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:1603.03202 · Physical Review A

Spin Hall effect in a spinor dipolar Bose-Einstein condensate

T. Oshima, Yuki Kawaguchi

Published May 5, 2016• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.93.053605

Related papers

Spontaneous magnetic ordering in a ferromagnetic spinor dipolar Bose-Einstein condensate

Yuki Kawaguchi, Hiroki Saito, Kazue Kudo +1 more

We study the spin dynamics of a spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction (MDDI) based on the Gross-Pitaevskii and Bogoliubov theories. We find that various magnetic structures such as checkerboards and stripes emerge in the course of the dynamics due to the combined effects of spin-exchange interaction, MDDI, quadratic Zeeman and finite-size effects, and nonstationary initial conditions. However, the short-range magnetic order observed by the Berkeley group [Phys. Rev. Lett. 100, 170403 (2008)] is not fully reproduced in our calculations; the periodicity of the order differs by a factor of 3 and the checkerboard pattern eventually dissolves in the course of time. Possible reasons for the discrepancy are discussed.

arXiv:0909.0565•Physical Review A•Oct 27, 2010•37 citations

Spinor-Dipolar Aspects of Bose-Einstein Condensation

Masahito Ueda

Selected topics on spinor-dipolar aspects of Bose-Einstein condensation are overviewed. Spinor aspects include spin correlations, fragmentation, dynamical symmetries, and quantum mass acquisition. Dipolar aspects include magnetostriction, d-wave collapse, roton-maxon spectrum, supersolidity, and ferrofluidity. Finally, spinor-dipolar aspects concern the Einstein–de Haas effect and spontaneous mass and spin currents in the ground state. Introduction Bose-Einstein condensation is a phenomenon in which a macroscopic number of particles occupy the same single-particle state as a consequence of symmetrization of a many-body wave function and thereby quantum effects are amplified to the macroscopic level. The amplified single-particle state serves as a complex order parameter whose phase behaves as an emergent thermodynamic quantity, with its temporal and spatial variations giving the chemical potential and the superfluid velocity, respectively. If the interparticle interaction is repulsive, a Bose-Einstein condensate (BEC) acquires stability against excitations out of the condensate because they would cost the Fock exchange energy. This rigidity of the order parameter or the condensate wave function endows a BEC with several remarkable transport properties which are collectively known as superfluidity. In particular, the superfluid fraction can be 100% at zero temperature even though the condensate fraction is depleted due to interparticle interactions. Interparticle interactions also make excited particles phase-locked to the condensate, leading to Bogoliubov quasiparticles, which are the manifestation of phase-coherent particle– hole excitations. When constituent particles have spin degrees of freedom, a BEC features magnetism and spin nematicity which conspire with superfluidity to produce a rich phase diagram. In the absence of an external magnetic field, the mean-field groundstate phase diagram includes two [1, 2], five [3, 4, 5], and eleven phases [6, 7] for spin-1, 2, and 3 BECs, respectively. BECs with spin degrees of freedom are called spinor condensates. Moreover, the magnetic dipole–dipole interaction (MDDI) between atoms lends distinct twists to spinor condensates because it is long-ranged and anisotropic in sharp contrast with other interactions, which are short-ranged and isotropic. In this chapter, we will present a brief overview on the spinordipolar aspects of BEC. An early experimental work of spinor BECs is reviewed in Ref. [8]. Later developments with an emphasis on theoretical aspects are described in Ref. [9]. Many-body physics of polarized dipolar gases is reviewed in Ref. [10].

Cambridge University Press eBooks•Oct 4, 2018•0 citations

Spinor Dipolar Bose-Einstein Condensates: Classical Spin Approach

Masahiro O. Takahashi, Sankalpa Ghosh, Takeshi Mizushima +1 more

Bose-Einstein condensates which are dominated by magnetic dipole-dipole interaction are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from the large spin limit to obtain an effective minimal Hamiltonian. This is a version extended from a nonlinear sigma model. By solving the Gross-Pitaevskii equation, we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.

arXiv:0704.0122•Physical Review Letters•Jun 25, 2007•38 citations

Can Spinor Dipolar Effects Be Observed in Bose-Einstein Condensates?

