Confinement of Half-quantized Vortices in Coherently Coupled Bose-Einstein Condensates: Simulating Quark Confinement in QCD

We demonstrate that the confinement of half-quantized vortices (HQVs) in coherently coupled Bose-Einstein condensates (BECs) simulates certain aspects of the confinement in $SU(2)$ quantum chromodynamics (QCD) in 2+1 space-time dimensions. By identifying the circulation of superfluid velocity as the baryon number and the relative phase between two components as a dual gluon, we identify HQVs in a single component as electrically charged particles with a half baryon number. Further, we show that only singlet states of the relative phase of two components can stably exist as bound states of vortices, that is, a pair of vortices in each component (a baryon) and a pair of a vortex and an antivortex in the same component (a meson). We then study the dynamics of a baryon and meson; baryon is static at the equilibrium and rotates once it deviates from the equilibrium, while a meson moves with constant velocity. For both baryon and meson we verify a linear confinement and determine that they are broken, thus creating other baryons or mesons in the middle when two constituent vortices are separated by more than some critical distance, resembling QCD.