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/0311382 · Physical Review A

Spontaneous squeezing of a vortex in an optical lattice

J.-P. Martikainen, Henk T. C. Stoof

Published Jul 8, 2004• 11 citations
arXivHTMLPDF

Abstract

We study the equilibrium states of a vortex in a Bose-Einstein condensate in a one-dimensional optical lattice. We find that quantum effects can be important and that it is even possible for the vortex to be strongly squeezed, which reflects itself in a different quantum-mechanical uncertainty of the vortex position in two orthogonal directions. The latter is observable by measuring the atomic density after an expansion of the Bose-Einstein condensate in the lattice.

DOI
10.1103/physreva.70.013604

Related papers

Quantum theory of a vortex line in an optical lattice

J.-P. Martikainen, Henk T. C. Stoof

We investigate the quantum theory of a vortex line in a stack of weakly coupled two-dimensional Bose-Einstein condensates, that is created by a one-dimensional optical lattice. We derive the dispersion relation of the Kelvin modes of the vortex line and also study the coupling between the Kelvin and quadrupole modes. We solve the coupled dynamics of the vortex line and the quadrupole modes, both classically as well as quantum mechanically. The quantum mechanical solution reveals the possibility of generating nonequilibrium squeezed vortex states by strongly driving the quadrupole modes.

arXiv:cond-mat/0402052•Physical Review A•May 18, 2004•24 citations

Pinning of Vortices in a Bose-Einstein Condensate by an Optical Lattice

J. W. Reijnders, R. A. Duine

We consider the ground state of vortices in a Bose-Einstein condensate. We show that turning on a weak optical periodic potential leads to a transition from the triangular Abrikosov vortex lattice to phases where the vortices are pinned by the optical potential. We discuss the phase diagram of the system for a two-dimensional optical periodic potential with one vortex per optical lattice cell. We also discuss the influence of a one-dimensional optical periodic potential on the vortex ground state. The latter situation has no analog in other condensed-matter systems.

arXiv:cond-mat/0401583•Physical Review Letters•Aug 4, 2004•88 citations

Effect of soliton and vortex geometry on the transport of Bose-Einstein condensates in optical lattices

R. G. Scott, A. Martin, T. M. Fromhold

We investigate the effect of solitons and vortices, with a range of different topologies, on the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. The solitons and vortices are imposed on the initial state of the atom cloud, which is set in oscillatory motion by a sudden displacement of the harmonic trap. We study this motion using both quantum-mechanical calculations, based on the nonlinear Schr\"odinger equation, and a semiclassical model for transport through the lowest energy band of the optical lattice. We demonstrate that the geometry of the vortices and solitons in the initial state plays a crucial role in the evolution of the atom cloud. In particular, we find that the center-of-mass motion of a condensate containing a vortex is only weakly damped if the vortex core lies parallel to the optical lattice direction, but is strongly damped when the core is orientated perpendicular to the lattice direction. Severe damping is observed for a condensate containing a soliton whose nodal plane is perpendicular to the optical lattice.

Physical Review A•Jun 11, 2004•1 citation

Three-dimensional Bose—Einstein condensate vortex solitons under optical lattice and harmonic confinements

Ying Wang, Feng-De Zong, Feng-Bo Li

We predict three-dimensional vortex solitons in a Bose—Einstein condensate under a complex potential, which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction. The vortex solitons are built in the form of a layer-chain structure made of several fundamental vortices along the optical-lattice direction. This has not been reported before in the three-dimensional Bose—Einstein condensate. By using a combination of the energy density functional method with direct numerical simulation, we find three-dimensional vortex solitons with topological charges χ = 1, χ = 2, and χ = 3. Moreover, the macroscopic quantum tunneling and chirp phenomena of the vortex solitons are shown in the evolution. Therein, the occurrence of macroscopic quantum tunneling provides the possibility for the experimental realization of quantum tunneling. Specifically, we successfully manipulate the vortex solitons along the optical lattice direction. The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.

Chinese Physics B•Mar 1, 2013•3 citations

Theory of vortex-lattice melting in a one-dimensional optical lattice

Michiel Snoek, Henk T. C. Stoof

We investigate quantum and temperature fluctuations of a vortex lattice in a one-dimensional optical lattice. We discuss in particular the Bloch bands of the Tkachenko modes and calculate the correlation function of the vortex positions along the direction of the optical lattice. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Moreover, the fluctuations in the vortex positions are inhomogeneous due to the inhomogeneous density. As a result, the melting of the lattice occurs from the outside inwards. However, tunneling between neighboring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations. On the other hand, nonzero temperatures increase the size of the fluctuations dramatically. We calculate the crossover temperature from quantum melting to classical melting. We also investigate melting in the presence of a quartic radial potential, where a liquid can form in the center instead of at the outer edge of the pancake Bose-Einstein condensates.

arXiv:cond-mat/0605699•Physical Review A•Sep 21, 2006•14 citations

Vortex comb: Eliminating vortices from Bose-Einstein condensates using optical lattices

