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Matter wave soliton solutions for driven Gross–Pitaevskii equation with distributed coefficients
摘要： We have obtained the matter wave soliton solution for the driven nonautonomous GP equation with quadratic-cubic nonlinearities. We have revealed their interesting dynamical features for the experimentally realizable form of nonlinear interactions. Additionally, we have described that by suitably choosing some system parameters, we can control their characteristics such as amplitude and width etc. We have found that our results/solutions are stable and can be applied for future applications.
关键词： Bose-Einstein condensates,GP equation,Matter wave solitons,Quadratic-cubic nonlinearity
更新于2025-09-23 15:23:52
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Ring modes supported by concentrated cubic nonlinearity
摘要： We consider the one-dimensional Schr?dinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, con?ned to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the nonlinearity coef?cient represented by the δ function, all stationary states are obtained in an exact analytical form. The states with positive chemical potentials are found in alternating bands for the cases of the self-repulsion and attraction, while solutions with negative chemical potentials exist only in the latter case. These results provide a possibility to obtain exact solutions for band-gap states in the nonlinear system. Approximating the δ function by a narrow Gaussian, stability of the stationary modes is addressed through numerical computation of eigenvalues for small perturbations, and veri?ed by simulations of the perturbed evolution. For positive chemical potentials, the stability is investigated in three lowest bands. In the case of the self-attraction, each band contains a stable subband, the transition to instability occurring with the increase of the total norm. As a result, multipeak states may be stable in higher bands. In the case of the self-repulsion, a single-peak ground state is stable in the ?rst band, while the two higher ones are populated by weakly unstable two- and four-peak excited states. In the case of the self-attraction and negative chemical potentials, single-peak modes feature instability which transforms them into persistently oscillating states.
关键词： cubic nonlinearity,Bose-Einstein condensates,stationary states,optics,Schr?dinger equation,stability analysis
更新于2025-09-23 15:21:01
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Entangled States of Atomic Solitons for Quantum Metrology
摘要： The formation of multiparticle maximally path-entangled states (known as N00N-states) are considered along with their use in quantum metrology. It is shown how the standard quantum limit can be overcome and the Heisenberg limit can be reached when measuring the linear phase shift. It is also shown how the Heisenberg limit can be overcome when measuring the parameters of a medium in nonlinear quantum metrology.
关键词： quantum metrology,Heisenberg limit,Bose–Einstein condensates,standard quantum limit,N00N-states
更新于2025-09-23 15:19:57
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Vortex solitons in Bose–Einstein condensates with spin–orbit coupling and Gaussian optical lattices
摘要： We investigate the generation and stability of three-dimensional (3D) solitons in binary atomic Bose–Einstein condensates with spin–orbit coupling (SOC) and Super-Gaussian optical lattices. We examine the stability of 3D solitons using their norm and energy. The evolution of solitons is made more stable and their resistance to collapse more robust by the introduction of Gaussian lattices. Depending on the relative strength of SOC, the nonlinearity modulation parameter, and the lattice parameters, we observe stable solitons of the semi-vortex and mixed-mode type. In addition, we demonstrate the robustness of solitons in propagation and collisions.
关键词： Spin–orbit coupling,Gaussian lattices,Bose–Einstein condensates,Vortex solitons
更新于2025-09-19 17:15:36
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[Advances In Atomic, Molecular, and Optical Physics] Volume 66 || Efficient Description of Bose–Einstein Condensates in Time-Dependent Rotating Traps
摘要： Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable sources for the coherent matter waves in these devices are Bose–Einstein condensates. A reliable prediction of their dynamics, which is governed by the Gross–Pitaevskii equation, requires suitable analytical and numerical methods, which take into account the center-of-mass motion of the condensate, its rotation, and its spatial expansion by many orders of magnitude. In this chapter, we present an efficient way to study their dynamics in time-dependent rotating traps that meet this objective. Both an approximate analytical solution for condensates in the Thomas–Fermi regime and dedicated numerical simulations on a variable adapted grid are discussed. We contrast and relate our approach to previous alternative methods and provide further results, such as analytical expressions for the one- and two-dimensional spatial density distributions and the momentum distribution in the long-time limit that are of immediate interest to experimentalists working in this field of research.
