Abstract
In this work, we consider vortex lattices in rotating Bose–Einstein condensates composed of two species of bosons having different masses. Previously (Barnett et al 2008 New J. Phys.10 043030), it was claimed that the vortices of the two species form bound pairs and the two vortex lattices lock. Remarkably, the two condensates and the external drive all rotate at different speeds owing to the disparity of the masses of the constituent bosons. In this paper, we study the system by solving the full two-component Gross–Pitaevskii equations numerically. Using this approach, we verify the stability of the putative locked state that is found to exist within a disc centered on the axis of rotation and that depends on the mass ratio of the two bosons. We also derive a refined estimate for the locking radius tailored to the experimentally relevant case of a harmonic trap and show that this agrees with the numerical results. Finally, we analyze in detail the rotation rates of the different components in the locked and unlocked regimes.
Highlights
We study the system by using numerical integration of the full two-component Gross–Pitaevskii equation (GPE)
Our analysis starts with the two-component Gross–Pitaevskii energy functional in the frame of reference rotating at angular rate d
We rotate the system at 0.9 times the critical rate at which the condensate becomes unstable due to centrifugal forces
Summary
Our analysis starts with the two-component Gross–Pitaevskii energy functional in the frame of reference rotating at angular rate d. This is given by E = E1 + E2 + E12, where. In these equations, V1 and V2 are the confining potentials of the BECs, which we will assume to be harmonic. The intraspecies and interspecies scattering strengths are defined as g1,2 and g12, respectively. The angular momentum operator, as usual, is defined as Lz = x py − ypx , where px,y ≡ −ih ∂x,y. In appendix B, we describe how these coupled equations are solved numerically to find minima of the energy E
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