Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Abstract

We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-1 2 ) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling g ↑↓ to the intracomponent one g > 0. This time-reversalinvariant setting represents a bosonic analogue of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for g ↑↓ up to as large as g. For g ↑↓ = −g, we find the exact many-body ground state in which particles in different spin states form pairs. This gives the exact critical line beyond which the system collapses.

Collective modes of vortex lattices in two-component Bose–Einstein condensates under synthetic gauge fields

“…We have studied collective excitation modes of vortex lattices in two-component BECs subject to synthetic magnetic fields in parallel or antiparallel directions. Our motivation for studying the two types of synthetic fields stems from the fact that they lead to the same mean-field ground-state phase diagram [45] consisting of a variety of vortex-lattice phases [41,42]-it is interesting to investigate what similarities and differences arise in collective modes. Our analyses are based on a microscopic calculation using the Bogoliubov theory and an analytical calculation using a low-energy effective field theory.…”

“…antiparallel parallel [45]. This implies that within the GP theory, the ground-state wave function of one case can be obtained from that of the other through the complex conjugation of the spin- component 4 .…”

“…If the antiparallel fields are made even higher, such systems are expected to show a rich phase diagram consisting of vortex lattices and (fractional) quantum spin Hall states [45,50,51]. Notably, it has been shown within the GP mean-field theory that BECs in antiparallel magnetic fields exhibit the same vortex-lattice phase diagram as BECs in parallel magnetic fields [45] (see also section 2.1). It is thus interesting to ask whether and how the difference between the two types of systems arises in other properties such as collective modes.…”

“…In particular, mutually antiparallel synthetic magnetic fields have been induced in two-component BECs, leading to the observation of the spin Hall effect [49]. If the antiparallel fields are made even higher, such systems are expected to show a rich phase diagram consisting of vortex lattices and (fractional) quantum spin Hall states [45,50,51]. Notably, it has been shown within the GP mean-field theory that BECs in antiparallel magnetic fields exhibit the same vortex-lattice phase diagram as BECs in parallel magnetic fields [45] (see also section 2.1).…”

“…It is thus interesting to ask whether and how the difference between the two types of systems arises in other properties such as collective modes. In this context, it is worth noting that in the quantum Hall regime, which is far beyond the mean-field description, the two types of systems exhibit markedly different phase diagrams [45,[52][53][54][55], which has been interpreted in light of pseudopotentials and entanglement formation [55].…”