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arXiv:1908.06668 · Physical Review A

Vortices with massive cores in a binary mixture of Bose-Einstein condensates

Andrea Richaud, Vittorio Penna, R. Mayol, M. Guilleumas

Published Jan 23, 2020• 63 citations
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Abstract

We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating boxlike circular trap, i.e., states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length, and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting.

DOI
10.1103/physreva.101.013630

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We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating boxlike circular trap, i.e., states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length, and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting.
We thoroughly analyze a notable class of states peculiar to a bosonic repulsive binary mixture loaded in a rotating box-like circular trap, i.e. states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully-analytic framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each condensed species, the vortices healing length and the cores characteristic size. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that the vortices drag the massive cores which they host thus conveying them their same motion of precession, but there is no evidence of quantum viscous friction between the two fluids, since the cores keep their orientation constant while orbiting.
Abstract We study the motion of superfluid vortices with filled massive cores. Previous point-vortex models already pointed out the impact of the core mass on the vortex dynamical properties, but relied on an assumption that is questionable in many physical systems where the immiscibility condition is barely satisfied: the fact that the massive core always lays at the very bottom of the effective confining potential constituted by the hosting vortex. Here, we relax this assumption and present a new point-vortex model where quantum vortices are harmonically coupled to their massive cores. We thoroughly explore the new dynamical regimes offered by this improved model; we then show that the functional dependence of the system normal modes on the microscopic parameters can be correctly interpreted only within this new generalized framework. Our predictions are benchmarked against the numerical simulations of coupled Gross–Pitaevskii equations for a realistic mixture of atomic Bose–Einstein condensates.
We study the massive point-vortex model introduced in Richaud et al. [A. Richaud, V. Penna, R. Mayol, and M. Guilleumas, Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.
We consider massive vortices in binary condensates, where the immiscibility condition entails the trapping of the minority component in the vortex cores of the majority component. We study such vortices by means of a two-dimensional pointlike model, and show how the relevant dynamical equations exhibit vortex-pair solutions characterized by different vortex masses and circular orbits of different radii aaa and bbb. These solutions are validated by the simulations of the Gross-Pitaevskii equations for binary condensates. After examining the properties of the vortex-pair rotational frequency $\mathrm{\ensuremath{\Omega}}$ as a function of the vortex masses for a given pair geometry, we define the rotational-state diagram D\mathcal{D}D, describing all the possible vortex-pair solutions in terms of the orbit radii at given $\mathrm{\ensuremath{\Omega}}$. This includes solutions with equal-mass pairs but $a\ensuremath{\ne}b$ or with one of the two masses (or both) equal to zero. Also, we analytically find the minimum value of $\mathrm{\ensuremath{\Omega}}$ for the existence of such solutions, and obtain numerically the critical frequency ${\mathrm{\ensuremath{\Omega}}}_{c}$ below which D\mathcal{D}D changes its structure and the transition to an unstable vortex-pair regime takes place. Our paper highlights an indirect measurement scheme to infer the vortex masses from the orbits' radii aaa and bbb, and a link between the vortex masses and the vortex-pair small-oscillation properties.
The dynamics of a filled massive vortex is studied numerically and analytically using a two-dimensional model of a two-component Bose–Einstein condensate trapped in a harmonic trap. This condensate exhibits phase separation. In the framework of the coupled Gross–Pitaevskii equations, it is demonstrated that, in a certain range of parameters of the nonlinear interaction, the precession of a sufficiently massive vortex around the center is strongly slowed down and even reverses its direction with a further increase in the mass. An approximate ordinary differential equation is derived that makes it possible to explain this behavior of the system.
We examine the dynamics associated with the miscibility-immiscibility transition of trapped two-species Bose-Einstein condensates (TBECs) of dilute atomic gases in the presence of vortices. In particular, we consider TBECs of Rb hyperfine states and Rb-Cs mixture. In the case of a singly charged vortex in only one of the condensates, there is enhancement when the vortex is present in the species which occupies the edges at phase separation. But suppression occurs when the vortex is in the species which occupies the core region. To examine the role of the vortex, we quench the interspecies interactions to drive the TBECs from miscible to immiscible phase, and use the time-dependent Gross-Pitaevskii equation to probe the phenomenon of phase separation. We also examine the effects of higher charged vortex to phase separation.