The dynamics of pseudo-spin-1/2 Bose-Einstein condensates with weak spin-orbit coupling through a moving obstacle potential are studied numerically. Four types of wakes are observed and the phase diagrams are determined for different spin-orbit coupling strengths. The conditions to form Bénard-von Kármán vortex street are rather rigorous, and we investigate in detail the dynamical characteristics of the vortex streets. The two point vortices in a pair rotate around their center, and the angular velocity and their distance oscillate periodically. The oscillation intensifies with increasing spin-orbit coupling strengths, and it makes part of the vortex pairs dissociate into separate vortices or combine into single ones and destroys the vortex street in the end. The width b of the street and the distance l between two consecutive vortex pairs of the same circulation are determined by the potential radius and its moving velocity, respectively. The b/l ratios are independent of the spin-orbit coupling strength and fall in the range 0.19-0.27, which is a little smaller than the stability criterion 0.28 for classical fluids. Proper b/l ratios are necessary to form Bénard-von Kármán vortex street, but the spin-orbit coupling strength affects the stability of the street patterns. Finally, we propose a protocol to experimentally realize the vortex street in ^{87}Rb spin-orbit-coupling Bose-Einstein condensates.
The dynamics of pseudo-spin-1/2 Bose-Einstein condensates with weak spin-orbit coupling through a moving obstacle potential are studied numerically. Four types of wakes are observed and the phase diagrams are determined for different spin-orbit coupling strengths. The conditions to form Bénard-von Kármán vortex street are rather rigorous, and we investigate in detail the dynamical characteristics of the vortex streets. The two point vortices in a pair rotate around their center, and the angular velocity and their distance oscillate periodically. The oscillation intensifies with increasing spin-orbit coupling strengths, and it makes part of the vortex pairs dissociate into separate vortices or combine into single ones and destroys the vortex street in the end. The width b of the street and the distance l between two consecutive vortex pairs of the same circulation are determined by the potential radius and its moving velocity, respectively. The b/l ratios are independent of the spin-orbit coupling strength and fall in the range 0.19-0.27, which is a little smaller than the stability criterion 0.28 for classical fluids. Proper b/l ratios are necessary to form Bénard-von Kármán vortex street, but the spin-orbit coupling strength affects the stability of the street patterns. Finally, we propose a protocol to experimentally realize the vortex street in ^{87}Rb spin-orbit-coupling Bose-Einstein condensates.
The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street’ is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately 0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.
Abstract The dynamical behaviors of a quasi-2D Bose–Einstein condensate (BEC) with three-body interactions through a moving obstacle potential are studied numerically. Various vortex structures are discovered under different strength of three-body interactions when the two-body interaction is attractive or repulsive. When the width and moving velocity of the obstacle potential reach critical value, periodic anti-symmetric double-row vortex pairs will be released alternately in BEC, and a Bénárd–von Kármán (BvK) vortex street will be formed eventually. We noticed that the BvK vortex street can be excited when the three-body interactions are taken into account even if the two-body interaction is attractive. The mean value of the distance between two vortex rows to the distance between two vortex pairs in the same row is about 0.2. It is slightly smaller than the stability condition 0.28 without considering the three-body interaction. The parameter regions of vortex patterns at different three-body interaction are determined. It is found that an appropriate value of three-body interaction with larger velocity and lesser width is favorable to the formation of BvK vortex street. In a pair of point vortices, the distance and angular velocity between them are nearly invariant while they rotate around their center. The internal rule of vortex pair are also analyzed by calculating the drag force acting on the obstacle potential. Finally, we proposed an experimental protocol to realize the vortex street in 87Rb BEC with three-body interactions.
