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arXiv:1702.04892 · Physical Review A

Confinement of half-quantized vortices in coherently coupled Bose-Einstein condensates: Simulating quark confinement in a QCD-like theory

Minoru Eto, Muneto Nitta

Published Feb 8, 2018• 49 citations
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Abstract

We demonstrate that the confinement of half-quantized vortices (HQVs) in coherently coupled Bose-Einstein condensates simulates certain aspects of the confinement in a theory like $\text{SU}(2)$ 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; a baryon is static at equilibrium and rotates once it deviates from the equilibrium, while a meson moves with constant velocity. For both baryons and mesons 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.

DOI
10.1103/physreva.97.023613

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We demonstrate that the confinement of half-quantized vortices (HQVs) in coherently coupled Bose-Einstein condensates simulates certain aspects of the confinement in a theory like SU(2)\text{SU}(2)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; a baryon is static at equilibrium and rotates once it deviates from the equilibrium, while a meson moves with constant velocity. For both baryons and mesons 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.
Coherently coupled two-component Bose-Einstein condensates (BEC) exhibit vortex confinement resembling quark confinement in quantum chromodynamics (QCD).Fractionally quantized vortices winding only in one of two components are attached by solitons, and they cannot stably exist alone.Possible stable states are "hadrons" either of mesonic type, i.e., molecules made of a vortex and antivortex in the same component connected by a soliton, or of baryonic type, i.e., molecules made of two vortices winding in two different components connected by a soliton.Mesonic molecules move straight with a constant velocity while baryonic molecules rotate.We numerically simulate collision dynamics of mesonic and baryonic molecules and find that the molecules swap partners in collisions in general like chemical and nuclear reactions, as well as summarizing all collisions as vortex reactions, and describe those by Feynman diagrams.We find a selection rule for final states after collisions of vortex molecules, analogous to that for collisions of hadrons in QCD.
The dynamic behavior of vortex pairs in two-component coherently (Rabi) coupled Bose-Einstein condensates is investigated in the presence of harmonic trapping. We discuss the role of the surface tension associated with the domain wall connecting two vortices in condensates of atoms occupying different spin states and its effect on the precession of the vortex pair. The results, based on the numerical solution of the Gross-Pitaevskii equations, are compared with the predictions of an analytical macroscopic model and are discussed as a function of the size of the pair, the Rabi coupling, and the intercomponent interaction. We show that the increase of the Rabi coupling results in the disintegration of the domain wall into smaller pieces, connecting vortices of newly created vortex pairs. The resulting scenario is the analog of quark confinement and string breaking in quantum chromodynamics.
We report the observation of half-quantum vortices (HQVs) in the easy-plane polar phase of an antiferromagnetic spinor Bose-Einstein condensate. Using in-situ magnetization-sensitive imaging, we observe that a singly charged quantum vortex dissociates into a pair of HQVs with opposite core magnetization. The dissociation dynamics is investigated by measuring the temporal evolution of the separation distance of the HQV pair. The separating behavior of the HQVs shows the short-range nature of their interactions. We observe that the dissociation process is activated faster with larger thermal spin fluctuations in the condensate, confirming the energetic instability of a singly charged vortex state.
Quantum vortices with half the quantum circulation, known as half-quantum vortices (HQVs), have been observed in various spinor superfluid systems recently. Because of their nonsingular cores, the interaction of HQVs is expected to be different from that of vortices in a conventional scalar superfluid, which can lead to a new class of superfluid dynamics. Here, we report on a collision experiment of two HQV pairs in an antiferromagnetic spinor Bose-Einstein condensate. The observed scattering motions of the HQVs reveal the short range interactions that arise from their ferromagnetic cores. Additionally, we investigate the relaxation dynamics of turbulent superflow containing many HQVs to find that spin wave excitations are generated and maintained by the collisional motions of the HQVs during dissipative evolution. These results provide new insight into the vortex dynamics in spinor superfluids.
We study the interaction and dynamics of two half-quantized vortices in two-component Bose-Einstein condensates. Using the Pad\'e approximation for the vortex core profile, we calculate the intervortex potential, whose asymptotic form for a large distance has been derived by Eto et al. [Phys. Rev. A 83, 063603 (2011)]. Through numerical simulations of the two-dimensional Gross-Pitaevskii equations, we reveal different kinds of dynamical trajectories of the vortices depending on the combinations of signs of circulations and the intercomponent density coupling. Under the adiabatic limit, we derive the equations of motion for the vortex coordinates, in which the motion is caused by the balance between Magnus force and the intervortex forces. The initial velocity of the vortex motion can be explained quantitatively by this point vortex approximation, but understanding the long-time behavior of the dynamics needs more consideration beyond our model.
We numerically investigate the dynamics of vortex generation in a two-dimensional, two-component Bose-Einstein condensate subjected to an oscillatory magnetic obstacle. The obstacle creates both repulsive and attractive Gaussian potentials for the two symmetric spin-$\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ components, respectively. We demonstrate that, as the oscillating frequency fff increases, two distinct critical dynamics arise in the generation of half-quantum vortices (HQVs) with different spin circulations. Spin-$\ensuremath{\uparrow}$ vortices are nucleated directly from the moving obstacle at low fff, while the spin-$\ensuremath{\downarrow}$ vortices are created at high fff by breaking a spin wave pulse in front of the obstacle. We find that vortex generation is suppressed for sufficiently weak obstacles, in agreement with recent experimental results by Kim et al. [Phys. Rev. Lett. 127, 095302 (2021)]. This suppression is caused by the finite sweeping distance of the oscillating obstacle and the reduction in friction in a supersonic regime. Finally, we show that the characteristic length scale of the HQV generation dynamics is determined by the spin healing length of the system.