We study the ground-state topology and quasiparticle properties in bosonic Mott insulators with two-dimensional spin-orbit couplings in cold atomic optical lattices. We show that the many-body Chern and spin-Chern number can be expressed as an integral of the quasihole Berry curvatures over the Brillouin zone. Using a strong-coupling perturbation theory, for an experimentally feasible spin-orbit coupling, we compute the Berry curvature and the spin Chern number and find that these quantities can be generated purely by interactions. We also compute the quasiparticle dispersions, spectral weights, and the quasimomentum space distribution of particle and spin density, which can be accessed in cold-atom experiments and used to deduce the Berry curvature and Chern numbers.We study the ground-state topology and quasiparticle properties in bosonic Mott insulators with two-dimensional spin-orbit couplings in cold atomic optical lattices. We show that the many-body Chern and spin-Chern number can be expressed as an integral of the quasihole Berry curvatures over the Brillouin zone. Using a strong-coupling perturbation theory, for an experimentally feasible spin-orbit coupling, we compute the Berry curvature and the spin Chern number and find that these quantities can be generated purely by interactions. We also compute the quasiparticle dispersions, spectral weights, and the quasimomentum space distribution of particle and spin density, which can be accessed in cold-atom experiments and used to deduce the Berry curvature and Chern numbers.

arXiv:1307.3594Physical Review ANov 25, 201310 citations

Spin Transport in Spin-Orbit Coupled BECs

Robert Niffenegger, Chunlei Qu, Abraham J. Olson +2 more

Bulletin of the American Physical SocietyJun 5, 20140 citations

Effects of Berry Curvature on the Collective Modes of Ultracold Gases

Hannah M. Price, Nigel R. Cooper

Topological energy bands have important geometrical properties described by the Berry curvature. We show that the Berry curvature changes the hydrodynamic equations of motion for a trapped Bose-Einstein condensate, and causes significant modifications to the collective mode frequencies. We illustrate our results for the case of two-dimensional Rashba spin-orbit coupling in a Zeeman field. Using an operator approach, we derive the effects of Berry curvature on the dipole mode in very general settings. We show that the sizes of these effects can be large and readily detected in experiment. Collective modes therefore provide a sensitive way to measure geometrical properties of energy bands.Topological energy bands have important geometrical properties described by the Berry curvature. We show that the Berry curvature changes the hydrodynamic equations of motion for a trapped Bose-Einstein condensate, and causes significant modifications to the collective mode frequencies. We illustrate our results for the case of two-dimensional Rashba spin-orbit coupling in a Zeeman field. Using an operator approach, we derive the effects of Berry curvature on the dipole mode in very general settings. We show that the sizes of these effects can be large and readily detected in experiment. Collective modes therefore provide a sensitive way to measure geometrical properties of energy bands.

arXiv:1306.4796Physical Review LettersNov 27, 201324 citations

Experimental investigation of spin-orbit coupled BECs

Peter Engels

Bulletin of the American Physical SocietyMar 6, 20140 citations

Imaging the topological sign of a Dirac mass with spin-polarized tunneling

Payman Kazemikhah, Ruolun Zhang, Byunghoon Kim +5 more

A Dirac mass is characterized not only by its magnitude but also by its sign, which influences the Berry curvature, Hall response, and the propagation direction of chiral boundary modes. However, local spectroscopy of magnetic topological surfaces has so far accessed only the gap magnitude $|M|$ . Here we show how the topological sign of $M$ can be determined locally. We first establish the sign information that spin-resolved tunneling can access and the reference required to obtain an absolute Hall sign. Although spin--orbital entanglement generally obscures the relation between measured spin and Dirac pseudospin, crystalline rotation symmetry alleviates this ambiguity at the band edge. On a $C_3$ axis, an axial tip couples to a fully spin-polarized state whose tunneling asymmetry directly reveals the sign of the occupied-band Berry curvature, independent of orbital composition. We further show that the zeroth Landau level provides an independent mass-sign measurement with an unpolarized tip, while opposite domains and their chiral domain-wall modes provide self-consistency checks. These results pave the way for imaging the locations where the topological character changes within a material, rather than merely identifying where a spectral gap appears.A Dirac mass is characterized not only by its magnitude but also by its sign, which influences the Berry curvature, Hall response, and the propagation direction of chiral boundary modes. However, local spectroscopy of magnetic topological surfaces has so far accessed only the gap magnitude $|M|$. Here we show how the topological sign of $M$ can be determined locally. We first establish the sign information that spin-resolved tunneling can access and the reference required to obtain an absolute Hall sign. Although spin--orbital entanglement generally obscures the relation between measured spin and Dirac pseudospin, crystalline rotation symmetry alleviates this ambiguity at the band edge. On a $C_3$ axis, an axial tip couples to a fully spin-polarized state whose tunneling asymmetry directly reveals the sign of the occupied-band Berry curvature, independent of orbital composition. We further show that the zeroth Landau level provides an independent mass-sign measurement with an unpolarized tip, while opposite domains and their chiral domain-wall modes provide self-consistency checks. These results pave the way for imaging the locations where the topological character changes within a material, rather than merely identifying where a spectral gap appears.

quant-pharXiv:2610.17464Oct 14, 2026

Experiments on BECs with Synthetic Gauge Fields and Spin Orbit Coupling

Robert Niffenegger, Abraham J. Olson, Yong P. Chen

Bulletin of the American Physical SocietyMar 21, 20130 citations

|M|

. Here we show how the topological sign of

M

can be determined locally. We first establish the sign information that spin-resolved tunneling can access and the reference required to obtain an absolute Hall sign. Although spin--orbital entanglement generally obscures the relation between measured spin and Dirac pseudospin, crystalline rotation symmetry alleviates this ambiguity at the band edge. On a

C_3

axis, an axial tip couples to a fully spin-polarized state whose tunneling asymmetry directly reveals the sign of the occupied-band Berry curvature, independent of orbital composition. We further show that the zeroth Landau level provides an independent mass-sign measurement with an unpolarized tip, while opposite domains and their chiral domain-wall modes provide self-consistency checks. These results pave the way for imaging the locations where the topological character changes within a material, rather than merely identifying where a spectral gap appears.