Bose–Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years—particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes—gap solitons and soliton clusters—are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.
Bose–Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years—particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes—gap solitons and soliton clusters—are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.
Optical lattices have been used as a versatile toolbox to control Bose-Einstein condensates (BECs) in recent years, and a wealth of emergent nonlinear phenomena have been found, including bright gap solitons and dark ones, among which the former has been realized in experiments. The latter, however, has only theoretical results and its fundamental properties are still not well understood. Here we theoretically and numerically explore an open issue of creating stable matter-wave dark gap solitons in a one-dimensional optical lattice, onto which the BECs with self-defocusing quintic nonlinearity are loaded. Using linear-stability analysis and direct simulations, the formation, structures, and properties of dark gap solitons in quintic nonlinearity have been compared to those upheld by cubic Kerr nonlinearity. In particular, we uncover that the dark gap solitons and soliton clusters are robustly stable in the first finite band gap of the underlying linear spectrum, and are hard to be stabilized in the second gap. The predicted dark gap solitons are observable in current experiments on dense ultracold atoms, using an optical lattice technique, and in the optics domain for nonlinear light propagation in periodic optical media with quintic nonlinearity.
In past years, optical lattices have been demonstrated as an excellent platform for making, understanding, and controlling quantum matters at nonlinear and fundamental quantum levels. Shrinking experimental observations include matter-wave gap solitons created in ultracold quantum degenerate gases, such as Bose–Einstein condensates with repulsive interaction. In this paper, we theoretically and numerically study the formation of one-dimensional gap soliton molecules and clusters in ultracold coherent atom ensembles under electromagnetically induced transparency conditions and trapped by an optical lattice. In numerics, both linear stability analysis and direct perturbed simulations are combined to identify the stability and instability of the localized gap modes, stressing the wide stability region within the first finite gap. The results predicted here may be confirmed in ultracold atom experiments, providing detailed insight into the higher-order localized gap modes of ultracold bosonic atoms under the quantum coherent effect called electromagnetically induced transparency.
By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose–Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.
, are versatile tools to study the dynamical and static properties of ultracold atoms. OLs with subwavelength spatial structure have been realized in recent quantum-gas experiment, offering new possibility for nonlinear and quantum control of ultracold atoms at the nano scale. Herein, we study theoretically and numerically the formation, property, and dynamics of matter-wave localized gap modes of Bose-Einstein condensates loaded in a one-dimensional nanoscale dark-state OL consisted of an array of optical subwavelength barriers. The nonlinear localized modes, in the forms of on- and off-site fundamental gap solitons, and dipole ones, are demonstrated; and we uncover that, counterintuitively, these modes exhibit always a cusplike (side peaks) mode even for a deeply subwavelength adiabatic lattice, contrary to the previously reported results in conventional deep OLs where the localized gap modes are highly confined in a single lattice cell. The (in)stability features of all the predicted localized modes are verified through the linear-stability analysis and direct perturbed simulations. Our predicted results are attainable in current ultracold atoms experiments with the cutting-edge technique, pushing the nonlinear control of ultracold atoms with short-period OLs as an enabling technology into subwavelength structures.
Abstract In ultracold atomic gases, optical lattices and spin-orbit coupling are two important and useful linear means to study and control the nonlinear and quantum dynamics of matter waves, and both have been well realized in experiments. Here, nonlinear localization of spin-orbit-coupled Bose-Einstein condensates in moiré optical lattices is revealed theoretically, stressing the existence and stability of localized modes of diverse types including fundamental, half-vortex matter-wave gap solitons, and full-vortex ones (of both components). Notably, to our knowledge, a new type of vector vortex gap solitons, which is composed of a gap vortex soliton (singular mode) and a rhombic-array gap vortex (quadruple mode), is predicted in our two-component theoretical framework. It is also found that the model exhibits unique linear Bloch band structures including band splitting and extremely-flat bands, because of which all the predicted localized modes tend to be robustly stable, backed by our direct perturbed simulations. Our results demonstrate that the moiré pattern (and its joint cooperation with spin-orbit coupling) provides great possibilities to explore flat-band and moiré physics in ultracold atoms, and to further investigate the nonlinear dynamics.
Moiré superlattices, a twisted functional structure crossing the periodic and nonperiodic potentials, have recently attracted great interest in multidisciplinary fields, including optics and ultracold atoms, because of their unique band structures, physical properties, and potential implications. Driven by recent experiments on quantum phenomena of bosonic gases, the atomic Bose–Einstein condensates in moiré optical lattices, by which other quantum gases such as ultracold fermionic atoms are trapped, could be readily achieved in ultracold atom laboratories, whereas the associated nonlinear localization mechanism remains unexploited. Here, we report the nonlinear localization theory of ultracold atomic Fermi gases in two-dimensional moiré optical lattices. The linear Bloch-wave spectrum of such a twisted structure exhibits rich nontrivial flat bands, which are separated by different finite bandgaps wherein the existence, properties, and dynamics of localized superfluid Fermi gas structures of two types, gap solitons and gap vortices (topological modes) with vortex charge S=1, are studied numerically. Our results demonstrate the wide stability regions and robustness of these localized structures, opening up a new avenue for studying soliton physics and moiré physics in ultracold atoms beyond bosonic gases.