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Register a new userQuantum Information Approach to Rotating Bose-Einstein Condensate
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We investigate the 2D weakly interacting Bose-Einstein condensate in a rotating trap by the tools of quantum information theory. The critical exponents of the ground state fidelity susceptibility and the correlation length of the system are obtained for the quantum phase transition when the frst vortex is formed. We also find the single-particle entanglement can be an indicator of the angular momentums for some real ground states. The single-particle entanglement of fractional quantum Hall states such as Laughlin state and Pfaffian state is also studied.
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We study the information entropy, order, disorder, and complexity for the two-dimensional (2D) rotating and nonrotating Bose-Einstein condensates. The choice of our system is a complete theoretical laboratory where the complexity is controlled by the two-body contact interaction strength and the rotation frequency ($Omega$) of the harmonic trap. The 2D nonrotating condensate shows the complexity of the category I where the disorder-order transition is triggered by the interaction strength. In the rotating condensates, $Omega$ is chosen as the disorder parameter when the interaction strength is fixed. With respect to $Omega$, the complexity shifts between the maximum and minimum confirm the existence of category II complexity in the rotating condensate. Also, We consider the interaction strength as the disorder parameter when $Omega$ is unchanged and complexity as a function of interaction strength exhibits category III complexity. The present work also includes the calculation of upper bound and lower bound of entropy for 2D quantum systems.
The ground state of a Bose-Einstein condensate in a two-dimensional trap potential is analyzed numerically at the infinite-particle limit. It is shown that the anisotropy of the many-particle position variance along the $x$ and $y$ axes can be opposite when computed at the many-body and mean-field levels of theory. This is despite the system being $100%$ condensed, and the respective energies per particle and densities per particle to coincide.
We have computed phase diagrams for rotating spin-1 Bose-Einstein condensates with long-range magnetic dipole-dipole interactions. Spin textures including vortex sheets, staggered half-quantum- and skyrmion vortex lattices and higher order topological defects have been found. These systems exhibit both superfluidity and magnetic crystalline ordering and they could be realized experimentally by imparting angular momentum in the condensate.
The excitation spectrum of a highly-condensed two-dimensional trapped Bose-Einstein condensate (BEC) is investigated within the rotating frame of reference. The rotation is used to transfer high-lying excited states to the low-energy spectrum of the BEC. We employ many-body linear-response theory and show that, once the rotation leads to a quantized vortex in the ground state, already the low-energy part of the excitation spectrum shows substantial many-body effects beyond the realm of mean-field theory. We demonstrate numerically that the many-body effects grow with the vorticity of the ground state, meaning that the rotation enhances them even for very weak repulsion. Furthermore, we explore the impact of the number of bosons $N$ in the condensate on a low-lying single-particle excitation, which is describable within mean-field theory. Our analysis shows deviations between the many-body and mean-field results which clearly persist when $N$ is increased up to the experimentally relevant regime, typically ranging from several thousand up to a million bosons in size. Implications are briefly discussed.
We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a gaussian ansatz.
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