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arXiv:1508.06167 · Frontiers of Physics

Trapped Bose–Einstein condensates in synthetic magnetic field

Qiang Zhao, Qiang Gu

Published Oct 1, 2015• 10 citations
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Abstract

The rotational properties of Bose–Einstein condensates in a synthetic magnetic field are studied by numerically solving the Gross–Pitaevskii equation and comparing the results to those of condensates confined in a rotating trap. It appears to be more difficult to add a large angular momentum to condensates spun up by the synthetic magnetic field than by the rotating trap. However, strengthening the repulsive interaction between atoms is an effective and realizable route to overcoming this problem and can at least generate vortex-lattice-like structures. In addition, the validity of the Feynman rule for condensates in the synthetic magnetic field is verified.

DOI
10.1007/s11467-015-0505-x

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The rotational properties of Bose–Einstein condensates in a synthetic magnetic field are studied by numerically solving the Gross–Pitaevskii equation and comparing the results to those of condensates confined in a rotating trap. It appears to be more difficult to add a large angular momentum to condensates spun up by the synthetic magnetic field than by the rotating trap. However, strengthening the repulsive interaction between atoms is an effective and realizable route to overcoming this problem and can at least generate vortex-lattice-like structures. In addition, the validity of the Feynman rule for condensates in the synthetic magnetic field is verified.
We consider theoretically static and dynamic properties of vortex formation in trapped Bose-Einstein condensates in synthetic magnetic field and compare the results created by rotating frame method.As the first step, we discuss the ground state properties and show that the number of vortices and rotational frequency is a linear relation.We further deduce the analytical results and find it qualitatively agrees with numerical solutions.In addition, we explore the vortex dynamics, focusing on the difference between the two rotational methods.Numerical results indicate that synthetic magnetic field is more difficult to add a large angular momentum.However, this issue can be effectively improved by increasing the contact interaction.
We study the formation of vortices in a dipolar Bose–Einstein condensate in a synthetic magnetic field by numerically solving the Gross–Pitaevskii equation. The formation process depends on the dipole strength, the rotating frequency, the potential geometry, and the orientation of the dipoles. We make an extensive comparison with vortices created by a rotating trap, especially focusing on the issues of the critical rotating frequency and the vortex number as a function of the rotating frequency. We observe that a higher rotating frequency is needed to generate a large number of vortices and the anisotropic interaction manifests itself as a perceptible difference in the vortex formation. Furthermore, a large dipole strength or aspect ratio also can increase the number of vortices effectively. In particular, we discuss the validity of the Feynman rule.
In this paper, we study the static and dynamic properties of vortices formation in a rotating Bose–Einstein condensate in synthetic magnetic field. The condensate is confined in a harmonic potential and an optical lattice potential. We numerically solve the time-dependent Gross–Pitaevskii equation in two dimensions and compare the vortices formation process with rotating frame method. We derive the two expressions about vortex number N[Formula: see text] and chemical potential [Formula: see text] as a function of rotational frequency [Formula: see text], which show that the number of vortices N[Formula: see text] increases linearly with [Formula: see text], while the chemical potential [Formula: see text] remains nearly unchanged with increasing [Formula: see text]. The analytical results are in qualitative agreement with the numerical ones. Moreover, we also investigate the vortex dynamics. Numerical results indicate that the time spent for the formation of steady state vortices is reduced drastically if the optical lattice is considered. Nevertheless, the synthetic magnetic field approach is still low efficient to generate more vortices.
In this article, we study the vortex formation in spin-1 spin–orbit coupling rotating Bose–Einstein condensates. Numerical results are obtained by solving the spinor Gross–Pitaevskii equation. We mainly focus on the influences of external magnetic fields on vortex structures and dynamics properties. With the increase in magnetic field strength, the populations of magnetic components j=±1 reach the identical value. For the density profile, the three components present identical density structures, and the size of condensates is nearly the same. In addition, some related physical quantities, such as the time taken for the arrival of a steady population and root-mean-square size, kinetic energy, and total angular momentum, are calculated. The results show that these quantities decrease as the magnetic field strength increases. Moreover, we also investigate the time evolution of angular momentum. It is seen that the dynamic behavior of the magnetic components j=±1 is exactly consistent, and the total angular momentum reduces in the presence of the strong magnetic field. This reflects the fact that the introduction of the strong magnetic field makes it difficult to rotate the condensate, and thus, it is disadvantageous for generating more vortices.
We investigate the expansion dynamics of spin-orbit-coupled Bose-Einstein condensates subjected to a synthetic magnetic field, after their release from an external harmonic trap. Our findings reveal that the condensate experiences a spin-dependent rotation and separation due to the rigid-like rotational velocity field, which leads to a spin-density deflection. The deflection angle reaches a peak at an expansion time that is inversely related to the trap frequency. When the detuning gradient is below a critical value for vortex nucleation, our analytical results derived from a spinor hydrodynamic theory align closely with numerical results using the coupled Gross-Pitaevskii equations. Beyond this critical value, we also numerically simulated the expansion dynamics of the condensates containing vortices with negative circulation. Our findings highlight the pivotal role of the rigid-like rotational velocity field on the dynamics of the condensate and may stimulate further experimental investigations into the rich superfluid dynamics induced by synthetic magnetic fields.
We investigate the ground states and rich dynamics of vortices in spin-orbit coupled Bose-Einstein condensates (BEC) subject to position-dependent detuning. Such a detuning plays the role of an effective rotational frequency, causing the generation of a synthetic magnetic field. Through scanning the detuning gradient, we numerically obtain static vortex lattice structures containing 1 to 6 vortices using the coupled Gross-Pitaevskii equations. When quenching detuning gradient below its initial value, the vortex lattices exhibit interesting periodic rotation motion, and their dynamical stability can persist for up to 1000ms. In particular, depending on the detuning gradient, the twin vortices exhibit either a scissors-like rotational oscillation or a clockwise periodic rotation, reflecting the response to the magnetic field gradient experienced by the condensates. We fit the numerical results to quantitatively analyze the relation between rotation dynamics and magnetic field gradients. When quenching the detuning gradient beyond its initial value, additional vortices appear. Our findings may motivate further experimental studies of vortex dynamics in synthetic magnetic fields and offer insights for engineering a BEC-based magnetic field gradiometer.