We describe a variety of intriguing mode-coupling effects which can occur in a confined Bose–Einstein condensed system at finite temperature. These arise from strong interactions between a condensate fluctuation and resonances of the thermal cloud yielding strongly nonlinear behaviour. We show how these processes can be affected by altering the aspect ratio of the trap, thereby changing the relevant mode-matching conditions. We illustrate how direct driving of the thermal cloud can lead to significant shifts in the excitation spectrum for a number of modes and provide further experimental scenarios in which the dramatic behaviour observed for the m =0 mode at JILA can be repeated. Our theoretical description is based on a successful second-order finite-temperature quantum field theory which includes the full coupled dynamics of the condensate and thermal cloud and all relevant finite-size effects.We describe a variety of intriguing mode-coupling effects which can occur in a confined Bose–Einstein condensed system at finite temperature. These arise from strong interactions between a condensate fluctuation and resonances of the thermal cloud yielding strongly nonlinear behaviour. We show how these processes can be affected by altering the aspect ratio of the trap, thereby changing the relevant mode-matching conditions. We illustrate how direct driving of the thermal cloud can lead to significant shifts in the excitation spectrum for a number of modes and provide further experimental scenarios in which the dramatic behaviour observed for the m =0 mode at JILA can be repeated. Our theoretical description is based on a successful second-order finite-temperature quantum field theory which includes the full coupled dynamics of the condensate and thermal cloud and all relevant finite-size effects.

arXiv:cond-mat/0503561Proceedings of the Royal Society A Mathematical Physical and Engineering SciencesSep 15, 20053 citations

Three-Dimensional Nonlinear Dynamics of Cold Atoms in an Optical Lattice and its Realizations

Sergey V. Prants, Leonid E. Kon’kov, A. A. Didov

Journal of Russian Laser ResearchSep 1, 20211 citation

3D Nonlinear Localized Gap Modes in Bose‐Einstein Condensates Trapped by Optical Lattices and Space‐Periodic Nonlinear Potentials

Jiawei Li, Yanpeng Zhang, Jianhua Zeng

Optical lattices and Feshbach resonance management are two mighty and widely used techniques for studying, both experimentally and theoretically, various physical issues and the underlying nonlinear dynamics of Bose−Einstein condensates. Both techniques show great power for studying solitons of different types, and particularly, the former technique realizes the creation of 1D bright matter‐wave gap solitons, whose formation and properties in multidimensional systems, however, are much less known. Herein, both techniques and study are combined, theoretically and numerically, the formation and dynamics of 3D nonlinear localized gap modes, including fundamental gap solitons and their higher‐order ones as soliton clusters, as well as gap vortices with topological charge s = 1. The stability regions of all the localized gap modes are identified by means of direct perturbed numerical simulations, revealing important insights into soliton physics in multidimensional space.Optical lattices and Feshbach resonance management are two mighty and widely used techniques for studying, both experimentally and theoretically, various physical issues and the underlying nonlinear dynamics of Bose−Einstein condensates. Both techniques show great power for studying solitons of different types, and particularly, the former technique realizes the creation of 1D bright matter‐wave gap solitons, whose formation and properties in multidimensional systems, however, are much less known. Herein, both techniques and study are combined, theoretically and numerically, the formation and dynamics of 3D nonlinear localized gap modes, including fundamental gap solitons and their higher‐order ones as soliton clusters, as well as gap vortices with topological charge s = 1. The stability regions of all the localized gap modes are identified by means of direct perturbed numerical simulations, revealing important insights into soliton physics in multidimensional space.

Advanced Photonics ResearchFeb 20, 20228 citations

Localization of quantum particles with long-range hopping in 3D lattices of finite size

Joshua T. Cantin, Tianrui Xu, Roman V. Krems

Non-interacting particles with long-range hopping are known to be delocalized in disordered systems of infinite size. It is thus natural to assume that such particles can traverse any finite-size lattice. Here, we demonstrate that this is not generally true. The delocalization mechanism is induced by resonances between distant lattice sites. The number of such resonances diverges with the system size. For a finite-size lattice the number of resonances is finite and may not be sufficient to result in delocalization. We consider particles with long-range (dipolar) hopping in three-dimensional lattices with diagonal disorder and random dilution. We compute the wavepacket dynamics of particles placed in an individual lattice site, the inverse participation ratios and the fluctuations of the wavefunctions with disorder. We show that, for certain finite-size disordered lattices, particles remain localized within a finite volume much smaller than the lattice size, and that the wavefunctions exhibit the log-normal fluctuations characteristic of Anderson localization. We characterize the localization properties as functions of dilution and diagonal disorder. We combine our results with scaling theory to obtain the size dependence of the localization--diffusion crossover. Our results indicate that particles with long-range hopping undergo exponential localization in lattices of finite size, even macroscopically finite. Our phase diagrams illustrate a rather unusual phenomenon: quantum particles can diffuse through a lattice of size $10A$ , but not through a lattice of size $A$ .Non-interacting particles with long-range hopping are known to be delocalized in disordered systems of infinite size. It is thus natural to assume that such particles can traverse any finite-size lattice. Here, we demonstrate that this is not generally true. The delocalization mechanism is induced by resonances between distant lattice sites. The number of such resonances diverges with the system size. For a finite-size lattice the number of resonances is finite and may not be sufficient to result in delocalization. We consider particles with long-range (dipolar) hopping in three-dimensional lattices with diagonal disorder and random dilution. We compute the wavepacket dynamics of particles placed in an individual lattice site, the inverse participation ratios and the fluctuations of the wavefunctions with disorder. We show that, for certain finite-size disordered lattices, particles remain localized within a finite volume much smaller than the lattice size, and that the wavefunctions exhibit the log-normal fluctuations characteristic of Anderson localization. We characterize the localization properties as functions of dilution and diagonal disorder. We combine our results with scaling theory to obtain the size dependence of the localization--diffusion crossover. Our results indicate that particles with long-range hopping undergo exponential localization in lattices of finite size, even macroscopically finite. Our phase diagrams illustrate a rather unusual phenomenon: quantum particles can diffuse through a lattice of size $10A$, but not through a lattice of size $A$.

Apr 6, 20160 citations

Quantum nonlinear Schrödinger equation on a lattice

N. M. Bogoliubov, V. E. Korepin

Theoretical and Mathematical PhysicsMar 1, 19868 citations

10A

, but not through a lattice of size

A