空间调制作用下Bessel型光晶格中物质波孤立子的稳定性

利用变分法和数值计算方法研究了空间调制作用下Bessel型光晶格中玻色-爱因斯坦凝聚体系中孤立子的稳定性, 给出了存在随空间非周期变化的线性Bessel型光晶格和非线性光晶格(原子之间非线性相互作用的空间调制)时, 各种参数组合下涡旋和非涡旋孤立子的稳定性条件. 首先, 利用圆对称的高斯型试探波函数得出描述体系稳定性参数满足的Euler-Lagrange方程和变分法分析体系稳定性所需要的有效作用势能的表达式. 然后, 根据有效作用势能是否具有局域最小值判断体系是否具有稳定状态, 得出体系具有稳定状态时参数所满足的条件. 最后, 利用有限差分法求解Gross-Pitaevskii方程验证变分法结果的正确性, 所得结果和变分法结果一致. 关键词： Bessel型光晶格 非线性光晶格 孤立子 稳定性     

Modulated optical lattice as an atomic fabry-perot interferometer

We propose to engineer the atomic band structure in optical lattices in order to design a Fabry-Perot interferometer with large mode spacing and strong nonlinear coupling to be employed in atom optics. The use of an optical lattice allows for a significant reduction of the atomic effective mass, while the slow modulation of its parameters spatially confines the matter waves on a length scale of a few dozen optical wavelengths. As a consequence, the mode spacing in such a cavity would be as high as one-tenth of the recoil energy, allowing for a very efficient filter action, while the nonlinear coupling due to interatomic interactions could lead to bistability and limiting effects in the transmission of the atomic beam.     

Cloaking of matter waves

Invariant transformation for quantum mechanical systems is proposed. A cloaking of matter wave can be realized at given energy by designing the potential and effective mass of the matter waves in the cloaking region. The general conditions required for such a cloaking are determined and confirmed by both the wave and particle (classical) approaches. We show that it may be possible to construct such a cloaking system for cold atoms using optical lattices.     

Matter-wave bright solitons in effective bichromatic lattice potentials

Matter-wave bright solitons in bichromatic lattice potentials are considered and their dynamics for different lattice environments are studied. Bichromatic potentials are created from superpositions of (i) two linear optical lattices and (ii) a linear and a nonlinear optical lattice. Effective potentials are found for the solitons in both bichromatic lattices and a comparative study is done on the dynamics of solitons with respect to the effective potentials. The effects of dispersion on solitons in bichromatic lattices are studied and it is found that the dispersive spreading can be minimized by appropriate combinations of lattice and interaction parameters. Stability of nondispersive matter-wave solitons is checked from phase portrait analysis.     

Self-trapped spatially localized states in combined linear-nonlinear periodic potentials

We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes,gap solitons and truncated nonlinear Bloch waves,in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity,supported by a combination of linear and nonlinear periodic lattice potentials.The former is found to be stable once placed inside a single well of the nonlinear lattice,it is unstable otherwise.Contrary to the case with constant self-focusing nonlinearity,where the latter solution is always unstable,here,we demonstrate that it nevertheless can be stabilized by the nonlinear lattice since the model under consideration combines the unique properties of both the linear and nonlinear lattices.The practical possibilities for experimental realization of the predicted solutions are also discussed.     

<Emphasis Type="Italic">q</Emphasis>-Breathers in discrete nonlinear Schrödinger arrays with weak disorder

Nonlinearity and disorder are key players in vibrational lattice dynamics, responsible for localization and derealization phenomena. q-Breathers—periodic orbits in nonlinear lattices, exponentially localized in the reciprocal linear mode space—is a fundamental class of nonlinear oscillatory modes, currently found in disorder-free systems. In this paper we generalize the concept of q-breathers to the case of weak disorder, taking the Discrete Nonlinear Schrödinger chain as an example. We show that g-breathers retain exponential localization near the central mode, provided that disorder is sufficiently small. We analyze statistical properties of the instability threshold and uncover its sensitive dependence on a particular realization. Remarkably, the threshold can be intentionally increased or decreased by specifically arranged inhomogeneities. This effect allows us to formulate an approach to controlling the energy flow between the modes. The relevance to other model arrays and experiments with miniature mechanical lattices, light and matter waves propagation in optical potentials is discussed.     

