# name
Tonks-Girardeau gas in different potential traps by exact diagonalization

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Màster Oficial en Física Avançada, Facultat de Física, Universitat de Barcelona, Curs: 2014, Tutors: M.A. Garcia-March i A. Polls

# metadata.dc.description.abstract[].value
We computed the second-quantized many-mode Hamiltonian for spinless ultracold bosons trapped
in di erent one-dimensional potentials and diagonalized it for a small number of atoms. We observed
the transition from the non-interacting gas to the Tonks-Girardeau gas, i.e. the fermionization process,
as we increase the strength of the interactions between the atoms. We computed the energy
spectrum, the one-body density matrix, the two-body correlations, the momentum distribution, the
natural orbitals and the occupations for di erent interaction strengths. We compared the fermionization
in di erent potentials with special attention to the largest occupation of the natural orbits,
the build up of quantum many-body correlations between di erent parts of the system, and the
energy of the ground and excited states.

# metadata.dc.title[].value
Tonks-Girardeau gas in different potential traps by exact diagonalization