Coupled matter–wave solitons in optical lattices

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ 1) is less than that of the LOL (V 0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ 1 > V 0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ 1 < V 0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.

We study the dynamics of one-dimensional solitons in attractive and repulsive Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that, in the repulsive BEC, where the soliton is of the gap type, its effective mass is negative. This gives rise to a prediction for the experiment: such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing slow harmonic oscillations, with a period that is estimated to be ∼0.01 s in realistic experimental conditions) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to interaction with the OL. At a later stage, the damped motion becomes chaotic. We also investigate the evolution of a two-soliton pulse in the attractive model. The pulse generates a persistent breather, if its amplitude is not too large; otherwise, fusion into a single fundamental soliton takes place. Collisions between two solitons captured in the parabolic trap or anti-trap are considered too. Depending on their amplitudes and phase difference, the solitons either perform stable oscillations, colliding indefinitely many times, or merge into a single soliton. Effects reported in this work for BECs can also be formulated for optical solitons in nonlinear photonic crystals. In particular, the capture of the negative-mass soliton in the anti-trap implies that a bright optical soliton in a self-defocusing medium with a periodic structure of the refractive index may be stable in an anti-waveguide.

We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.

We report a family of solitons generated by Hermite-Gaussian beams that are supported in optical lattices, also described by Hermite-Gaussian functions in combination with a harmonic potential that is modelled by a (1+1)D nonlinear Schrödinger equation. We find that this kind of solitons is stable during propagation, provided they remain below a level of the power threshold. The pure local nonlinear system studied here can mimic, up to a certain extent, a strongly nonlocal medium, thus allowing generation of accessible solitons. These Hermite-Gaussian profiles constitute a kind of uncommon analytical solitons that allow the study of nonlinear wave behavior phenomena in a more tractable and closed form.

We report on the existence and stability of mixed-gap vector surface solitons at the interface between a uniform medium and an optical lattice with fractional-order diffraction. Two components of these vector surface solitons arise from the semi-infinite and the first finite gaps of the optical lattices, respectively. It is found that the mixed-gap vector surface solitons can be stable in the nonlinear fractional Schrödinger equations. For some propagation constants of the first component, the stability domain of these vector surface solitons can also be widened by decreasing the Lévy index. Moreover, we also perform stability analysis on the vector surface solitons, and it is corroborated by the propagations of the perturbed vector surface solitons.

The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.

We demonstrate that matter-wave solitary pulses formed from Bose condensed atoms moving inside optical lattices continuously radiate dispersive matter waves with prescribed momentum. Our analytical results for the radiation parameters and the soliton decay rate are found to be in excellent agreement with numerical modeling performed for experimentally relevant parameters.

We address the formation and propagation of vector solitons in optical lattices in the presence of anisotropy-induced walk-off between ordinary and extraordinary polarized field components. Stable vector solitons trapped by the lattice form above a threshold power, while decreasing the lattice depth below a critical value results in the abrupt release of the caged solitons that then move across the lattice and may get trapped in a desired lattice channel.

The dynamical behavior of matter-wave solitons of two-component Bose-Einstein condensates (BEC) in combined linear and nonlinear optical lattices (OLs) is investigated. In particular, the dependence of the frequency of the oscillating dynamics resulting from initially slightly displaced components is investigated both analytically, by means of a variational effective potential approach for the reduced collective coordinate dynamics of the soliton, and numerically, by direct integrations of the mean field equations of the BEC mixture. We show that for small initial displacements binary solitons can be viewed as point masses connected by elastic springs of strengths related to the amplitude of the OL and to the intra- and interspecies interactions. Analytical expressions of symmetric and antisymmetric mode frequencies are derived and occurrence of beatings phenomena in the displaced dynamics is predicted. These expressions are shown to give a very good estimation of the oscillation frequencies for different values of the intraspecies interatomic scattering length, as confirmed by direct numerical integrations of the mean field Gross-Pitaevskii equations (GPE) of the mixture. The possibility to use displaced dynamics for indirect measurements of BEC mixture characteristics such as number of atoms and interatomic interactions is also suggested.

Summary form only given. Recent research is rapidly moving toward all-optical confinement of Bose-Einstein condensate (BEC) in optical traps. The optical trap provides an effective tool to manipulate the dynamics of BEC for practical purposes. In particular it opens the possibilities to study BEC in an optical lattice. In this work, we focus on studying the properties of propagation of a weak probe light through a BEC confined in an optical lattice. The key point in the topic is that the ground state of the lattice BEC acts as a periodic dielectric medium for the probe light propagating through it. We show that photonic, or rather polaritonic band gaps are created for probe light due to the spatial periodicity of the ground state of the lattice BEC. However being different from the ordinary periodic dielectric, the lattice BEC can experience elementary excitations which lead to a perturbative distortion of the periodicity of the lattice BEC. Such non-periodic perturbations are similar to lattice defects in solid state physics. Here they will produce defect states inside the photonic band gaps. By analyzing the elementary excitations of the lattice BEC, we study the frequency spectrum of photonic band gaps and defect states induced by such excitations in the lattice BEC. These photonic defect states may technically have the potential to be employed to acquire knowledge about the quantum degeneracy in an optical lattice.

