Computational study of low-dimensional quantum systems

Résumé

In this dissertation we studied the phase diagrams of different systems with two common characteristics: the particles that constitute them are confined to a more or lesser extent, and their masses are small enough for quantum effects to be appreciable. In addition, we considered only the regime in which the temperature is close to absolute zero, what means that the corresponding ground states are expected to be good descriptions of those arrangements. To obtain those ground states we used the diffusion Monte Carlo method, a stochastic technique that allows us to calculate the lowest energy state of any bosonic system within statistical accuracy and taking into account the atom-atom correlations. The first part of this work will focus on the phase diagram of D_2 on C-graphane, the hydrogenated version of graphene, a compound synthesised for the first time in 2009. Our study is a continuation of a long series of efforts in which the behaviour of quantum gases such as He-4, H_2, He-3, D_2, on quasi-two dimensional (graphite, graphene) or quasi-one dimensional (carbon nanotubes) confinements were considered. The ultimate goal was the experimental discovery or the theoretical prediction of new phases, different from the full three-dimensional homogeneous ones. Within this frame, we calculated the complete phase diagram of ortho-D_2 on graphane, finding it very similar to the one obtained previously for the same adsorbate on graphite [Phys. Rev. B 42, 587(1990), Phys. Rev. 85, 155427(1998)], even though the ground state was a different registered solid "delta" instead of "sqrt(3) x sqrt(3)". The second part of this dissertation is concerned with the behaviour of neutral atoms loaded in quasi-one-dimensional optical lattices. An optical lattice is a periodic pattern of potential wells created by the constructive interference of two or more laser beams. The seminal work of Jaksch [Phys. Lett. 81, 3108(1998)] opened the door to many theoretical works on the subject by establishing the equivalence, under certain conditions, of the full optical lattice Hamiltonian and the well-known Bose Hubbard model. That identification proved to be successful when Greiner et al [Nature 415, 39(2002)], found experimentally a Mott insulator, one of the phases known to be supported by the Bose-Hubbard discrete Hamiltonian. Unfortunately, neutral atoms in optical lattices are not always well described by a Bose-Hubbard model. To show that, we computed the phase diagrams of different quasi-one dimensional optical lattices using their full continuous Hamiltonians. We did so both for homogeneous and longitudinally confined systems, finding that even though the phases (or states) were similar for both Hamiltonians, the Bose-Hubbard model underestimates the optical potential depths necessary to create insulator phases (or insulator domains in finite systems). In the same line, a separate study on a disordered system concluded that in a continuous description the stability zone of the Bose glass decreases with respect to the results for with a Bose-Hubbard model.