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Quantum Phase of a Bose-Einstein Condensate with an Arbitrary Number of Atoms

Kevin Vanslette

Published Apr 28, 2011• 0 citations
OpenAlex

Abstract

This project focused on learning and reproducing aspects of BECs. This was accomplished through background research, calculating its density of energy states when inside a parabolic trap, finding the relationship for the critical BEC temperature for BEC inside a parabolic trap, looking in depth into the paper "Quantum Phase of a Bose-Einstein Condensate with an Arbitrary Number of Atoms" [1], performing MATLAB simulations using the paper's interference phase building method, and evaluating some simulation results.

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This project focused on learning and reproducing aspects of BECs. This was accomplished through background research, calculating its density of energy states when inside a parabolic trap, finding the relationship for the critical BEC temperature for BEC inside a parabolic trap, looking in depth into the paper "Quantum Phase of a Bose-Einstein Condensate with an Arbitrary Number of Atoms" [1], performing MATLAB simulations using the paper's interference phase building method, and evaluating some simulation results.
The recent developments of microgravity experiments with ultracold atoms have produced a relevant boost in the study of shell-shaped ellipsoidal Bose-Einstein condensates. For realistic bubble-trap parameters, here we calculate the critical temperature of Bose-Einstein condensation, which, if compared to the one of the bare harmonic trap with the same frequencies, shows a strong reduction. We simulate the zero-temperature density distribution with the Gross-Pitaevskii equation, and we study the free expansion of the hollow condensate. While part of the atoms expands in the outward direction, the condensate self-interferes inside the bubble trap, filling the hole in experimentally observable times. For a mesoscopic number of particles in a strongly interacting regime, for which more refined approaches are needed, we employ quantum Monte Carlo simulations, proving that the nontrivial topology of a thin shell allows superfluidity. Our work constitutes a reliable benchmark for the forthcoming scientific investigations with bubble traps.
We derive and discuss the temperature dependence of the condensate and noncondensate density profile of a Bose-Einstein condensate gas with Feshbach resonance in a parabolic trap. These quantities are calculated self-consistently using the generalized Hartree-Fock-Bogoliubov (HFB) equations within the Bogoliubov approximation. At zero temperature, the HFB equation can be solved by means of a variation method that gives the low-excitation spectrum. Moreover, within the two-body collision theory, we estimate the relationship between the number of atoms in the condensate and the external magnetic field B . The result is in good agreement with data from recent experiments.
We investigate the Bose-Einstein condensation (BEC, superfluidity) of particle-hole pairs in ultracold fermionic atoms with repulsive interactions and arbitrary polarization, which are trapped within optical lattices. In the strongly repulsive limit, the dynamics of particle-hole pairs can be described by a hard-core Bose-Hubbard model. The insulator-superfluid and charge-density-wave- (CDW) superfluid phase transitions can be induced by decreasing and increasing the potential depths with controlling the trapping laser intensity, respectively. The parameter and polarization dependence of the critical temperatures for the ordered states (BEC and/or CDW) are discussed simultaneously.