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arXiv:1409.0323 · Physical Review A

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

Shachar Klaiman, Axel U. J. Lode, Alexej I. Streltsov, L. S. Cederbaum, Ofir E. Alon

Published Oct 20, 2014• 35 citations
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Abstract

A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed using a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs.

DOI
10.1103/physreva.90.043620

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A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed using a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs.
An essentially exact approach to compute the wave function in the time-dependent many-boson Schrödinger equation is derived and employed to study accurately the process of splitting a trapped condensate. As the trap transforms from a single to double well the ground state changes from a coherent to a fragmented state. We follow the role played by many-body excited states during the splitting process. Among others, a "counterintuitive" regime is found in which the evolution of the condensate when the splitting is sufficiently slow is not to the fragmented ground state, but to a low-lying excited state which is a coherent state. Experimental implications are discussed.
The fragmentation of the ground state of a repulsive condensate immersed into a double-trap potential is found to be a general and critical phenomenon. It takes place for a given number of bosons if their scattering length is larger than some critical value or for a given value of the scattering length if the number of bosons is above some critical number. We demonstrate that the geometry of the inner trap determines these critical parameters while the number of the fragments and the fraction of bosons in the various fragments can be manipulated by the outer trap. There is also a maximal number of bosons for which the ground state is fragmented. If this number is exceeded, the fragmented state becomes a very low-lying excited state of the condensate. This maximal number of bosons can be substantially manipulated by varying the inner and outer traps. To study threefold fragmentation we have chosen a potential well with two barriers as the inner trap and embedded in two types of outer ones. A manifold fragmentation is also addressed.
The theoretical investigation of rotating Bose-Einstein condensates has mainly focused on the emergence of quantum vortex states and the condensed properties of such systems. In the present work, we concentrate on other facets by examining the impact of rotation on the ground state of weakly interacting bosons confined in anharmonic potentials computed both at the mean-field level and particularly at the many-body level of theory. For the many-body computations, we employ the well-established many-body method known as the multiconfigurational time-dependent Hartree method for bosons. We present how various degrees of fragmentation can be generated following the breakup of the ground state densities in anharmonic traps without ramping up a potential barrier for strong rotations. The breakup of the densities is found to be associated with the acquisition of angular momentum in the condensate due to the rotation. In addition to fragmentation, the presence of many-body correlations is examined by computing the variances of the many-particle position and momentum operators. For strong rotations, the many-body variances become smaller than their mean-field counterparts, and one even finds a scenario with opposite anisotropies of the mean-field and many-body variances. Further, it is observed that for higher discrete symmetric systems of order k, namely three-fold and four-fold symmetry, breakup to k sub-clouds and emergence of k-fold fragmentation take place. All in all, we provide a thorough many-body investigation of how and which correlations build up when a trapped Bose-Einstein condensate breaks up under rotation.
We study the dynamic process of splitting a condensate by raising a potential barrier in the center of a harmonic trap. We use a two-mode model to describe the phase coherence between the two halves of the condensate. Furthermore, we explicitly consider the spatial dependence of the mode funtions, which varies depending on the potential barrier. This allows us to get the tunneling coupling between the two wells and the on-site energy as a function of the barrier height. Moreover, we can get some insight into the collective modes that are excited by raising the barrier. We describe the internal and external degrees of freedom by variational ansatz. We distinguish the possible regimes as a function of the characteristic parameters of the problem and identify the adiabaticity conditions.
We explore the energy dynamics of a two dimensional (2D) harmonically trapped Bose-Einstein condensate inside a box potential, excited by a moving red-detuned laser potential (RDLP). For an RDLP velocity vvv less than a critical value vcv_cvc​, energy oscillations are observed to begin simultaneously with the motion of the RDLP. For v>vcv > v_cv>vc​, these oscillations are delayed through a transient in the energy. At the end of the delay time tonst_{ons}tons​, the energy oscillations are regenerated again, and tonst_{ons}tons​ is found to depend on vvv through universal relations for two cases: one for an RDLP depth sufficient to break off a BEC fragment, another for a depth insufficient to split the BEC. In the case of splitting, tonst_{ons}tons​ exactly equals the time it takes the BEC fragment (dragged by the RDLP trough) to reach the hard wall of the box potential.
We study the quantum dynamics of a Bose–Einstein condensate trapped in a double-well potential with a rising interwell barrier. We analytically find the characteristic timescales of the splitting process and compare our results with numerical analyses available in the literature. In the first stage of the dynamics, the relative phase of the two condensates evolves adiabatically. At a critical time t ad , small-amplitude phase fluctuations around the average trajectory increase exponentially fast, signalling the breakdown of adiabaticity. After this stage, it is still not possible to neglect the tunnelling exchange between the two wells. We find highly non-trivial dependences of the dephasing time on t ad and on the ramping time of the interwell barrier.