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Gasos quàntics unidimensionals: de pocs a molts cossos

Amorós Binefa, Júlia

Published Jul 7, 2016• 0 citations
OpenAlex

Abstract

Following a recent experimental study [Wenz et al. Science 342, 457 (2013)] on the achievement of the thermodynamic limit in a system of one-dimensional (1D) fermions, the project aims to investigate theoretically a similar problem for 1D Bose gases. By considering a system of bosons confined in a 1D harmonic trap and interacting with a single impurity, the plan is to calculate the binding energy of the impurity as the number of bosons in the bath is increased. The analysis will be performed by varying both the coupling strength of the bath and the interspecies interactio

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Following a recent experimental study [Wenz et al. Science 342, 457 (2013)] on the achievement of the thermodynamic limit in a system of one-dimensional (1D) fermions, the project aims to investigate theoretically a similar problem for 1D Bose gases. By considering a system of bosons confined in a 1D harmonic trap and interacting with a single impurity, the plan is to calculate the binding energy of the impurity as the number of bosons in the bath is increased. The analysis will be performed by varying both the coupling strength of the bath and the interspecies interactio
Following a recent experimental study [Wenz et al. Science 342, 457 (2013)] on the achievement of the thermodynamic limit in a system of one-dimensional (1D) fermions, the project aims to investigate theoretically a similar problem for 1D Bose gases. By considering a system of bosons confined in a 1D harmonic trap and interacting with a single impurity, the plan is to calculate the binding energy of the impurity as the number of bosons in the bath is increased. The analysis will be performed by varying both the coupling strength of the bath and the interspecies interactio
The transition from ``few to many'' has recently been probed experimentally in an ultracold harmonically confined one-dimensional lithium gas, in which a single impurity atom interacts with a background gas consisting of one, two, or more identical fermions [A. N. Wenz et al., Science 342, 457 (2013)]. For repulsive interactions between the background or majority atoms and the impurity, the interaction energy for relatively moderate system sizes was analyzed and found to converge toward the corresponding expression for an infinitely large Fermi gas. Motivated by these experimental results, we apply perturbative techniques to determine the interaction energy for weak and strong coupling strengths and derive approximate descriptions for the interaction energy for repulsive interactions with varying strength between the impurity and the majority atoms and any number of majority atoms.
We study a system of ultra-cold dipolar Bose gas atoms confined in a two-dimensional (2D) harmonic trap with a dipolar impurity implanted at the center of the trap. Due to recent experimental progress in dipolar condensates, we focused on calculating properties of dipolar impurity systems that might guide experimentalists if they choose to study impurities in dipolar gases. We used the Gross–Pitaevskii formalism solved numerically via the split-step Crank–Nicolson method. We chose parameters of the background gas to be consistent with dysprosium (Dy), one of the strongest magnetic dipoles and of current experimental interest, and used chromium (Cr), erbium (Er), terbium (Tb), and Dy for the impurity. The dipole moments were aligned by an external field along what was chosen to be the z-axis, and we studied 2D confinements that were perpendicular or parallel to the external field. We show density contour plots for the two confinements, 1D cross-sections of the densities, calculated self-energies of the impurities while varying both number of atoms in the condensate and the symmetry of the trap. We also calculated the time evolution of the density of an initially pure system where an impurity is introduced. Our results show that while the self-energy increases in magnitude with increasing number of particles, it is reduced when the trap anisotropy follows the natural anisotropy of the gas, i.e., elongated along the z-axis in the case of parallel confinement. This work builds upon work conducted in Bose gases with zero-range interactions and demonstrates some of the features that could be found when exploring dipolar impurities in 2D Bose gases.