Yuki Kawaguchi, Hiroki Saito, Masahito Ueda

Weak dipolar effects in atomic Bose-Einstein condensates (BECs) have recently been predicted to develop spin textures. However, observation of the spin textures requires us to decrease the magnetic field down to approximately 10 microG for spin-1 alkali BECs, so that they are not washed out by the Zeeman effect. We present a scheme to observe the magnetic dipole-dipole interaction in alkali BECs under a realistic magnetic field of approximately 100 mG. Our scheme enables us to extract genuine dipolar effects and should apply also to (52)Cr BECs.

arXiv:cond-mat/0611131•Physical Review Letters•Mar 14, 2007•68 citations

Effects of magnetic dipole-dipole interactions in atomic Bose-Einstein condensates with tunable s -wave interactions

Abraham J. Olson, Daniel Whitenack, Yong P. Chen

The $s$-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the $s$-wave interaction in many atomic species. This opens the possibilities to study magnetic dipole-dipole interactions (MDDIs) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDIs on the statics and dynamics of atomic BECs with tunable $s$-wave interactions for a variety of species, including both nonalkali metals with large magnetic dipole moments (${}^{52}$Cr, ${}^{164}$Dy, ${}^{168}$Er) and alkali metals (with much smaller magnetic dipole moments). A parameter of magnetic Feshbach resonances, ${\ensuremath{\epsilon}}_{dd,\text{max}}$, is used to quantitatively indicate the feasibility of experimentally observing MDDI effects in different atomic species. We find that strong MDDI effects should be observable in both in-trap and time-of-flight behaviors, not only for the strongly magnetic dipolar species but also for the alkali-metal BECs of ${}^{7}$Li, ${}^{39}$K, and ${}^{133}$Cs. In addition, we predict several effects which should be experimentally observable. Our results provide a helpful guide for experimentalists to realize and study atomic dipolar quantum gases.

arXiv:1204.1510•Physical Review A•Oct 8, 2013•28 citations

Symmetry-breaking magnetization dynamics of spinor dipolar Bose-Einstein condensates

Shoichi Hoshi, Hiroki Saito

The symmetry-breaking magnetization dynamics of a spin-1 Bose-Einstein condensate (BEC) due to the dipole-dipole interaction are investigated using the mean-field and Bogoliubov theories. When a magnetic field is applied along the symmetry axis of a pancake-shaped BEC in the $m=0$ hyperfine sublevel, transverse magnetization develops breaking the chiral or axial symmetry. A variety of magnetization patterns are formed depending on the strength of the applied magnetic field. The proposed phenomena can be observed in $^{87}\mathrm{Rb}$ and $^{23}\mathrm{Na}$ condensates.