The paper investigate the effect and control of loss for the beam propagation in Kerr-type nonlinear optical lattices, and the loss compensation by the longitudinal depth of the modulation analytically and numerically. It is shown that media loss reduce the peak power of lattice soliton, decreasing the nonlinear effects, disturbing the balance between the diffraction and nonlinear effects. As a result, lattice soliton can't propagate steadily and optical beam dispersed finally. It is possible that proper changing the longitudinal lattice depth can complete suppression of the loss's influence and the beam can be regenerated successfully. There are analogy characteristic in the action of periodic lattice's potential of optical and nonlinear. The periodic potential offers the better method to control the lattice soliton formation and propagation.

We propose a scheme for making a Bose-Einstein condensate (BEC) of molecules from a BEC of atoms in a strongly confining two-dimensional optical lattice and a weak one-dimensional optical lattice in the third dimension. The stable solutions obtained for the order parameters take the form of a different type of gap soliton, with both atomic and molecular BECs, and also standard gap solitons with only a molecular BEC. The strongly confining dimensions of the lattice stabilize the BEC against inelastic energy transfer in atom-molecule collisions. The solitons with atoms and molecules may be obtained by starting with an atomic BEC, and gradually tuning the resonance by changing the external magnetic-field strength until the desired atom-molecule soliton is obtained. A gap soliton of a BEC of only molecules may be obtained nonadiabatically by starting from an atom-only gap soliton, far from a Feshbach resonance and adjusting the magnetic field to near Feshbach resonance. After a period of time in which the dimer field grows, change the magnetic field such that the detuning is large and negative and Feshbach effects wash out, turn off the optical lattice in phase with the atomic BEC, and turn on an optical lattice in phase with the molecules. The atoms disperse, leaving a gap soliton composed of a molecular BEC. Regarding instabilities in the dimension of the weak optical lattice, the solitons which are comprised of both atoms and molecules are sometimes stable and sometimes unstable---we present numerically obtained results. Gap solitons comprised of only molecules have the same stability properties as the standard gap solitons: stable from frequencies slightly below the middle of the band gap to the top, and unstable below that point. Instabilities are only weakly affected by the soliton velocities, and all instabilities are oscillatory.

Quantum phase transition of ultracold atomic gas is one of the core contents in the study of quantum correlational many-body systems. In this paper, two-dimensional (2D) optical lattices are generated by a single fold retroreflected laser beam, and this scheme is used to experimentally design and implement the 2D optical lattice of double wells suitable for isolating and manipulating an array of individual pairs of atoms and predict a topological semimetal in the high orbital bands in this 2D lattice. Two types of optical lattice structures are produced by controlling the laser polarization. One type is the usual 2D optical lattice, which is formed by two independent one-dimensional(1D) optical lattices in two directions and named in-plane lattice, and the other type is the lattice that is formed by the interference between two one-dimensional optical lattices in two directions and called out-plane lattice. When &lt;sup&gt;87&lt;/sup&gt;Rb BEC (Bose-Einstein condensation) is loaded into the 2D optical lattice, the quantum phase transition between superfluid state and Mott insulator state is observed by controlling the tunneling and in-site interaction. And the phase transition from superfluid state to Mott insulator is judged by observing whether there are interferential lattice points in momentum space. The lattice depths of two cases can be calibrated by Kapitza-Dirac scattering in the ultracold atomic experiment through the time-of-flight absorption imaging. In the in-plane optical lattice, some incorrect points appear in the 45° direction, because the linear polarization degree of beam is impure after being reflected by mirrors and two direction of beam are not completely orthogonal to each other. It is obvious that the two cases have different phase transition points, which is due mainly to the difference in structure. For the in-plane lattice, there are two independent 1D optical lattices, and for the out-plane lattice, the two direction beams mutually interfere with each other, therefore, two optical lattices are not independent of each other. The atoms come back to BEC by reducing the potentials of optical lattice to zero; the temperature of system is slightly higher, because of the jitter of the light lattice. The different behaviors of quantum phase transition are analyzed for two types of optical lattices. This work will provide a platform for the future study of large spin system and strong correlation physics in optical lattices.

A method to find discrete solitons in nonlinear lattices is introduced. Using nonlinear optical waveguide arrays as a prototype application, both stationary and traveling-wave solitons are investigated. In the limit of small wave velocity, a fully discrete perturbative analysis yields formulas for the mode shapes and velocity.

From the linear stability analysis，the modulational instability (MI) of two-component dipolar Bose-Einstein condensates (BECs) in an optical lattice is studied. The relation of the region of MI with the on-site interaction and the site-to-site interaction induced by the dipole-dipole interaction is obtained. The results show that there is a great influence of site-to-site interaction on the MI of the two-component dipolar BECs in the optical lattices. This gives us some useful information for manipulating two-component dipolar BECs in practice.