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arXiv:2211.03176 · Scientific Reports

Fragmentation and correlations in a rotating Bose–Einstein condensate undergoing breakup

Sunayana Dutta, Axel U. J. Lode, Ofir E. Alon

Published Feb 27, 2023• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41598-023-29516-w

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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.
The ground state properties of strongly rotating bosons confined in an asymmetric anharmonic potential exhibit a split density distribution. However, the out-of-equilibrium dynamics of this split structure remain largely unexplored. Given that rotation is responsible for the breakup of the bosonic cloud, we investigate the out-of-equilibrium dynamics by abruptly changing the rotation frequency. Our study offers insights into the dynamics of trapped Bose-Einstein condensates in both symmetric and asymmetric anharmonic potentials under different rotation quench scenarios. In a rotationally symmetric trap, angular momentum is a good quantum number. Therefore, a rotation quench has no impact on the density distribution. In contrast, the absence of angular momentum conservation in asymmetric traps results in more complex dynamics. This allows rotation quenches to either inject into or extract angular momentum from the system. We observe and analyze these intricate dynamics both for the mean-field condensed and the many-body fragmented systems. The dynamical evolution of the condensed system and the fragmented system exhibits similarities in several observables during small rotation quenches. However, these similarities diverge notably for larger quenches. Additionally, we investigate the formation and the impact of the vortices on the angular momentum dynamics of the evolving split density. All in all, our findings offer valuable insights into the dynamics of trapped interacting bosons under different rotation quenches.
Abstract The ground state of a rotating Bose-Einstein condensate trapped in a two-dimensional anharmonic–anisotropic potential is analyzed numerically at the limit of an infinite number of particles. We find that the density breaks up along the x direction in position space and along the py direction in momentum space together with the acquisition of angular momentum. Side by side, the anisotropies of the many-particle position variances along the x and y directions and of the many-particle momentum variances along the py and px directions become opposite when computed at the many-body and mean-field levels of theory. All in all, the rotating bosons are found to possess unique correlations at the limit of an infinite number of particles, both in position and momentum spaces, although their many-body and mean-field energies per particle and densities per particle coincide and the condensate fraction is 100%. Implications are briefly discussed.
In this Dissertation the physics of trapped, attractive Bose-Einstein condensates in two and three spatial dimensions are examined. Particular emphasis is put on the collapse of the gas, when the attractive interparticle interaction is raised above a critical value. The states of the system that possess good angular momentum quantum numbers are scrutinized and connections between the angular momentum and the fragmentation of the states are investigated. In two spatial dimensions mean-field states can describe states of good angular momentum. Using a mean-field ansatz, analytical results for the energy, the occupation numbers and the stability of the ground state carrying L quanta of angular momentum are obtained. In three dimensions, however, a mean-field theory does not suffice for the proper description of angular momentum states. The eigenstates of both total angular momentum operators (L^2 and L_z) are derived and it is shown that they are generally many-body states. It is shown, moreover, that angular momentum has a general stabilizing effect on the gas and this connection is expressed quantitatively. Finally, the ground state of the gas is examined, when its container is set into external rotation. It is found that due to the attraction the symmetry of the ground state does not change, angular momentum is not transfered from the rotation to the gas and thus no significant impact in the stability is seen.
We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances.
The production of quantized vortices having diverse structures is a remarkable effect of rotating Bose-Einstein condensates. Vortex formation described by the mean-field theory is valid only in the regime of weak interactions. The exploration of the rich and diverse physics of strongly interacting BEC requires a more general approach. This study explores the vortex formation of strongly interacting and rapidly rotating BEC from a general ab initio many-body perspective. We demonstrate that the quantized vortices form various structures that emerge from an intricate interplay between the angular momentum and many-body interaction. We examine the distinct impact of the angular velocity and interaction energy on the vortex formation. Our analysis shows that, while the angular rotation generally augments the vortex formation, the interactions can enhance as well as impede the vortices production.
Recently Liu et al. [PRL 87, 030404 (2001)] examined the lowest state of a weakly-interacting Bose-Einstein condensate. In addition to other interesting results, using the method of the pair correlation function, they questioned the validity of the mean-field picture of the formation of vortices and stated that the vortices are generated at the center of the cloud. This is in apparent contradiction to the Gross-Pitaevskii approach, which predicts that the vortices successively enter the cloud from its outer parts as L/N (where N is the number of atoms in the trap and hbar(L) is the angular momentum of the system) increases. We have managed to reproduce the results of Liu et al. however a more careful analysis presented below confirms the validity of the mean-field approach.