arXiv:0911.2741•Physical Review A•Jan 27, 2010•12 citations
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\ensuremath{-}1\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.
We study the spin dynamics of a spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interaction (MDDI) based on the Gross-Pitaevskii and Bogoliubov theories. We find that various magnetic structures such as checkerboards and stripes emerge in the course of the dynamics due to the combined effects of spin-exchange interaction, MDDI, quadratic Zeeman and finite-size effects, and nonstationary initial conditions. However, the short-range magnetic order observed by the Berkeley group [Phys. Rev. Lett. 100, 170403 (2008)] is not fully reproduced in our calculations; the periodicity of the order differs by a factor of 3 and the checkerboard pattern eventually dissolves in the course of time. Possible reasons for the discrepancy are discussed.
Selected topics on spinor-dipolar aspects of Bose-Einstein condensation are overviewed. Spinor aspects include spin correlations, fragmentation, dynamical symmetries, and quantum mass acquisition. Dipolar aspects include magnetostriction, d-wave collapse, roton-maxon spectrum, supersolidity, and ferrofluidity. Finally, spinor-dipolar aspects concern the Einstein–de Haas effect and spontaneous mass and spin currents in the ground state. Introduction Bose-Einstein condensation is a phenomenon in which a macroscopic number of particles occupy the same single-particle state as a consequence of symmetrization of a many-body wave function and thereby quantum effects are amplified to the macroscopic level. The amplified single-particle state serves as a complex order parameter whose phase behaves as an emergent thermodynamic quantity, with its temporal and spatial variations giving the chemical potential and the superfluid velocity, respectively. If the interparticle interaction is repulsive, a Bose-Einstein condensate (BEC) acquires stability against excitations out of the condensate because they would cost the Fock exchange energy. This rigidity of the order parameter or the condensate wave function endows a BEC with several remarkable transport properties which are collectively known as superfluidity. In particular, the superfluid fraction can be 100% at zero temperature even though the condensate fraction is depleted due to interparticle interactions. Interparticle interactions also make excited particles phase-locked to the condensate, leading to Bogoliubov quasiparticles, which are the manifestation of phase-coherent particle– hole excitations. When constituent particles have spin degrees of freedom, a BEC features magnetism and spin nematicity which conspire with superfluidity to produce a rich phase diagram. In the absence of an external magnetic field, the mean-field groundstate phase diagram includes two [1, 2], five [3, 4, 5], and eleven phases [6, 7] for spin-1, 2, and 3 BECs, respectively. BECs with spin degrees of freedom are called spinor condensates. Moreover, the magnetic dipole–dipole interaction (MDDI) between atoms lends distinct twists to spinor condensates because it is long-ranged and anisotropic in sharp contrast with other interactions, which are short-ranged and isotropic. In this chapter, we will present a brief overview on the spinordipolar aspects of BEC. An early experimental work of spinor BECs is reviewed in Ref. [8]. Later developments with an emphasis on theoretical aspects are described in Ref. [9]. Many-body physics of polarized dipolar gases is reviewed in Ref. [10].
Bose-Einstein condensates which are dominated by magnetic dipole-dipole interaction are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from the large spin limit to obtain an effective minimal Hamiltonian. This is a version extended from a nonlinear sigma model. By solving the Gross-Pitaevskii equation, we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.
Weak dipolar effects in atomic Bose-Einstein condensates (BECs) have recently been predicted to develop spin textures. However, observation of the spin textures requires us to decrease the magnetic field down to approximately 10 microG for spin-1 alkali BECs, so that they are not washed out by the Zeeman effect. We present a scheme to observe the magnetic dipole-dipole interaction in alkali BECs under a realistic magnetic field of approximately 100 mG. Our scheme enables us to extract genuine dipolar effects and should apply also to (52)Cr BECs.
The sss-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the sss-wave interaction in many atomic species. This opens the possibilities to study magnetic dipole-dipole interactions (MDDIs) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDIs on the statics and dynamics of atomic BECs with tunable sss-wave interactions for a variety of species, including both nonalkali metals with large magnetic dipole moments (52{}^{52}52Cr, 164{}^{164}164Dy, 168{}^{168}168Er) and alkali metals (with much smaller magnetic dipole moments). A parameter of magnetic Feshbach resonances, ${\ensuremath{\epsilon}}_{dd,\text{max}}$, is used to quantitatively indicate the feasibility of experimentally observing MDDI effects in different atomic species. We find that strong MDDI effects should be observable in both in-trap and time-of-flight behaviors, not only for the strongly magnetic dipolar species but also for the alkali-metal BECs of 7{}^{7}7Li, 39{}^{39}39K, and 133{}^{133}133Cs. In addition, we predict several effects which should be experimentally observable. Our results provide a helpful guide for experimentalists to realize and study atomic dipolar quantum gases.
The symmetry-breaking magnetization dynamics of a spin-1 Bose-Einstein condensate (BEC) due to the dipole-dipole interaction are investigated using the mean-field and Bogoliubov theories. When a magnetic field is applied along the symmetry axis of a pancake-shaped BEC in the m=0m=0m=0 hyperfine sublevel, transverse magnetization develops breaking the chiral or axial symmetry. A variety of magnetization patterns are formed depending on the strength of the applied magnetic field. The proposed phenomena can be observed in 87Rb^{87}\mathrm{Rb}87Rb and 23Na^{23}\mathrm{Na}23Na condensates.