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

Chinese Physics Letters

Evolution of Matter Wave Interference of Bose-Condensed Gas in a 1D Optical Lattice

Xu Zhi-Jun, Dongmei Zhang

Published Aug 23, 2007• 0 citations
Publisher

Abstract

For a Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattice, using the mean-field Gross–Pitaevskii (G-P) equation and the propagator method, we obtain the analytical result of the order parameter for matter wave interference at any time. The evolution of the interference pattern under a variation of the relative phase Δϕ between successive subcondensates trapped on an optical lattices is also studied. For Δϕ = π, the interference pattern is symmetric with two sharp peaks, which are symmetrically located on a straight line on both sides of a vacant central peak and moving apart from each other. This work is in agreement with available experimental results.

DOI
10.1088/0256-307x/24/9/009

Related papers

Interference of Bose-condensed gas in a 1D optical lattice

Xu Zhi-Jun, Dongmei Wang, Li Zhen +1 more

For the Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattice, using the mean-field Gross-Pitaevskii (G-P) equation and the propagator method, we study the formation of matter-wave interference upon releasing the condensate from the combined potential. The analytical result of the wave function for matter wave interference at any time t is given, and the relation between the interference fringe period and the optical lattice period is obtained. The interference pattern of Bose-condensed gas in the optical lattices is analogous to the multiple slit interference pattern in optics, and coincides with the results of experiment performed by Andrews et al. and Peil et al. and the numerical solution of the G-P equation by Sadhan K. Adhikari.

Acta Physica Sinica•Jan 1, 2007•3 citations

Evolution of Matter Wave Interference of Bose-Condensed Gas in a 2D Optical Lattice

Xu Zhi-Jun, Guo-Cheng Lin, Jun Xu +1 more

We investigate the average particle-number distribution of the atoms in the combined potential of 2D optical lattices and 3D harmonic magnetic trap based on the Gross–Pitaevskii equation. After the combined potential is switched off, and only the optical lattice is switched off, we give the analytical results of the wavefunction of the Bose-condensed gas at any time t by using a propagator method. For both disk-shaped and cigar-shaped Bose-condensed gas, we discuss the evolution process of the central and side peaks of the interference pattern.

Communications in Theoretical Physics•Jul 1, 2005•2 citations

Interference patterns of Bose-condensed gases in a two-dimensional optical lattice

Shujuan Liu, Hongwei Xiong, Xu Zhi-Jun +1 more

For the Bose-condensed gas confined in a magnetic trap and in a two-dimensional optical lattice, the non-uniform distribution of atoms in different lattice sites is considered based on Gross-Pitaevskii equation. A propagator method is used to investigate the time evolution of 2D interference patterns after (i)only the optical lattice is swithed off, and (ii)both the optical lattice and the magnetic trap are swithed off. An analytical description on the motion of side peaks in the interference patterns is presented by using the density distribution in a momentum space.

arXiv:cond-mat/0211628•Journal of Physics B Atomic Molecular and Optical Physics•May 7, 2003•26 citations

The groud-state wave function and evolution of the interference pattern for a Bose-condensed gas in 3D optical lattices

Xu Zhi-Jun, Cheng Cheng, Yang Huan-Song +3 more

Based on the Gross-Pitaevskii equation and by using the effective chemical poten tial,we study the distribution of the Bose-condensed gas in the combined potenti als (magnetic trap and three-dimensional optical lattices).The normalized ground-state wave function is given from the distribution of the Bose-condensed gas.The analytical expression of the density distribution of the Bose-condensed gas is given by using the propagator method when the combined potentials and only the optical lattices are switched off,respectively.When the combined potentials are switched off,the theoretical results of this work agree well with the experiment by Greiner et al.When only the optical lattices are switched off,it is show n that the interference pattern will oscillate in the magnetic trap.In addition,the evolution of the interference pattern is also investigated in the case of an isotropic magnetic trap.

