Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0611146 · Physical Review A

Effect of interactions on the localization of a Bose-Einstein condensate in a quasiperiodic lattice

Jessica Lye, L. Fallani, C. Fort, Vera Guarrera, Michele Modugno, Diederik Sybolt Wiersma, M. Inguscio

Published Jun 14, 2007• 81 citations
arXivHTMLPDF

Abstract

The transport properties of a Bose-Einstein condensate in a 1D incommensurate bichromatic lattice are investigated both theoretically and experimentally. We observe a blockage of the center of mass motion with low atom number, and a return of motion when the atom number is increased. Solutions of the Gross-Pitaevskii equation show how the localization due to the quasidisorder introduced by the incommensurate bichromatic lattice is affected by the interactions.

DOI
10.1103/physreva.75.061603

Related papers

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

Sadhan K. Adhikari, Luca Salasnich

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC [Roati et al., Nature (London) 453, 895 (2008)], can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential [Billy et al., Nature (London) 453, 891 (2008)]. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms.

arXiv:0907.3498•Physical Review A•Aug 11, 2009•80 citations

Dimensional Reduction and Localization of a Bose-Einstein Condensate in a Quasi-1D Bichromatic Optical Lattice

Luca Salasnich, Sadhan K. Adhikari

We analyze the localization of a Bose-Einstein condensate in a one-dimensional bichromatic quasi-periodic optical-lattice potential by numerically solving the 1D Gross-Pitaevskii equation (1D GPE).We first derive the 1D Gross-Pitaevskii equation from the dimensional reduction of the 3D quantum field theory of interacting bosons obtaining two coupled differential equations (for axial wave fuction and space-time dependent transverse width) which reduce to the 1D Gross-Pitaevskii equation under strict conditions.Then, by using the 1D Gross-Pitaevskii equation we report the suppression of localization in the interacting Bose-Einstein condensate when the repulsive scattering length between bosonic atoms is sufficiently large.

arXiv:1511.02501•Acta Physica Polonica A•Dec 1, 2015•7 citations

Localization of a spin-orbit-coupled Bose-Einstein condensate in a bichromatic optical lattice

Yongshan Cheng, Gaohui Tang, Sadhan K. Adhikari

We study the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) with spin-orbit coupling loaded in a quasiperiodic bichromatic optical lattice potential using the numerical solution and variational approximation of a binary mean-field Gross-Pitaevskii equation with two pseudospin components. We confirm the existence of the stationary localized states in the presence of the spin-orbit and Rabi couplings for an equal distribution of atoms in the two components. We find that the interaction between the spin-orbit and Rabi couplings favors the localization or delocalization of the BEC depending on the phase difference between the components. We also studied the oscillation dynamics of the localized states for an initial population imbalance between the two components.

arXiv:1404.4017•Physical Review A•Jun 3, 2014•67 citations

Localization of a Bose-Einstein-condensate vortex in a bichromatic optical lattice

Sadhan K. Adhikari

By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasiperiodic optical-lattice (OL) potential generated by the superposition of two standing-wave polarized laser beams with incommensurate wavelengths. We also study the localization of a (nonrotating) BEC in two and three dimensions by bichromatic OL potentials along orthogonal directions. This is a generalization of the localization of a BEC in a one-dimensional bichromatic OL as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We demonstrate the stability of the localized state by considering its time evolution in the form of a stable breathing oscillation in a slightly altered potential for a large period of time. Finally, we consider the localization of a BEC in a random one-dimensional potential in the form of several identical repulsive spikes arbitrarily distributed in space.

arXiv:1003.6047•Physical Review A•Apr 29, 2010•40 citations

Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice

Yongshan Cheng, Sadhan K. Adhikari

By direct numerical simulation and variational solution of the Gross-Pitaevskii equation, we studied the stationary and dynamic characteristics of a cigar-shaped, localized, collisionally inhomogeneous Bose-Einstein condensate trapped in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a Bose-Einstein condensate [Roati et al., Nature (London) 453, 895 (2008)]. The effective potential characterizing the spatially modulated nonlinearity is obtained. It is found that the collisional inhomogeneity has influence not only on the central region but also on the tail of the Bose-Einstein condensate. The influence depends on the sign and value of the spatially modulated nonlinearity coefficient. We also demonstrate the stability of the stationary localized state by performing a standard linear stability analysis. Where possible, the numerical results are shown to be in good agreement with the variational results.

arXiv:1101.3972•Physical Review A•Feb 28, 2011•23 citations

Bose-Einstein condensates in quasiperiodic lattices: Bosonic Josephson junction, self-trapping, and multimode dynamics

