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Chinese Physics Letters

Behaviour of Rotating Bose–Einstein Condensates Under Shrinking

Zhai Hui, Qi Zhou

Published Dec 23, 2004• 0 citations
Publisher

Abstract

When the repulsive interaction strength between atoms decreases, the size of a rotating Bose–Einstein condensate will consequently shrink. We find that the rotational frequency will increase during the shrinking of condensate, which is a quantum mechanical analogy to ballet dancing. Compared to a non-rotating condensate, the size of a rotating BEC will eventually be saturated at a finite value when the interaction strength is gradually reduced. We also calculate the vortex dynamics induced by the atomic current, and discuss the difference of vortex dynamics in this case and that observed in a recent experiment carried out by the JILA group [Phys. Rev. Lett. 90 (2003) 170405].

DOI
10.1088/0256-307x/22/1/008

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When the repulsive interaction strength between atoms decreases, the size of a rotating Bose–Einstein condensate will consequently shrink. We find that the rotational frequency will increase during the shrinking of condensate, which is a quantum mechanical analogy to ballet dancing. Compared to a non-rotating condensate, the size of a rotating BEC will eventually be saturated at a finite value when the interaction strength is gradually reduced. We also calculate the vortex dynamics induced by the atomic current, and discuss the difference of vortex dynamics in this case and that observed in a recent experiment carried out by the JILA group [Phys. Rev. Lett. 90 (2003) 170405].
When the repulsive interaction strength between atoms decreases, the size of a rotating Bose-Einstein condensate will consequently shrink. We find that the rotational frequency will increase during the shrinking of condensate, which is a quantum mechanical analogy to ballet dancing. Compared to a non-rotating condensate, the size of a rotating BEC will eventually be saturated at a finite value when the interaction strength is gradually reduced. We also calculate the vortex dynamics induced by the atomic current, and discuss the difference of vortex dynamics in this case and that observed in a recent experiment carried out by the JILA group [Phys. Rev. Lett.90 (2003) 170405].
We investigate the impact of interplay between the contact interaction and the dipole-dipole interaction on the rotational properties of dipolar Bose-Einstein condensate, rotating in an axially confined double-well potential. The dynamics is governed by a quasi-two-dimensional Gross-Pitaevskii equation with phenomenological dissipation and non-local dipole-dipole interaction integral. In the present study, we consider using three different dipolar atoms namely 52Cr, 168Er and 164Dy with increasing order of dipole-dipole interaction strength respectively. From our numerical simulation, we see, at the critical frequency, the vortex core starts to emerge from the peripheries of the BEC. Further, we observe that the critical frequency of vortex nucleation decreases with an increase of dipole-dipole interaction strength and contact interaction strength and these interactions also enhance the number of vortices. We also find that the increase in average angular momentum per atom with rotational frequency suddenly shifts from linear to non-linear progression after attaining the critical rotational frequency. From the results obtained in the present study, it is quite clear that dipole-dipole interaction and contact interaction compliments with each other, has a considerable influence on the rotational properties of dipolar BECs.
In this paper, we study the dynamics of a single vortex and a corotating vortex pair in dipolar Bose-Einstein condensates under rotation.The results are obtained by numerically solving the nonlinear Gross-Pitaevskii equation.It is displayed that the dynamics behaviour is strongly dependent on the polarization angle and the rotation frequency.For a single vortex, the clockwise rotation occurs with an increasing rotation frequency, and the rotation direction is constant.The x coordinate and y coordinate as a function of time show that the single vortex is accelerated.The oscillation frequency is larger in the case of the totally repulsive dipolar interaction than for the anisotropic dipolar interaction.For a corotating vortex pair, the dynamic is different than in the case of a single vortex.When the rotation frequency is gradually increased, the corotating vortex pair spins from anti-clockwise to clockwise direction and the anisotropic dipolar interaction is fully embodied.In this process, the system has a critical rotation frequency to accomplish such transition.In addition, the vortex motion is confined to a small extent at this critical rotation frequency.These results reflect a competition between rotation and dipolar interaction.
Trapped Bose-Einstein condensates (BECs) differ considerably from the standard textbook example of a uniform Bose gas. In an isotropic harmonic potential V(r) = ½Mω2 r 2, the single-particle ground state introduces a new intrinsic scale of length [the ground-state size d = √ℏ/(Mω)] and energy [the ground-state energy E 0 = 32 \frac{3} {2} 23​ ℏω]. When the trap rotates at a low angular velocity, the behavior of a single vortex illustrates the crucial role of discrete quantized vorticity. For more rapid rotation, the condensate contains a vortex array. The resulting centrifugal forces expand the condensate radially and shrink it axially; thus, the condensate becomes effectively two dimensional. If the external rotation speed approaches the frequency of the radial harmonic confining potential, the condensate enters the “lowest-Landau-level” regime, and a simple description again becomes possible. Eventually, the system is predicted to make a quantum phase transition to a highly correlated state analogous to the fractional quantum Hall states of electrons in a strong magnetic field.
Starting from the equations of rotational hydrodynamics we study the macroscopic behavior of a trapped Bose-Einstein condensate containing a large number of vortices. The stationary configurations of the system, the frequencies of the collective excitations, and the expansion of the condensate are investigated as a function of the angular velocity of the vortex lattice. The time evolution of the condensate and of the lattice geometry induced by a sudden deformation of the trap is also discussed and compared with the recent experimental results of P. Engels et al. [Phys. Rev. Lett. 89, 100403 (2002)].
We develop a stochastic Gross-Pitaveskii theory suitable for the study of Bose-Einstein condensation in a rotating dilute Bose gas. The theory is used to model the dynamical and equilibrium properties of a rapidly rotating Bose gas quenched through the critical point for condensation, as in the experiment of Haljan et al. [Phys. Rev. Lett. 87, 210403 (2001)]. In contrast to stirring a vortex-free condensate, where topological constraints require that vortices enter from the edge of the condensate, we find that phase defects in the initial noncondensed cloud are trapped en masse in the emerging condensate. Bose-stimulated condensate growth proceeds into a disordered vortex configuration. At sufficiently low temperature the vortices then order into a regular Abrikosov lattice in thermal equilibrium with the rotating cloud. We calculate the effect of thermal fluctuations on vortex ordering in the final gas at different temperatures, and find that the BEC transition is accompanied by lattice melting associated with diminishing long-range correlations between vortices across the system.