Spatiotemporal engineering of matter-wave solitons in Bose–Einstein condensates

Abstract

• A review is focused on 1D, 2D, and 3D matter-wave solitons in Bose-Einstein condensates under the action of spatiotemporally modulated cubic nonlinearity and time-dependent trapping potentials • Most essential problems under the consideration is the shape and stability of solitons and other coherent structures, including stabilization against the critical collapse • Both analytical results (exact and approximate ones) and systematically produced numerical findings are summarized • The modulational instability in these models and its nonlinear development is addressed in detail • Stability and motion of multi-component solitons in binary and spinor (triple) solitons is considered

Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice

“…To produce a spatially localized solution of Equation ( 2), following the general scheme used for engineering matter-wave configurations [36,37], we choose an ansatz,…”

Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements

“…[ 23–30 ] Using nonlinear Schrö dinger equation as the model equation for slowly modulated waves propagating in NLTNs, some interesting nonlinear phenomena of NLTNs have been discovered, such as modulation instability, solitons, and rogue waves (RWs). [ 20,29,31–36 ] In recent decades, these nonlinear phenomena have undergone much theoretical and experimental research. [ 37 ] Mathematically, the concept of RWs is generally thought of as rational polynomials construct based on the integrability of a class of nonlinear partial differential equations such as the focusing nonlinear Schrödinger (NLS) equation.…”

One-dimensional purely Lee-Huang-Yang fluids dominated by quantum fluctuations in two-component Bose-Einstein condensates

“…Realizations of Bose-Einstein condensates (BECs) in 1995 for rubidium-87 [1], sodium-23 [2] and Lithium-7 [3] atoms had heralded the landmark of modern physics, then studies of coherent matter waves sparked renewed attention of scientists from various fields [4][5][6][7][8][9][10][11][12][13][14], evidenced by numerous theoretical predictions [15][16][17][18] and the subsequent experimental observations of novel quantum states of matter driven by BECs, which include degenerate quantum Fermi gases [19,20], Tonks-Girardeau gases with impenetrable (hard-core) bosons [21][22][23], spin-orbit-coupled BEC [24][25][26], and quantum droplets [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Particularly, quantum droplets [27,…”

“…LHY physics describing for weak quantum fluctuations has been demonstrated in ultracold atomic gases experiments, such as BECs loaded in optical lattices (which decrease kinetic energy of a single particle and increase atom-atom interactions) [50][51][52], quantum phase transitions from superfluid to Mott insulators [53][54][55][56][57], quantum criticality [58] and the Tomonaga-Luttinger liquids [59]. Another setting is provided by Feshbach resonance management that can tune the sign and value of interatomic interactions by controlling the associated scattering length [14,[60][61][62][63], according to initial experimental confirmations of the frequency shifts in collective oscillations [64] and density profiles [65,66], both deviated from mean-field theory, in the fermionic condensates. In strongly interacting bosonic gases, effects of tunable interaction strengths beyond the mean-field regime were also experimentally observed in excitation spectrum of ultracold rubidium-85 atoms [67] and in the state equation of lithium-7 condensates [68].…”