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:0901.1969 · Physical Review B

Hall effect in spinor condensates

Mathieu Taillefumier, E. K. Dahl, Arne Brataas, Walter Hofstetter

Published Jul 28, 2009• 4 citations
arXivHTMLPDF

Abstract

We consider a neutral spinor condensate moving in a periodic magnetic field. The spatially dependent magnetic field induces an effective spin-dependent Lorentz force, which in turn gives rise to a spin-dependent Hall effect. Simulations of the Gross-Pitaevskii equation quantify the Hall effect. We discuss possible experimental realizations.

DOI
10.1103/physrevb.80.020407

Related papers

Observation of a Geometric Hall Effect in a Spinor Bose-Einstein Condensate

Jae-yoon Choi, Seji Kang, Sang Won Seo +2 more

For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.

•Oct 1, 2013•1 citation

Observation of a Geometric Hall Effect in a Spinor Bose-Einstein Condensate with a Skyrmion Spin Texture

Jae-yoon Choi, Seji Kang, Sang Won Seo +2 more

For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.

arXiv:1310.0134•Physical Review Letters•Dec 10, 2013•37 citations

Spin Hall effect in a spinor dipolar Bose-Einstein condensate

T. Oshima, Yuki Kawaguchi

We theoretically show that the spin Hall effect arises in a Bose-Einstein condensate (BEC) of neutral atoms interacting via the magnetic dipole-dipole interactions (MDDIs). Since the MDDI couples the total spin angular momentum and the relative orbital angular momentum of two colliding atoms, it works as a spin-orbit coupling. Thus, when we prepare a BEC in a magnetic sublevel $m=0$, thermally and quantum-mechanically excited atoms in the $m=1$ and $\ensuremath{-}1$ states feel the Lorentz-like forces in the opposite directions. This is the origin for the emergence of the spin Hall effect. We define the mass-current and spin-current operators from the equations of continuity and calculate the spin Hall conductivity from the off-diagonal current-current correlation function within the Bogoliubov approximation. We find that the correction of the current operators due to the MDDI significantly contributes to the spin Hall conductivity. A possible experimental situation is also discussed.

arXiv:1603.03202•Physical Review A•May 5, 2016•13 citations

Bose-Einstein Condensates in Artificial Gauge Fields

Lindsay J. LeBlanc, Ian B. Spielman

Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.

Cambridge University Press eBooks•Oct 4, 2018•3 citations

Spin Hall Effects for Cold Atoms in a Light-Induced Gauge Potential

Shi-Liang Zhu, Hao Fu, Congjun Wu +2 more

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light-induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.

arXiv:cond-mat/0607127•Physical Review Letters•Dec 12, 2006•255 citations

Observation of Dipole-Induced Spin Texture in an Rb87 Bose-Einstein Condensate

Yujiro Eto, Hiroki Saito, Takuya Hirano

We report the formation of spin texture resulting from the magnetic dipole-dipole interaction in a spin-2 87Rb Bose-Einstein condensate. The spinor condensate is prepared in the transversely polarized spin state and the time evolution is observed under a magnetic field of 90 mG with a gradient of 3 mG/cm using Stern-Gerlach imaging. The experimental results are compared with numerical simulations of the Gross-Pitaevskii equation, which reveals that the observed spatial modulation of the longitudinal magnetization is due to the spin precession in an effective magnetic field produced by the dipole-dipole interaction. These results show that the dipole-dipole interaction has considerable effects even on spinor condensates of alkali metal atoms.

arXiv:1402.7071•Physical Review Letters•May 9, 2014•54 citations
We consider a neutral spinor condensate moving in a periodic magnetic field. The spatially dependent magnetic field induces an effective spin-dependent Lorentz force, which in turn gives rise to a spin-dependent Hall effect. Simulations of the Gross-Pitaevskii equation quantify the Hall effect. We discuss possible experimental realizations.
For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.
For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.
We theoretically show that the spin Hall effect arises in a Bose-Einstein condensate (BEC) of neutral atoms interacting via the magnetic dipole-dipole interactions (MDDIs). Since the MDDI couples the total spin angular momentum and the relative orbital angular momentum of two colliding atoms, it works as a spin-orbit coupling. Thus, when we prepare a BEC in a magnetic sublevel m=0m=0m=0, thermally and quantum-mechanically excited atoms in the m=1m=1m=1 and $\ensuremath{-}1$ states feel the Lorentz-like forces in the opposite directions. This is the origin for the emergence of the spin Hall effect. We define the mass-current and spin-current operators from the equations of continuity and calculate the spin Hall conductivity from the off-diagonal current-current correlation function within the Bogoliubov approximation. We find that the correction of the current operators due to the MDDI significantly contributes to the spin Hall conductivity. A possible experimental situation is also discussed.
Quantum mechanically, static or applied gauge fields manifest themselves by directly coupling to a system's phase. Artificial gauge field techniques manipulate the phase of a Bose-Einstein condensate's order parameter, yielding effects present in condensed matter systems subject to magnetic fields, electric fields, or spin-orbit coupling. In this chapter, we explore the impact of these artificial gauge fields on Bose- Einstein condensates and explain the consequences. Several analogues to traditional condensed matter systems are enabled by these techniques, including the Hall effect, superfluid vortex nucleation in systems with artificial magnetic fields, and magnetic-like phase transitions in systems with spin-orbit coupling. Introduction Since the first experiments with Bose-Einstein condensates (BECs), researchers have exploited the universality of physical laws to draw analogies between the behavior of ultracold quantum gases and systems ranging from material to astrophysical. These analogous situations are deliberately engineered, giving cold-atom “quantum simulators” [1] that exhibit behavior either observed or predicted in analogous quantum systems. Superfluidity was one of the first many-body quantum phenomena demonstrated in BECs. For example, several experiments showed superfluid behavior by rapidly rotating the condensates and observing the formation of vortices [2, 3, 4, 5] – quantized point-defects in the BEC's order parameter. In the rotating frame of these experiments, this nucleation of vortices could be understood as the consequence of an artificial magnetic field [6] that arises via the formal equivalence of the rotating-frame Coriolis force and the Lorentz force, which we describe in Section 15.4.1. Together with other measurements, these results proved to be in excellent agreement with the predictions of the Gross-Pitaevskii equation (GPE) [7], a decades-old idealization of superfluid helium. Buoyed by the prospect for studying magnetic field–driven strongly correlated systems using these nearly ideal quantum gases, proposals for alternate techniques to simulate gauge fields were developed. These methods primarily employ an internal state–selective atom–light coupling, where the photon momentum provides the forces necessary to mimic a Lorentz force [8, 9, 10, 11, 12, 13, 14, 15, 16]. The first demonstration of this type of technique used a spatially dependent Ramantransition scheme to effect a magnetic field [17], and experiments demonstrating artificial electric fields [18] and spin-orbit coupling [19, 20, 21, 22, 23, 24] soon followed.
We report the formation of spin texture resulting from the magnetic dipole-dipole interaction in a spin-2 87Rb Bose-Einstein condensate. The spinor condensate is prepared in the transversely polarized spin state and the time evolution is observed under a magnetic field of 90 mG with a gradient of 3 mG/cm using Stern-Gerlach imaging. The experimental results are compared with numerical simulations of the Gross-Pitaevskii equation, which reveals that the observed spatial modulation of the longitudinal magnetization is due to the spin precession in an effective magnetic field produced by the dipole-dipole interaction. These results show that the dipole-dipole interaction has considerable effects even on spinor condensates of alkali metal atoms.