We demonstrate that the three-dimensional Skyrmion, which has remained elusive so far, spontaneously appears as the ground state of SU(2) symmetric Bose-Einstein condensates coupled with a non-Abelian gauge field. The gauge field is a three-dimensional analogue of the Rashba spin-orbit coupling. Upon squashing the SO(3) symmetric gauge field to one- or two-dimensional shapes, we find that the ground state continuously undergoes a change from a three-dimensional to a one- or two-dimensional Skyrmion, which is identified by estimating winding numbers and helicity. All of the emerged Skyrmions are physically understandable with the concept of the helical modulation in a unified way. These topological objects might potentially be realizable in two-component Bose-Einstein condensates experimentally.We demonstrate that the three-dimensional Skyrmion, which has remained elusive so far, spontaneously appears as the ground state of SU(2) symmetric Bose-Einstein condensates coupled with a non-Abelian gauge field. The gauge field is a three-dimensional analogue of the Rashba spin-orbit coupling. Upon squashing the SO(3) symmetric gauge field to one- or two-dimensional shapes, we find that the ground state continuously undergoes a change from a three-dimensional to a one- or two-dimensional Skyrmion, which is identified by estimating winding numbers and helicity. All of the emerged Skyrmions are physically understandable with the concept of the helical modulation in a unified way. These topological objects might potentially be realizable in two-component Bose-Einstein condensates experimentally.

arXiv:1204.3177Physical Review LettersJul 2, 2012173 citations

Spinor Bose-Einstein Condensates Under Synthetic Gauge Field

Xiaoqiang Xu, Jung Hoon Han

Bulletin of the American Physical SocietyFeb 28, 20120 citations

BCS-BEC crossover induced by a synthetic non-Abelian gauge field

Jayantha P. Vyasanakere, Shizhong Zhang, Vijay B. Shenoy

We investigate the ground state of interacting spin- $\frac{1}{2}$ fermions in three dimensions at a finite density ($\ensuremath{\rho}\ensuremath{\sim}{k}_{F}^{3}$) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector $\ensuremath{\lambda}\ensuremath{\equiv}({\ensuremath{\lambda}}_{x},{\ensuremath{\lambda}}_{y},{\ensuremath{\lambda}}_{z})$, whose magnitude $\ensuremath{\lambda}$ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $({k}_{F}|{a}_{s}|\ensuremath{\lesssim}1)$, the ground state in the absence of the gauge field ($\ensuremath{\lambda}=0$) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum $(\ensuremath{\lambda}=0)$. For large gauge couplings $(\ensuremath{\lambda}/{k}_{F}\ensuremath{\gg}1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)---we call these bosons ``rashbons.'' In the absence of interactions (${a}_{s}={0}^{\ensuremath{-}}$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling ${\ensuremath{\lambda}}_{T}$. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\ensuremath{\lambda}$ near ${\ensuremath{\lambda}}_{T}$. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.We investigate the ground state of interacting spin-$\frac{1}{2}$ fermions in three dimensions at a finite density ($\ensuremath{\rho}\ensuremath{\sim}{k}_{F}^{3}$) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector $\ensuremath{\lambda}\ensuremath{\equiv}({\ensuremath{\lambda}}_{x},{\ensuremath{\lambda}}_{y},{\ensuremath{\lambda}}_{z})$, whose magnitude $\ensuremath{\lambda}$ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $({k}_{F}|{a}_{s}|\ensuremath{\lesssim}1)$, the ground state in the absence of the gauge field ($\ensuremath{\lambda}=0$) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum $(\ensuremath{\lambda}=0)$. For large gauge couplings $(\ensuremath{\lambda}/{k}_{F}\ensuremath{\gg}1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)---we call these bosons ``rashbons.'' In the absence of interactions (${a}_{s}={0}^{\ensuremath{-}}$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling ${\ensuremath{\lambda}}_{T}$. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\ensuremath{\lambda}$ near ${\ensuremath{\lambda}}_{T}$. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.

arXiv:1104.5633Physical Review BJul 25, 2011161 citations

Bose-Einstein Condensates in Non-abelian Gauge Fields

Tin-Lun Ho, Shizhong Zhang

The recent success of the NIST group in generating abelian gauge field in cold atoms has created opportunities to simulate electronic transports in solids using atomic gases. Very recently, the NIST group has also announced in a DARPA Meeting the creation of non-abelian gauge fields in a pseudo spin-1/2 Bose gas. While there have been considerable theoretical activities in synthetic gauge fields, non-abelian fields have not been generated until now. Here, we show that in a non-abelian gauge field, a spinor condensate will develop a spontaneous stripe structure in each spin component, reflecting a ground state made up of two non-orthogonal dressed states with different momenta. Depending on interactions, this ground state can reduce back to a single dressed state. These momentum carrying stripes are the {\em macroscopic} bosonic counterpart of the spin-orbit phenomena in fermions that are being actively studied in electron physics today.The recent success of the NIST group in generating abelian gauge field in cold atoms has created opportunities to simulate electronic transports in solids using atomic gases. Very recently, the NIST group has also announced in a DARPA Meeting the creation of non-abelian gauge fields in a pseudo spin-1/2 Bose gas. While there have been considerable theoretical activities in synthetic gauge fields, non-abelian fields have not been generated until now. Here, we show that in a non-abelian gauge field, a spinor condensate will develop a spontaneous stripe structure in each spin component, reflecting a ground state made up of two non-orthogonal dressed states with different momenta. Depending on interactions, this ground state can reduce back to a single dressed state. These momentum carrying stripes are the {\em macroscopic} bosonic counterpart of the spin-orbit phenomena in fermions that are being actively studied in electron physics today.

arXiv:1007.0650Jul 5, 20103 citations

We investigate the ground state of interacting spin-

\frac{1}{2}

fermions in three dimensions at a finite density ($\ensuremath{\rho}\ensuremath{\sim}{k}_{F}^{3}$) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector $\ensuremath{\lambda}\ensuremath{\equiv}({\ensuremath{\lambda}}_{x},{\ensuremath{\lambda}}_{y},{\ensuremath{\lambda}}_{z})$, whose magnitude $\ensuremath{\lambda}$ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $({k}_{F}|{a}_{s}|\ensuremath{\lesssim}1)$, the ground state in the absence of the gauge field ($\ensuremath{\lambda}=0$) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum $(\ensuremath{\lambda}=0)$. For large gauge couplings $(\ensuremath{\lambda}/{k}_{F}\ensuremath{\gg}1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)---we call these bosons ``rashbons.'' In the absence of interactions (${a}_{s}={0}^{\ensuremath{-}}$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling ${\ensuremath{\lambda}}_{T}$. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\ensuremath{\lambda}$ near ${\ensuremath{\lambda}}_{T}$. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.