线性与非线性光晶格中偶极孤立子的稳定性

利用变分法研究了线性和非线性交叉光晶格中偶极玻色-爱因斯坦凝聚(BEC)体系中物质波孤立子的稳定性.选用柱对称高斯型试探波函数,得出参数的Euler-Lagrange方程和体系的有效作用势能,根据有效势能是否具有局域最小值判断体系是否具有稳定孤立子解.结果表明,由于存在接触相互作用的空间调制,在排斥和吸引偶极相互作用下,均能形成稳定的孤立子解.给出了参数空间中存在稳定解的区域和物质波波包宽度随时间的变化曲线.     

Self-trapped nonlinear matter waves in periodic potentials

We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker, Phys. Rev. Lett. 94, 020403 (2005)10.1103/PhysRevLett.94.020403] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension.     

Nonlinear nanoscale localization of magnetic excitations in atomic lattices

Reviewed here is the nonlinear intrinsic localization expected for large amplitude spin waves in a variety of magnetically ordered lattices. Both static and dynamic properties of intrinsic localized spin wave gap modes and resonant modes are surveyed in detail. The modulational instability of extended nonlinear spin waves is discussed as a mechanism for dynamical localization of spin waves in homogeneous magnetic lattices. The interest in this particular nonlinear dynamics area stems from the realization that some localized vibrations in perfectly periodic but nonintegrable lattices can be stabilized by lattice discreteness. However, in this rapidly growing area in nonlinear condensed matter research the experimental identification of intrinsic localized modes is yet to be demonstrated. To this end the study of spin lattice models has definite advantages over those previously presented for vibrational models both because of the importance of intrasite and intersite nonlinear interaction terms and because the dissipation of spin waves in magnetic materials is weak compared to that of lattice vibrations in crystals. Thus, both from the theoretical and the experimental points of view, nonlinear magnetic systems may provide more tractable candidates for the investigation of intrinsic localized modes which display nanoscale dimensions as well as for the future exploration of the quantum properties of such excitations.     

Wave scattering by discrete breathers

We present a theoretical study of linear wave scattering in one-dimensional nonlinear lattices by intrinsic spatially localized dynamic excitations or discrete breathers. These states appear in various nonlinear systems and present a time-periodic localized scattering potential for plane waves. We consider the case of elastic one-channel scattering, when the frequencies of incoming and transmitted waves coincide, but the breather provides with additional spatially localized ac channels whose presence may lead to various interference patterns. The dependence of the transmission coefficient on the wave number q and the breather frequency Omega(b) is studied for different types of breathers: acoustic and optical breathers, and rotobreathers. We identify several typical scattering setups where the internal time dependence of the breather is of crucial importance for the observed transmission properties.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.      

Superfluid fermi gas in optical lattices: self-trapping, stable, moving solitons and breathers

We predict the existence of self-trapping, stable, moving solitons and breathers of Fermi wave packets along the Bose-Einstein condensation (BEC)-BCS crossover in one dimension (1D), 2D, and 3D optical lattices. The dynamical phase diagrams for self-trapping, solitons, and breathers of the Fermi matter waves along the BEC-BCS crossover are presented analytically and verified numerically by directly solving a discrete nonlinear Schr?dinger equation. We find that the phase diagrams vary greatly along the BEC-BCS crossover; the dynamics of Fermi wave packet are different from that of Bose wave packet.     

Bose-Einstein Condensates in Optical Lattices with Higher-Order Interactions

The higher-order interactions of Bose-Einstein condensate in multi-dimensional optical lattices are discussed both analytically and numerically.It is demonstrated that the effects of the higher-order atomic interactions on the sound speed and the stabilities of Bloch waves strongly depend on the lattice strength.In the presence of higher-order effects,tighter and high-dimensional lattices are confirmed to be two positive factors for maintaining the system's energetic stability,and the dynamical instability of Bloch waves can take place simultaneously with the energetic instability.In addition,we find that the higher-order interactions exhibit a long-range behavior and the long-lived coherent Bloch oscillations in a tilted optical lattice exist.Our results provide an effective way to probe the higher-order interactions in optical lattices.     

