. It appears that the observed charge states and electron temperatures are consistent with sequential, single-photon ionization and collisional ionization of ions that have had their ionization potential depressed by plasma continuum lowering in the cluster nanoplasma.

By invoking supersymmetry, we found a condition under which the Stark-effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable for the $|\mathrm{J̃}=m,m\rangle$ family of stretched states. The analytic expressions for the wave function and eigenenergy and other expectation values allow one to readily reverse-engineer the problem of finding the values of the interaction parameters required for creating quantum states with preordained characteristics. The method also allows the construction of families of isospectral potentials, realizable with combined fields.

We investigate the dynamics of an open Bose-Einstein condensate system consisting of two hyperfine states of the same atomic species which are coupled by a tunable Raman laser. It has already been suggested that the detuning between the laser frequency and transition frequency affect significantly the dynamics of the pure condensate. Here we show that the detuning effect is suppressed by noise and dissipation caused by the environment. The increase of coherence and purity are also displayed for specific parameters. As a verification of the lowest order approximation we derive the hierarchy of motion equations in the second-order approximation. It turns out that the former one can describe the dynamical evolution qualitatively for weak noise and dissipation and quantitatively for strong noise and dissipation.

This paper presents the results of our study on the dynamics of Jacobi's elliptic spatial waves in a nonlinear optical grating based on a generalized coupled-mode model. We discuss the characteristics of their amplitudes, widths, and spatial periods as well as their bifurcation in the associated phase plane. Our study on the dynamical propagation of perturbed profiles reveal that these waves can suffer breathing and broadening due to the diffraction effect. A remarkable split-off phenomenon of a spatial wave with wide stripes into several narrow and shallow oblique stripes is observed, as well as their passing and bouncing collisions.

Pulses in passively mode-locked lasers are often accompanied by dispersive waves that form spectral sidebands due to spatial inhomogeneities in the laser cavity. Here we present an explicit calculation of the amplitude, frequency, and precise shape of the sidebands accompanying a solitonlike pulse. We then extend the study to the global steady state of mode-locked lasers with a variable number of pulses, and present experimental results in a mode-locked fiber laser that confirm the theory. The strong correlation between the temporal width of the sidebands and the measured spacing between the pulses in a multipulse operation suggests that the sidebands have an important role in the interpulse interaction.

We make theoretical investigations of the nonlinear guided modes near the Dirac point (DP) in nonlinear negative-zero-positive index metamaterial (NZPIM) waveguide. When the nonlinearity is self-focusing, an asymmetric forbidden band exists near the DP that can be modulated by the strength of the nonlinearity. However, the self-defocusing nonlinearity can completely eliminate the asymmetric band gap. We also study the nonlinear surface waves in such nonlinear NZPIM waveguide. These results may predict analogous phenomena in nonlinear graphene.

Molecular high-order harmonic generation (MHOHG) from the polar diatomic molecule HeH${}^{2+}$ in short intense laser fields is studied numerically. Due to the nonadiabatic response of the molecular dipole to the rapid change of laser intensity, a spectral redshift is predicted in high-intensity and ultrashort laser pulses, contrary to the blueshift observed in the harmonics generated from atoms in long laser pulses. The MHOHG temporal structures are investigated by a wavelet time-frequency analysis, which shows that the enhanced excitation of localized long lifetime excited states shifts the harmonic generation spectrum in the falling part of short laser pulses, due to the presence of a permanent dipole moment, and thus is unique to polar molecules.

We develop an efficient Monte Carlo approach to describe the optical response of cold three-level atoms in the presence of electromagnetically induced transparency (EIT) and strong atomic interactions. In particular, we consider a Rydberg-EIT medium where one involved level is subject to large shifts due to strong van der Waals interactions with surrounding Rydberg atoms. Agreement with much more involved quantum calculations is excellent, demonstrating its applicability over a wide range of densities and interaction strengths. The calculations show that nonlinear absorption due to Rydberg-Rydberg atom interactions exhibits universal behavior.

We present a proof-of-principle experiment in which the population of an atomic level is spatially localized using the technique of electromagnetically induced transparency (EIT). The key idea is to utilize the sensitive dependence of the dark state of EIT on the intensity of the coupling laser beam. By using a sinusoidal intensity variation (standing wave), we demonstrate that the population of a specific hyperfine level can be localized much more tightly than the spatial period.

We report the experimental demonstration of electromagnetically-induced-transparency-based cross-phase-modulation at attojoule or, equivalently, few-hundred-photon levels. A phase shift of 0.005 rad of a probe pulse modulated by a signal pulse with an energy of $~100$ aJ, equivalent to $~400$ photons, was observed in a four-level system of cold ${}^{87}\mathrm{Rb}$ atoms.

We examine the entanglement entropy of the even half of a translationally invariant finite chain or lattice in its ground state. This entropy measures the entanglement between the even and odd halves (each forming a “comb” of $n/2$ sites) and can be expected to be extensive for short-range couplings away from criticality. We first consider bosonic systems with quadratic couplings, where analytic expressions for arbitrary dimensions can be provided. The bosonic treatment is then applied to finite spin chains and arrays by means of the random-phase approximation. Results for first-neighbor anisotropic $\mathit{XY}$ couplings indicate that, while at strong magnetic fields this entropy is strictly extensive, at weak fields important deviations arise, stemming from parity-breaking effects and the presence of a factorizing field (in the vicinity of which it becomes size-independent and identical to the entropy of a contiguous half). Exact numerical results for small spin $s$ chains are shown to be in agreement with the bosonic random-phase approximation prediction.

We investigate the possibility of chaining qubits by letting pairs of nearest-neighbor qubits dissipate into common environments. We then study entanglement dynamics within the chain and show that steady-state entanglement can be achieved.

We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have stringlike logical operators, which make the codes non-self-correcting. We introduce a notion of “logical string segments” to avoid difficulties in defining one-dimensional objects in discrete lattices. We prove that every stringlike logical operator of our code can be deformed to a disjoint union of short segments, each of which is in the stabilizer group. The code has surfacelike logical operators whose partial implementation has unsatisfied stabilizers along its boundary.