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:1507.02932 · Physical Review A

Quantum Hall effect with small numbers of vortices in Bose-Einstein condensates

Tim Byrnes, Jonathan P. Dowling

Published Aug 20, 2015• 7 citations
arXivHTMLPDF

Abstract

When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of $2\ensuremath{\pi}$. In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of $m/2h$, where $m$ is the mass of the atoms and $h$ is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.

DOI
10.1103/physreva.92.023629

Related papers

Geometric phases of a vortex in a superfluid

Rodney Polkinghorne, Andrew J. Groszek, Tapio Simula

We consider geometric phases of mobile quantum vortices in superfluid Bose--Einstein condensates (BECs). Haldane and Wu [Phys. Rev. Lett. 55, 2887 (1985)] showed that the geometric phase, ${\ensuremath{\gamma}}_{\mathcal{C}}=2\ensuremath{\pi}{N}_{\mathcal{C}}$, of such a vortex is determined by the number of condensate atoms ${N}_{\mathcal{C}}$ enclosed by the vortex trajectory. Considering an experimentally realistic freely orbiting vortex leads to an apparent disagreement with this prediction. We resolve it using the superfluid electrodynamics picture, which allows us to identify two additional contributions to the measured geometric phase: (i) A topologically protected edge current of vortices at the condensate boundary and (ii) a superfluid displacement current. Our results generalize to and pave the way for experimental measurements of vortex geometric phases using scalar and spinor BECs and superfluid Fermi gases.

arXiv:2101.07438•Physical Review A•Oct 26, 2021•4 citations

Non topological vortices in a Bose-Einstein condensate

Q‐Han Park, Joseph H. Eberly

Summary form only given. Vortex in a BEC is a circular flow with a quantized angular momentum. In a two-component BEC, the internal phase space can be enlarged to two sphere so that non topological vortices carrying continuous angular momentum are possible. In this talk, we present a novel class of non topological vortices and describe their rich static and dynamical properties. Each components of these non topological vortices can possess rich spatial structures while their total intensities have simple radial profiles similar to those of conventional topological vortices. These vortices carry continuous angular momenta varying between two integer momentum numbers m and -m, whose physical meaning will be explained in the Poincare sphere picture Particularly, we show that external drive can be coupled easily to a non topological vortex and be used to steer a vortex which sets internal spinor motions. We also make an experimental suggestion for a method to create such nontopological vortices.

Quantum Electronics and Laser Science Conference•Jun 25, 2003•0 citations

Bose-Einstein Condensates with Large Number of Vortices

Tin-Lun Ho

We show that as the number of vortices in a three dimensional Bose-Einstein condensate increases, the system reaches a "quantum Hall" regime where the density profile is a Gaussian in the xy plane and an inverted parabolic profile along z. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.

arXiv:cond-mat/0104522•Physical Review Letters•Jul 23, 2001•268 citations

Quantized vortices in atomic Bose-Einstein condensates

Kenichi Kasamatsu, Makoto Tsubota

In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.

arXiv:0709.1042•Sep 7, 2007•15 citations

Berry Phase Effects on the Dynamics of Quasiparticles in a Superfluid with a Vortex

Chuanwei Zhang, Artem M. Dudarev, Qian Niu

We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms' momentum distribution around a vortex.