Spatial solitons in optically induced gratings

We study experimentally nonlinear localization effects in optically induced gratings created by interfering plane waves in a photorefractive crystal. We demonstrate the generation of spatial bright solitons similar to those observed in arrays of coupled optical waveguides. We also create pairs of out-of-phase solitons, which resemble twisted localized states in nonlinear lattices.     

Nonlinear theory of waves in solid state with cardinally changing crystalline structure

A nonlinear theory of propagating periodic and nonlinear solitary waves (like kinks and solitons) related to the motion of defects in crystals and of specific periodic waves into which the former ones transform in the field of the compression stress was developed. The role of intense tension stress leading to the heavy structural rearrangement of the crystal as a result of the effect of the external stress on the interatomic potential barriers was taken into account as well. Crystals with a complex lattice consisting of two sublattices were considered. Arbitrarily large displacements of sublattices were analyzed. The nonlinear theory is based on an additional element of the translational symmetry typical for complex lattices but not introduced earlier in solid-state physics. The variational equations of macroscopic and microscopic displacements turn out to be a nonlinear generalization of the linear equations of acoustic and optical modes obtained by Carman, Born, and Huang Kun. The microscopic displacement fields are described by the nonlinear sine-Gordon equation. In the one-dimensional case, exact solutions of the nonlinear equations were found and their features were revealed. In the case of two-dimensional (2+1) fields, new methods of the exact solutions of the sine-Gordon equation were developed. They describe the interaction of the nonlinear waves with the structural inhomogeneities of solid state due to the external fields of stress and deformations.     

Tunneling control and localization for Bose-Einstein condensates in a frequency modulated optical lattice

The similarity between matter waves in periodic potential and solid-state physics processes has triggered the interest in quantum simulation using Bose-Fermi ultracold gases in optical lattices. The present work evidences the similarity between electrons moving under the application of oscillating electromagnetic fields and matter waves experiencing an optical lattice modulated by a frequency difference, equivalent to a spatially shaken periodic potential. We demonstrate that the tunneling properties of a Bose-Einstein condensate in shaken periodic potentials can be precisely controlled. We take additional crucial steps towards future applications of this method by proving that the strong shaking of the optical lattice preserves the coherence of the matter wavefunction and that the shaking parameters can be changed adiabatically, even in the presence of interactions. We induce reversibly the quantum phase transition to the Mott insulator in a driven periodic potential.     

Oscillatory instabilities of standing waves in one-dimensional nonlinear lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal 0,pi. Incommensurate analytic SWs with |Q|>pi/2 may however appear as "quasistable," as their instability growth rate is of higher order.     

Surface lattice solitons

We study theoretically nonlinear surface waves in optical lattices and show that solitons can exist at the heterointerface between two different semi-infinite 1D waveguide arrays, as well as at the boundaries of a 2D nonlinear lattice. The existence and properties of these surface soliton solutions are investigated in detail.     

Solitons in complex optical lattices

We present an overview of our recent results in the area of soliton excitation and control in optical lattices induced by different types of nondiffracting beams featuring unique symmetries. Optical lattices offer the possibility to engineer and to control the diffraction of light beams in media with transversally modulated optical properties, to manage the corresponding reflection and transmission bands, and to form specially designed defects. Consequently, they afford the existence of a rich variety of new families of nonlinear stationary waves and solitons, lead to new rich dynamical phenomena, and offer novel conceptual opportunities for all-optical shaping, switching and routing of optical signals encoded in soliton formats. In this overview, we consider different types of solitons, including fundamental, multipole, and vortex solitons in reconfigurable lattices optically induced by nondiffracting radially symmetric and azimuthally modulated single Bessel beams, soliton control in networks, couplers, and switches induced by several mutually coherent or incoherent Bessel beams, we address soliton properties in three-dimensional Bessel lattices, as well as in lattices produced by Mathieu and parabolic optical beams.