关键词： Bose–Einstein condensates,Thomas–Fermi approximation,matter-wave interferometry,Gross–Pitaevskii equation,quantum sensors
更新于2025-09-09 09:28:46
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Pinning Transition of Bose-Einstein Condensates in Optical Ring Resonators
摘要： We experimentally investigate the dynamic instability of Bose-Einstein condensates in an optical ring resonator that is asymmetrically pumped in both directions. We find that, beyond a critical resonator-pump detuning, the system becomes stable regardless of the pump strength. Phase diagrams and quenching curves are presented and described by numerical simulations. We discuss a physical explanation based on a geometric interpretation of the underlying nonlinear equations of motion.
关键词： dynamic instability,pinning transition,optical ring resonators,Bose-Einstein condensates
更新于2025-09-09 09:28:46
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A BOSE-EINSTEIN CONDENSATE WITH PT-SYMMETRIC DOUBLE-DELTA FUNCTION LOSS AND GAIN IN A HARMONIC TRAP: A TEST OF RIGOROUS ESTIMATES
摘要： We consider the linear and nonlinear Schr?dinger equation for a Bose-Einstein condensate in a harmonic trap with PT -symmetric double-delta function loss and gain terms. We verify that the conditions for the applicability of a recent proposition by Mityagin and Siegl on singular perturbations of harmonic oscillator type self-adjoint operators are ful?lled. In both the linear and nonlinear case we calculate numerically the shifts of the unperturbed levels with quantum numbers n of up to 89 in dependence on the strength of the non-Hermiticity and compare with rigorous estimates derived by those authors. We con?rm that the predicted 1/n1/2 estimate provides a valid upper bound on the shrink rate of the numerical eigenvalues. Moreover, we ?nd that a more recent estimate of log(n)/n3/2 is in excellent agreement with the numerical results. With nonlinearity the shrink rates are found to be smaller than without nonlinearity, and the rigorous estimates, derived only for the linear case, are no longer applicable.
关键词： perturbed harmonic oscillator,PT symmetry,Bose-Einstein condensates
更新于2025-09-09 09:28:46
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Rotating Atomic Quantum Gases with Light-Induced Azimuthal Gauge Potentials and the Observation of the Hess-Fairbank Effect
摘要： We demonstrate synthetic azimuthal gauge potentials for Bose-Einstein condensates from engineering atom-light couplings. The gauge potential is created by adiabatically loading the condensate into the lowest energy Raman-dressed state, achieving a coreless vortex state. The azimuthal gauge potentials act as effective rotations and are tunable by the Raman coupling and detuning. We characterize the spin textures of the dressed states, in agreements with the theory. The lowest energy dressed state is stable with a 4.5-s half-atom-number-fraction lifetime. In addition, we exploit the azimuthal gauge potential to demonstrate the Hess-Fairbank effect, the analogue of Meissner effect in superconductors. The atoms in the absolute ground state has a zero quasiangular momentum and transits into a polar-core vortex when the synthetic magnetic flux is tuned to exceed a critical value. Our demonstration serves as a paradigm to create topological excitations by tailoring atom-light interactions where both types of SO(3) vortices in the jh ?Fij ? 1 manifold, coreless vortices and polar-core vortices, are created in our experiment. The gauge field in the stationary Hamiltonian opens a path to investigating rotation properties of atomic superfluids under thermal equilibrium.
关键词： synthetic gauge fields,Hess-Fairbank effect,Bose-Einstein condensates,azimuthal gauge potentials,topological excitations
更新于2025-09-04 15:30:14