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arXiv:1209.6197 · Physical Review Letters

Topological Wigner Crystal of Half-Solitons in a Spinor Bose-Einstein Condensate

Hugo Terças, Dmitry D. Solnyshkov, G. Malpuech

Published Jan 15, 2013• 60 citations
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Abstract

We consider a one-dimensional gas of half-solitons in a spinor Bose-Einstein condensate. We calculate the topological interaction potential between the half-solitons. Using a kinetic equation of the Vlasov-Boltzmann type, we model the coupled dynamics of the interacting solitons. We show that the dynamics of the system in the gaseous phase is marginally stable and spontaneously evolves toward a Wigner crystal.

DOI
10.1103/physrevlett.110.035303

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We consider a one-dimensional gas of half-solitons in a spinor Bose-Einstein condensate. We calculate the topological interaction potential between the half-solitons. Using a kinetic equation of the Vlasov-Boltzmann type, we model the coupled dynamics of the interacting solitons. We show that the dynamics of the system in the gaseous phase is marginally stable and spontaneously evolves toward a Wigner crystal.
We discuss some recent advances in the spin dynamics in photonic systems and polariton superfluids. In particular, we describe how the spin degree of freedom affects the collective behaviour of the half-soliton gas. First, we demonstrate that the anisotropy in the intra- and interspin interaction leads to the formation of a one-dimensional ordered phase: the topologicalWigner crystal. Second, we show that half-solitons behave as magnetic monopoles in effective magnetic fields. We study the transport properties and demonstrate a deviation from the usual Ohm's law for moderate values of the magnetic field. Introduction Photonic systems offer great opportunities for the study of quantum fluids, due to the possibility of creation of macroscopically occupied states with well-controlled properties by coherent excitation with lasers, and the full access to the wavefunction of the quantum fluid by well-established optical methods [1]. The main distinctive feature of quantum fluids as compared with classical ones are the topological defects, which, once created, cannot be removed by a continuous transformation. The most well-known example of such defect is a quantum vortex, which can appear in two-dimensional (2D) and three-dimensional (3D) systems. Its analog in one-dimensional (1D) Bose-Einstein condensates (BECs) is a soliton [2]. In fact, solitons are ubiquitous in systems described by the self-defocussing nonlinear Schrödinger equations. Specifically, for Bose gases, they are associated with the excitations of type II of the Lieb and Liniger theory. Spinor BECs (particularly with two pseudospin projections) offer a plethora of nonlinear spin effects, including half-integer topological defects possible in BECs with spin-anisotropic interactions [3]. Recent experimental work reports on the emergent monopole behaviour of half-solitons in the presence of an effective magnetic field [4]. In this chapter, we highlight some theoretical advances concerning not only the dynamics but also the many-body aspects of the physics of half-solitons. A Topological Wigner Crystal It is commonly accepted that the Wigner crystal is one of the most simple yet dramatic many-body effects. In the seminal work published in 1931 [5], Wigner showed that as a result of the competition between the long-ranged potential and kinetic energies, electrons spontaneously form a self-organized crystal at low densities, in a state that strongly differs from the Fermi gas. Experimental observations of this effect have been reported in carbon nanotubes [6].
We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose-Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states: the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipoledipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose-Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons (half skyrmions) can be generated in the presence of spin-orbit coupling.