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Journal of Physics B Atomic Molecular and Optical Physics

Merging and splitting of Bose–Einstein condensates into two translating traps

Baoqing Sun, M. S. Pindzola

Published Jun 16, 2009• 2 citations
Publisher

Abstract

We investigate the process of merging and splitting Bose–Einstein condensates into two slowly translating traps, analogous to a dual input atomic beam splitter. With the help of direct three-dimensional numerical simulations, we explore the dependence of population distributions on the initial relative phase and the trap moving speed. For non-interacting Bose–Einstein condensates, we find that our numerical results are in good agreement with a simple theoretical prediction. However, for interacting Bose–Einstein condensates, our results show striking differences with the non-interacting case: the Bose–Einstein condensates are always split towards 50:50 in the slow translation regime. This bosonic anti-bunching effect is interpreted as a consequence of complicated flow patterns due to atomic interactions.

DOI
10.1088/0953-4075/42/14/145502

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•Jan 1, 2014•4 citations

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We investigate the process of merging and splitting Bose–Einstein condensates into two slowly translating traps, analogous to a dual input atomic beam splitter. With the help of direct three-dimensional numerical simulations, we explore the dependence of population distributions on the initial relative phase and the trap moving speed. For non-interacting Bose–Einstein condensates, we find that our numerical results are in good agreement with a simple theoretical prediction. However, for interacting Bose–Einstein condensates, our results show striking differences with the non-interacting case: the Bose–Einstein condensates are always split towards 50:50 in the slow translation regime. This bosonic anti-bunching effect is interpreted as a consequence of complicated flow patterns due to atomic interactions.
Motivated by an earlier proposal of splitting a one-dimensional atomic wave packet using two translating traps [Zhang et al., Phys. Rev. Lett. 97, 070403 (2006)], we report results of simulating the splitting dynamics for a three-dimensional Bose-Einstein condensate at zero temperature. Different from the single-atom case where the population in one of the traps shows full oscillations as a function of the translating velocity, we find that such oscillations are damped as the translating velocity decreases. As the interaction increases, we see a stronger damping effect. The damping mechanism is attributed to the formation of solitons which decay to vortex rings and cause complicated flow patterns to damp the population oscillations. Our conclusions are supported by results for N=5400N=5400N=5400 and N=54 000N=54\text{ }000N=54 000 87Rb^{87}\text{R}\text{b}87Rb atoms. In the adiabatically translating regime, the condensate can only be split 50:50. Therefore, a controlled splitting of the condensate in two symmetric traps can only be realized for a small number of atoms and away from the adiabatic regime.
Abstract We extend our previous work of splitting a single-species Bose-Einstein condensate in two translating traps to a two-species condensate. Different from the single species case where interaction is considered as a damping mechanism to the motion of the condensate, we find that, in the two species case, the damping effect is much less obvious and the splitting dynamics exhibit different behaviors. The distribution of each component are not damped towards 50:50 for large interaction strength in the two wells. Our conclusions are supported by investigating the dependence of the splitting on both the translation speed and the interspecies scattering length.
We study the dynamics of merging two initially independent Bose–Einstein condensates by adiabatically deforming the trap potential from a double well into a single well. The process of slowly decreasing the height of the central barrier of the double well is simulated by a full 3D calculation of the Gross–Pitaevskii equation. We investigate the dynamics by considering some factors relevant to experiments, e.g., the atom number, the initial state in each well, the initial relative phase between the two condensates. For a small number of 4400 atoms in each well and the same initial phase, we find for both condensates in the ground state or the p-wave soliton state that the final state is the ground state or the p-wave soliton state of the final trap potential. For cases in which both condensates are vortex states, we find much richer dynamics with the appearance of an extra vortex. We also discuss the cases for different initial relative phases. For comparison, we present results for 44 000 atoms corresponding to a larger nonlinear term in the Gross–Pitaevskii equation. In support of future experimental observations, we show both probability density and current maps.
In this Thesis we study steady state solutions and dynamical evolutions of two– component atomic Bose–Einstein Condensates. We initially investigate the equilibrium properties of condensate mixtures in harmonic trapping potentials at zero temperature. Subsequently we simulate the coupled growth of these condensates by inclusion of damping terms. Finally, we investigate the evolution of coupled Bose gases via the so-called classical–field method. A recent experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)] achieved Bose–Einstein Condensation of a two–species 87Rb–133Cs phase segregated mixture in harmonic trapping potentials. Depending on relative atom numbers of the two species, three distinct regimes of density distributions were observed. For these experimental parameters, we investigate the corresponding time–independent ground state solutions through numerical simulations of the coupled Gross–Pitaevskii equations. By including experimentally relevant shifts between the traps, we observe a range of structures including ‘ball and shell’ formations and axially/radially separated states. These are found to be very sensitive to the trap shifts. For all three experimental regimes, our numerical simulations reveal good qualitative agreement. The observed experimental profiles cannot be guaranteed to be fully equilibrated. This, coupled with the rapid sympathetic cooling of the experimental system, leads to a situation where growth may play a determining factor in the density structures formed. To investigate this further, we introduce phenomenological damping to describe the associated condensate growth/decay, revealing a range of transient structures. However, such a model always predicts the predominance of one condensate species over longer evolution times. Work undertaken by collaborators with the more elaborate Stochastic Projected Gross–Pitaevskii equations, which can describe condensate formation by coupling to a heat bath, predicts the spontaneous formation of dark–bright solitons. Motivated by this, we show how the presence of solitons can affect the condensate distribution, thus highlighting the overall dynamical role in the emerging patterns. Finally, we use classical field methods to analyse the evolution of non trapped Bose gases from strongly nonequilibrium initial distributions. The contrast between miscible (overlapping) and immiscible (phase segregated) components gives rise to important distinctions for condensate fractions and the formation of domains and vortices. In addition, splitting the particles of a single component thermalised state into two components is investigated. We then study the effects of suddenly quenching the strength of the interspecies interactions. Under suitable conditions, this quench generates isotropic vortex tangles. While this tangle subsequently decays over time, we propose how a repeat sequence of quenches at regular intervals could be employed to drive the tangle, thereby potentially providing a novel route to the generation of quantum turbulence.
We numerically study the interaction dynamics of two bright solitons with zero initial velocities in the one-dimensional dipolar Bose–Einstein condensates. Under different dipolar strengths, the two bright solitons can merge into a breathing wave, and then split or propagate constantly after several oscillating periods. We quantitatively study the breathing frequency of wave after merging and the asymmetry property of solitons after splitting,and analyze their formation mechanism by the system’s energy evolution. Also, the change of initial phase difference brings distinct effects on the soliton interaction. Our results provide insight into the new dynamical phenomena in dipolar systems and enrich the understanding for interaction between dipolar solitons.