arXiv:cond-mat/0507125•Physical Review Letters•Jul 28, 2006•28 citations

Ground states and dynamics of rotating Bose-Einstein condensates

Weizhu Bao

Since its realization in dilute bosonic atomic gases [], [], Bose-Einstein condensation of alkali atoms and hydrogen has been produced and studied extensively in the laboratory [], and has permitted an intriguing glimpse into the macroscopic quantum world. In view of potential applications [], [], [], the study of quantized vortices, which are well-known signatures of superfluidity, is one of the key issues. In fact, bulk superfluids are distinguished from normal fluids by their ability to support dissipationless flow. Such persistent currents are intimately related to the existence of quantized vortices, which are localized phase singularities with integer topological charge []. The superfluid vortex is an example of a topological defect that is well known in superconductors [] and in liquid helium []. The occurrence of quantized vortices in superfluids has been the focus of fundamental theoretical and experimental work []. Different research groups have obtained quantized vortices in Bose-Einstein condensates (BECs) experimentally, e.g., the JILA group [], [], the ENS group [] and the MIT group [], []. Currently, there are at least two typical ways to generate quantized vortices from a BEC ground state: (i) impose a laser beam rotating with an angular velocity on the magnetic trap holding the atoms to create a harmonic anisotropic potential [], [], []; or (ii) add to the stationary magnetic trap a narrow, moving Gaussian potential, representing a far-blue detuned laser [], [], [], [], [], [].

Birkhäuser Boston eBooks•Dec 2, 2007•9 citations
When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ. In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of m/2hm/2hm/2h, where mmm is the mass of the atoms and hhh is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.
We consider geometric phases of mobile quantum vortices in superfluid Bose--Einstein condensates (BECs). Haldane and Wu [Phys. Rev. Lett. 55, 2887 (1985)] showed that the geometric phase, ${\ensuremath{\gamma}}_{\mathcal{C}}=2\ensuremath{\pi}{N}_{\mathcal{C}}$, of such a vortex is determined by the number of condensate atoms NC{N}_{\mathcal{C}}NC​ enclosed by the vortex trajectory. Considering an experimentally realistic freely orbiting vortex leads to an apparent disagreement with this prediction. We resolve it using the superfluid electrodynamics picture, which allows us to identify two additional contributions to the measured geometric phase: (i) A topologically protected edge current of vortices at the condensate boundary and (ii) a superfluid displacement current. Our results generalize to and pave the way for experimental measurements of vortex geometric phases using scalar and spinor BECs and superfluid Fermi gases.
Summary form only given. Vortex in a BEC is a circular flow with a quantized angular momentum. In a two-component BEC, the internal phase space can be enlarged to two sphere so that non topological vortices carrying continuous angular momentum are possible. In this talk, we present a novel class of non topological vortices and describe their rich static and dynamical properties. Each components of these non topological vortices can possess rich spatial structures while their total intensities have simple radial profiles similar to those of conventional topological vortices. These vortices carry continuous angular momenta varying between two integer momentum numbers m and -m, whose physical meaning will be explained in the Poincare sphere picture Particularly, we show that external drive can be coupled easily to a non topological vortex and be used to steer a vortex which sets internal spinor motions. We also make an experimental suggestion for a method to create such nontopological vortices.
We show that as the number of vortices in a three dimensional Bose-Einstein condensate increases, the system reaches a "quantum Hall" regime where the density profile is a Gaussian in the xy plane and an inverted parabolic profile along z. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.
In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.
We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms' momentum distribution around a vortex.
Since its realization in dilute bosonic atomic gases [], [], Bose-Einstein condensation of alkali atoms and hydrogen has been produced and studied extensively in the laboratory [], and has permitted an intriguing glimpse into the macroscopic quantum world. In view of potential applications [], [], [], the study of quantized vortices, which are well-known signatures of superfluidity, is one of the key issues. In fact, bulk superfluids are distinguished from normal fluids by their ability to support dissipationless flow. Such persistent currents are intimately related to the existence of quantized vortices, which are localized phase singularities with integer topological charge []. The superfluid vortex is an example of a topological defect that is well known in superconductors [] and in liquid helium []. The occurrence of quantized vortices in superfluids has been the focus of fundamental theoretical and experimental work []. Different research groups have obtained quantized vortices in Bose-Einstein condensates (BECs) experimentally, e.g., the JILA group [], [], the ENS group [] and the MIT group [], []. Currently, there are at least two typical ways to generate quantized vortices from a BEC ground state: (i) impose a laser beam rotating with an angular velocity on the magnetic trap holding the atoms to create a harmonic anisotropic potential [], [], []; or (ii) add to the stationary magnetic trap a narrow, moving Gaussian potential, representing a far-blue detuned laser [], [], [], [], [], [].