Shrohan Mohapatra, Andrew J. Schaffer, P. G. Kevrekidis +2 more

In the present work we introduce and explore a technique for the efficient removal of vortices from an atomic Bose-Einstein condensate, through the application and subsequent removal of a one-dimensional optical lattice. We showcase a prototypical experimental realization of the technique that motivates a detailed theoretical study of vortex removal mechanisms. Through simulations of the condensate dynamics during application of the optical lattice, we also discover a vortex removal mechanism that arises in narrow, optical-lattice-induced atomic density channels for which the channel width is on the order of the nominal vortex core size and healing length. This mechanism involves the density profile typically associated with a vortex core spatially separating from the phase singularity associated with the vortex. By analyzing numerical experiments covering a wide range of variations of the optical lattice amplitude and fringe periodicity, we identify the existence of an optimal set of parameters that enables the efficient removal of all vortices from the condensate. This analysis paves the way for further studies aimed at understanding vortex dynamics in narrow channels, and adds to an experimental toolkit for working with vortices and controlling the dynamical states of condensates.

arXiv:2509.06364•Physical Review A•Jan 8, 2026•0 citations
We study the equilibrium states of a vortex in a Bose-Einstein condensate in a one-dimensional optical lattice. We find that quantum effects can be important and that it is even possible for the vortex to be strongly squeezed, which reflects itself in a different quantum-mechanical uncertainty of the vortex position in two orthogonal directions. The latter is observable by measuring the atomic density after an expansion of the Bose-Einstein condensate in the lattice.
We investigate the quantum theory of a vortex line in a stack of weakly coupled two-dimensional Bose-Einstein condensates, that is created by a one-dimensional optical lattice. We derive the dispersion relation of the Kelvin modes of the vortex line and also study the coupling between the Kelvin and quadrupole modes. We solve the coupled dynamics of the vortex line and the quadrupole modes, both classically as well as quantum mechanically. The quantum mechanical solution reveals the possibility of generating nonequilibrium squeezed vortex states by strongly driving the quadrupole modes.
We consider the ground state of vortices in a Bose-Einstein condensate. We show that turning on a weak optical periodic potential leads to a transition from the triangular Abrikosov vortex lattice to phases where the vortices are pinned by the optical potential. We discuss the phase diagram of the system for a two-dimensional optical periodic potential with one vortex per optical lattice cell. We also discuss the influence of a one-dimensional optical periodic potential on the vortex ground state. The latter situation has no analog in other condensed-matter systems.
We investigate the effect of solitons and vortices, with a range of different topologies, on the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. The solitons and vortices are imposed on the initial state of the atom cloud, which is set in oscillatory motion by a sudden displacement of the harmonic trap. We study this motion using both quantum-mechanical calculations, based on the nonlinear Schr\"odinger equation, and a semiclassical model for transport through the lowest energy band of the optical lattice. We demonstrate that the geometry of the vortices and solitons in the initial state plays a crucial role in the evolution of the atom cloud. In particular, we find that the center-of-mass motion of a condensate containing a vortex is only weakly damped if the vortex core lies parallel to the optical lattice direction, but is strongly damped when the core is orientated perpendicular to the lattice direction. Severe damping is observed for a condensate containing a soliton whose nodal plane is perpendicular to the optical lattice.
We predict three-dimensional vortex solitons in a Bose—Einstein condensate under a complex potential, which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction. The vortex solitons are built in the form of a layer-chain structure made of several fundamental vortices along the optical-lattice direction. This has not been reported before in the three-dimensional Bose—Einstein condensate. By using a combination of the energy density functional method with direct numerical simulation, we find three-dimensional vortex solitons with topological charges χ = 1, χ = 2, and χ = 3. Moreover, the macroscopic quantum tunneling and chirp phenomena of the vortex solitons are shown in the evolution. Therein, the occurrence of macroscopic quantum tunneling provides the possibility for the experimental realization of quantum tunneling. Specifically, we successfully manipulate the vortex solitons along the optical lattice direction. The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.
We investigate quantum and temperature fluctuations of a vortex lattice in a one-dimensional optical lattice. We discuss in particular the Bloch bands of the Tkachenko modes and calculate the correlation function of the vortex positions along the direction of the optical lattice. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Moreover, the fluctuations in the vortex positions are inhomogeneous due to the inhomogeneous density. As a result, the melting of the lattice occurs from the outside inwards. However, tunneling between neighboring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations. On the other hand, nonzero temperatures increase the size of the fluctuations dramatically. We calculate the crossover temperature from quantum melting to classical melting. We also investigate melting in the presence of a quartic radial potential, where a liquid can form in the center instead of at the outer edge of the pancake Bose-Einstein condensates.
In the present work we introduce and explore a technique for the efficient removal of vortices from an atomic Bose-Einstein condensate, through the application and subsequent removal of a one-dimensional optical lattice. We showcase a prototypical experimental realization of the technique that motivates a detailed theoretical study of vortex removal mechanisms. Through simulations of the condensate dynamics during application of the optical lattice, we also discover a vortex removal mechanism that arises in narrow, optical-lattice-induced atomic density channels for which the channel width is on the order of the nominal vortex core size and healing length. This mechanism involves the density profile typically associated with a vortex core spatially separating from the phase singularity associated with the vortex. By analyzing numerical experiments covering a wide range of variations of the optical lattice amplitude and fringe periodicity, we identify the existence of an optimal set of parameters that enables the efficient removal of all vortices from the condensate. This analysis paves the way for further studies aimed at understanding vortex dynamics in narrow channels, and adds to an experimental toolkit for working with vortices and controlling the dynamical states of condensates.