Bénard-von Kármán vortex street in dipolar Bose-Einstein Condensate (BEC) trapped by a square-like potential is investigated numerically. In the frame of mean-field theory, the nonlinear dynamic of the dipolar BEC can be described by the so-called two-dimensional Gross-Pitaevskii (GP) equation with long-range interaction. In this paper, we only consider the case that all the dipoles are polarized along the z-axis, which is perpendicular to the plane of disc-shaped BEC. Firstly, the stationary state of the BEC is obtained by the imaginary-time propagation approach. Secondly, the nonlinear dynamic of the BEC, when a moving Gaussian potential exists in such a system, is numerically investigated by the time-splitting Fourier spectral method, in which the stationary state obtained before is set to be the initial state. The results show that when the velocity of the cylindrical obstacle potential reaches a critical value, which depends on interaction strength and the shape of the potential, the vortex-antivortex pairs will be generated alternately in the super-flow behind the obstacle potential. However, in general, such a vortex-antivortex pair structure is dynamically unstable. When the velocity of the obstacle potential increases to a certain value and for a suitable potential width, a stable vortex structure called Bénard-von Kármán vortex street will be formed. While this phenomenon emerges, the vortices in pairs created by the obstacle potential have the same circulation. The pairs with opposite circulations are alternately released from the moving obstacle potential. For larger potential width and velocity, the shedding pattern becomes irregular. We also numerically investigate the effects of the dipole interaction strength, the width and the velocity of the obstacle potential on the vortex structures arising in the wake flow. As a result, the phase graph is presented by lots of numerical calculations for a group of given physical parameters. Thirdly, the drag force on the obstacle potential is also calculated and the mechanical mechanism of vortex pair is analyzed. Finally, we discuss how to find the phenomenon of Bénard-von Kármán vortex street in dipolar BEC experimentally.
Abstract Vortex shedding from a moving obstacle potential in a two-component Bose–Einstein condensate is investigated numerically. For a miscible two-component condensate composed of 23Na and 87Rb atoms, in the wake of obstacle, the Kármán vortex street is discovered in one component, while the Kármán-like vortex street named ‘half-quantum vortex street’ is formed in another component. The other patterns of vortex shedding, such as the vortex dipoles, V-shaped vortex pairs and corresponding ‘half-quantum vortex shedding’, can also be found. The drag force acting on obstacle potential is calculated and discussed. The parameter region for various vortex patterns and critical velocity for vortex emission are presented. In addition, a 85Rb–87Rb mixture is also considered, where the Kármán vortex street and other typical patterns exist in both components. Finally, we provide an experimental protocol for the above realization and observation.
The dynamics of a miscible two-component Bose-Einstein condensate (BEC) with PT (parity-time) symmetric potential are investigated numerically. The dynamical behaviors of the system is described by Gross-Pitaevskii (GP) equations under the mean-field theory. Firstly, the ground state of the system is obtained by the imaginary-time propagation method. Then dynamical behaviors are numerically simulated by the time-splitting Fourier pseudo-spectral approach under periodic boundary conditions. By adjusting the width and velocity of the obstacle potential, various patterns such as no vortex, oblique drifting vortex dipole, V-shaped vortex pairs, irregular quantum turbulence and combined modes are studied. It is noted that the shedding vortex pairs in components 1 and 2 are staggered, which is called “the asynchronous quantum Kármán vortex street”. Here, the ratio of the distance between two vortex pairs in one row to the distance between vortex rows is approximately 0.18, which is less than the stability criterion 0.28 of classical fluid. We calculated the drag force acting on the obstacle potential during generation of the asynchronous quantum Kármán vortex street. It is found that periodical oscillation of the drag force is generated via drifting up or down of the vortex pairs. Meanwhile, we analyzed the influence of the imaginary part of the PT symmetric potential with gain-loss for wake. The trajectory and frequency of the vortex are changed, due to the imaginary part breaks the local symmetry of the system. In addition, the imaginary part affects the stability of the asynchronous quantum Kármán vortex street. Lots of numerical simulations are carried out to determine the parameter regions of various vortex shedding modes. We also proposed an experimental protocol to realize the asynchronous quantum Kármán vortex street in the miscible two-component BEC with PT symmetric potential.