Analytical study of parameter regions of dynamical instability for two-component Bose-Einstein condensates with coaxial quantized vortices

We report detailed investigation of the existence and stability of mixed and demixed modes in binary atomic Bose-Einstein condensates with repulsive interactions in a ring-trap geometry. The stability of such states is examined through eigenvalue spectra for small perturbations, produced by the Bogoliubov-de Gennes equations, and directly verified by simulations based on the coupled Gross-Pitaevskii equations, varying inter-and intra-species scattering lengths so as to probe the entire range of miscibility-immiscibility transitions. In the limit of the one-dimensional (1D) ring, i.e. a very narrow one, stability of mixed states is studied analytically, including hidden-vorticity (HV) modes, i.e. those with opposite vorticities of the two components and zero total angular momentum. The consideration of demixed 1D states reveals, in addition to stable composite single-peak structures, double-and triplepeak ones, above a certain particle-number threshold. In the 2D annular geometry, stable demixed states exist both in radial and azimuthal configurations. We find that stable radially-demixed states can carry arbitrary vorticity and, counter-intuitively, the increase of the vorticity enhances stability of such states, while unstable ones evolve into randomly oscillating angular demixed modes. The consideration of HV states in the 2D geometry expands the stability range of radially-demixed states.

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“…and BEC [53,[78][79][80][81][82][83][84]. Most essential are analytical results for stability of these states.…”

mentioning

confidence: 99%

Immiscible and miscible states in binary condensates in the ring geometry

Chen

Proukakis

et al. 2019

New J. Phys.

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“…Unlike the present setting, such systems readily admit stationary states with different vorticities and different chemical potentials in the components. In particular, systems of this type give rise to stable states with "hidden vorticity", i.e., ones with opposite vorticities and equal norms in the two components, the total angular moment of the states being zero, as predicted in BEC [28][29][30][31][32][33][34][35][36] and optics [37][38][39].…”

Section: The Modelmentioning

confidence: 99%

Nonlinear dynamics of Josephson vortices in merging superfluid rings

Oliinyk

Malomed

Yakimenko

2020

Communications in Nonlinear Science and Numerical Simulation

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We consider merger of two parallel toroidal atomic Bose-Einstein condensates with different vorticities in a three-dimensional (3D) trap. In the tunnel-coupling regime, Josephson vortices (rotational fluxons) emerge in the barrier between the superflows. When the barrier is gradually eliminated, we observe essentially three-dimensional evolution of quantum vortices, which may include the development of the Kelvin-Helmholtz instability at the interface between the rings, in the framework of a weakly dissipative Gross-Pitaevskii equation. An initially more populated ring, carrying a persistent current, can drag an initially non-rotating less populated one into the same vortex state. The final state of the condensate crucially depends on an initial population imbalance in the double-ring set, as well as on the shape of the 3D trapping potential, oblate or prolate. In the prolate (axially elongated) configuration, robust 3D hybrid structures may appear as a result of the merger of persistent currents corresponding to different vorticities.

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“…where g = 4πa s h2 /M is the nonlinearity strength, M is the atomic mass (M = 3.819 × 10 −26 kg for 23 Na atoms), a s is the s-wave scattering length (positive a s = 2.75 nm, corresponding to the repulsion of sodium atoms, is used below), µ is the chemical potential of the equilibrium state, and γ ≪ 1 is a dimensionless phenomenological dissipative parameter. This form of the dissipative GPE has been used extensively in previous studies of vortex dynamics (see, e.g., [31,32,35,36]).…”

Section: The Modelmentioning

confidence: 99%

“…Unlike the present setting, such systems readily admit stationary states with different vorticities and different chemical potentials in the components. In particular, systems of this type give rise to stable states with "hidden vorticity", i.e., ones with opposite vorticities and equal norms in the two components, the corresponding total angular moment being zero, as predicted in BEC [18][19][20][21][22][23][24][25] and optics [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Symmetry Breaking in Interacting Ring-Shaped Superflows of Bose–Einstein Condensates

et al. 2019

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We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counterpropagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction with tunneling through the barrier) and strong (rings merging across a reduced barrier) interactions. For the weakly interacting toroidal Bose-Einstein condensates, formation of rotational fluxons (Josephson vortices) is associated with spontaneous breaking of the rotational symmetry of the tunneling superflows. The influence of a controllable symmetry breaking on the final state of the merging counter-propagating superflows is investigated in the framework of a weakly dissipative mean-field model. It is demonstrated that the population imbalance between the merging flows and the breaking of the underlying rotational symmetry can drive the double-ring system to final states with different angular momenta.PACS numbers:

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Analytical study of parameter regions of dynamical instability for two-component Bose-Einstein condensates with coaxial quantized vortices

Cited by 3 publications

References 26 publications

Immiscible and miscible states in binary condensates in the ring geometry

Immiscible and miscible states in binary condensates in the ring geometry

Nonlinear dynamics of Josephson vortices in merging superfluid rings

Symmetry Breaking in Interacting Ring-Shaped Superflows of Bose–Einstein Condensates

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