Acta Physica Sinica•Jan 1, 2004•8 citations

Second interference and amplification effect of a Bose-condensed gas

Xu Zhi-Jun, Penghua Li, 浙江工业大学应用物理系,杭州 320032

For a Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattices, the motional interference side peaks along the axis direction are formed after the combined potential is switched off. Based on this physical system, we make a new experimental suggestion which can be realized with current experimental technique to investigate the side peak superposition and discuss the second interference and amplification effect of a Bose condensate. In the region where the side peaks undergo constructive interference, the density of condensed atomic cloud will be amplified effectively.

Acta Physica Sinica•Jan 1, 2007•1 citation

Mean-field model for matter-wave interference from an one-dimensional optical trap

Sadhan K. Adhikari

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti {\it et al.} on atomic Josephson oscillation [Science {\bf 293}, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement with the more recent experiment by Cataliotti {\it et al.} [e-print cond-mat/0207139].

•Aug 14, 2002•0 citations
For a Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattice, using the mean-field Gross–Pitaevskii (G-P) equation and the propagator method, we obtain the analytical result of the order parameter for matter wave interference at any time. The evolution of the interference pattern under a variation of the relative phase Δϕ between successive subcondensates trapped on an optical lattices is also studied. For Δϕ = π, the interference pattern is symmetric with two sharp peaks, which are symmetrically located on a straight line on both sides of a vacant central peak and moving apart from each other. This work is in agreement with available experimental results.
For the Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattice, using the mean-field Gross-Pitaevskii (G-P) equation and the propagator method, we study the formation of matter-wave interference upon releasing the condensate from the combined potential. The analytical result of the wave function for matter wave interference at any time t is given, and the relation between the interference fringe period and the optical lattice period is obtained. The interference pattern of Bose-condensed gas in the optical lattices is analogous to the multiple slit interference pattern in optics, and coincides with the results of experiment performed by Andrews et al. and Peil et al. and the numerical solution of the G-P equation by Sadhan K. Adhikari.
We investigate the average particle-number distribution of the atoms in the combined potential of 2D optical lattices and 3D harmonic magnetic trap based on the Gross–Pitaevskii equation. After the combined potential is switched off, and only the optical lattice is switched off, we give the analytical results of the wavefunction of the Bose-condensed gas at any time t by using a propagator method. For both disk-shaped and cigar-shaped Bose-condensed gas, we discuss the evolution process of the central and side peaks of the interference pattern.
For the Bose-condensed gas confined in a magnetic trap and in a two-dimensional optical lattice, the non-uniform distribution of atoms in different lattice sites is considered based on Gross-Pitaevskii equation. A propagator method is used to investigate the time evolution of 2D interference patterns after (i)only the optical lattice is swithed off, and (ii)both the optical lattice and the magnetic trap are swithed off. An analytical description on the motion of side peaks in the interference patterns is presented by using the density distribution in a momentum space.
Based on the Gross-Pitaevskii equation and by using the effective chemical poten tial,we study the distribution of the Bose-condensed gas in the combined potenti als (magnetic trap and three-dimensional optical lattices).The normalized ground-state wave function is given from the distribution of the Bose-condensed gas.The analytical expression of the density distribution of the Bose-condensed gas is given by using the propagator method when the combined potentials and only the optical lattices are switched off,respectively.When the combined potentials are switched off,the theoretical results of this work agree well with the experiment by Greiner et al.When only the optical lattices are switched off,it is show n that the interference pattern will oscillate in the magnetic trap.In addition,the evolution of the interference pattern is also investigated in the case of an isotropic magnetic trap.
For a Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattices, the motional interference side peaks along the axis direction are formed after the combined potential is switched off. Based on this physical system, we make a new experimental suggestion which can be realized with current experimental technique to investigate the side peak superposition and discuss the second interference and amplification effect of a Bose condensate. In the region where the side peaks undergo constructive interference, the density of condensed atomic cloud will be amplified effectively.
Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti {\it et al.} on atomic Josephson oscillation [Science {\bf 293}, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement with the more recent experiment by Cataliotti {\it et al.} [e-print cond-mat/0207139].