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arXiv:1109.5496 · Physical Review A

Equilibrium vortex formation in ultrarapidly rotating two-component Bose-Einstein condensates

C.-H. Hsueh, Tzyy‐Leng Horng, Shih-Chuan Gou, W. C. Wu

Published Aug 5, 2011• 21 citations
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Abstract

Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency ${\ensuremath{\Omega}}_{c}$ is derived, which characterizes the structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency both above and below ${\ensuremath{\Omega}}_{c}$ and with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts.

DOI
10.1103/physreva.84.023610

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Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency \ensuremathΩc{\ensuremath{\Omega}}_{c}\ensuremathΩc​ is derived, which characterizes the structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency both above and below \ensuremathΩc{\ensuremath{\Omega}}_{c}\ensuremathΩc​ and with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts.
A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed $\ensuremath{\Omega}$ to exceed the radial harmonic frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$. In the regime $\ensuremath{\Omega}\ensuremath{\gtrsim}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity ${\ensuremath{\Omega}}_{h}$, a central hole appears in the condensate. Numerical studies confirm the predicted value of ${\ensuremath{\Omega}}_{h}$, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).
We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.
The phase separation and vortex states in a two-component Bose-Einstein condensate consisting of | F = 1, m f = 1〉 and |2, 1〉 internal spin states of 87 Rb atoms are considered in the framework of the Thomas-Fermi approximation. It is shown that in the nonrotating system, the atoms in the state |1, −1〉 form a shell around the atoms in the state |2, 1〉. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1〉 state can form a rotating ring around the resting core of the atoms in the |2, 1〉 state.
The phase separation and vortex states in two-component Bose-Einstein condensate consisting of |F = 1,mf = −1> and |2,1> internal spin states of 87Rb atoms are considered in the framework of Thomas-Fermi approximation. It is shown that in nonrotating system the atoms in the state |1, −1> form a shell about the atoms in the state |2,1>. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1> state can form a rotating ring about the resting core of the atoms in the state |2,1>. PACS:03.75.Fi; 05.30.Jp; 32.80.Pj. The realization of Bose-Einstein Condensation (BEC) in dilute atomic gases offers new opportunities for studying quantum degenerate fluids [1]. These condensates, which contain thousands of atoms confined to microscale clouds, have similarities to superfluidity and laser,
Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can exhibit a rich variety of vortex phases, including a vortex lattice, a vortex lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi variational approach to determine the ground state of the condensate in the rotating frame -- valid for sufficiently strongly interacting condensates -- we determine the transitions between these three phases for a quadratic-plus-quartic confining potential. Combining the present results with previous numerical simulations of small rotating condensates in such anharmonic potentials, we delineate the general structure of the zero temperature phase diagram.
The two-component rotating Bose-Einstein condensates confined in a harmonic plus quadric potential has been investigated by finite difference and image-time propagating numerical method.It found that the rotation velocity frequency can be larger than the harmonic vibration frequencyω⊥because of the quadric potential,even though the rotation velocityΩω⊥,the condensate would not diverge for the huge centrifugal force,moreover,as the increase of rotation velocityΩ,the ground state present vortex structure and the number of vortices decrease with the increase of centrifugal force of rotation,then the ground state phase become an giant-vortex.We also investigate the effect of inter-component strength on the ground state and find that the structure symmetry will be destroyed by the increase of inter-component strength.Especially,the ground state of condensate will go from separation phase to coexistence phase for the huge rotation velocity.