Henrique C. Prates, Dmitry A. Zezyulin, V. V. Konotop

A Bose-Einstein condensate loaded in a one-dimensional bichromatic optical lattice with constituent sublattices having incommensurate periods is considered. Using the rational approximations for the incommensurate periods, we show that below the mobility edge the localized states are distributed nearly homogeneously in the space and explore the versatility of such potentials. We show that superposition of symmetric and antisymmetric localized states can be used to simulate various physical dynamical regimes, known to occur in double-well and multiwell traps. As examples, we obtain an alternative realization of a bosonic Josephson junction, whose coherent oscillations display beatings or switching in the weakly nonlinear regime, and describe self-trapping and four-mode dynamics, mimicking coherent oscillations and self-trapping in four-well potentials. These phenomena can be observed for different pairs of modes, which are localized due to the interference rather than due to a confining trap. The results obtained using few-mode approximations are compared with the direct numerical simulations of the one-dimensional Gross-Pitaevskii equation. The localized states and the related dynamics are found to persist for long times even in the repulsive condensates. We also described bifurcations of the families of nonlinear modes, the symmetry breaking, and stable minigap solitons.

arXiv:2208.10376•Physical Review Research•Sep 19, 2022•17 citations
The transport properties of a Bose-Einstein condensate in a 1D incommensurate bichromatic lattice are investigated both theoretically and experimentally. We observe a blockage of the center of mass motion with low atom number, and a return of motion when the atom number is increased. Solutions of the Gross-Pitaevskii equation show how the localization due to the quasidisorder introduced by the incommensurate bichromatic lattice is affected by the interactions.
By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC [Roati et al., Nature (London) 453, 895 (2008)], can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential [Billy et al., Nature (London) 453, 891 (2008)]. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms.
We analyze the localization of a Bose-Einstein condensate in a one-dimensional bichromatic quasi-periodic optical-lattice potential by numerically solving the 1D Gross-Pitaevskii equation (1D GPE).We first derive the 1D Gross-Pitaevskii equation from the dimensional reduction of the 3D quantum field theory of interacting bosons obtaining two coupled differential equations (for axial wave fuction and space-time dependent transverse width) which reduce to the 1D Gross-Pitaevskii equation under strict conditions.Then, by using the 1D Gross-Pitaevskii equation we report the suppression of localization in the interacting Bose-Einstein condensate when the repulsive scattering length between bosonic atoms is sufficiently large.
We study the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) with spin-orbit coupling loaded in a quasiperiodic bichromatic optical lattice potential using the numerical solution and variational approximation of a binary mean-field Gross-Pitaevskii equation with two pseudospin components. We confirm the existence of the stationary localized states in the presence of the spin-orbit and Rabi couplings for an equal distribution of atoms in the two components. We find that the interaction between the spin-orbit and Rabi couplings favors the localization or delocalization of the BEC depending on the phase difference between the components. We also studied the oscillation dynamics of the localized states for an initial population imbalance between the two components.
By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasiperiodic optical-lattice (OL) potential generated by the superposition of two standing-wave polarized laser beams with incommensurate wavelengths. We also study the localization of a (nonrotating) BEC in two and three dimensions by bichromatic OL potentials along orthogonal directions. This is a generalization of the localization of a BEC in a one-dimensional bichromatic OL as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We demonstrate the stability of the localized state by considering its time evolution in the form of a stable breathing oscillation in a slightly altered potential for a large period of time. Finally, we consider the localization of a BEC in a random one-dimensional potential in the form of several identical repulsive spikes arbitrarily distributed in space.
By direct numerical simulation and variational solution of the Gross-Pitaevskii equation, we studied the stationary and dynamic characteristics of a cigar-shaped, localized, collisionally inhomogeneous Bose-Einstein condensate trapped in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a Bose-Einstein condensate [Roati et al., Nature (London) 453, 895 (2008)]. The effective potential characterizing the spatially modulated nonlinearity is obtained. It is found that the collisional inhomogeneity has influence not only on the central region but also on the tail of the Bose-Einstein condensate. The influence depends on the sign and value of the spatially modulated nonlinearity coefficient. We also demonstrate the stability of the stationary localized state by performing a standard linear stability analysis. Where possible, the numerical results are shown to be in good agreement with the variational results.
A Bose-Einstein condensate loaded in a one-dimensional bichromatic optical lattice with constituent sublattices having incommensurate periods is considered. Using the rational approximations for the incommensurate periods, we show that below the mobility edge the localized states are distributed nearly homogeneously in the space and explore the versatility of such potentials. We show that superposition of symmetric and antisymmetric localized states can be used to simulate various physical dynamical regimes, known to occur in double-well and multiwell traps. As examples, we obtain an alternative realization of a bosonic Josephson junction, whose coherent oscillations display beatings or switching in the weakly nonlinear regime, and describe self-trapping and four-mode dynamics, mimicking coherent oscillations and self-trapping in four-well potentials. These phenomena can be observed for different pairs of modes, which are localized due to the interference rather than due to a confining trap. The results obtained using few-mode approximations are compared with the direct numerical simulations of the one-dimensional Gross-Pitaevskii equation. The localized states and the related dynamics are found to persist for long times even in the repulsive condensates. We also described bifurcations of the families of nonlinear modes, the symmetry breaking, and stable minigap solitons.