Large scattering lengths and long-range interactions in ultracold atomic gases

Risto Sarjonen

Research output: ThesisDoctoral ThesisCollection of Articles


This thesis studies bosonic and fermionic quantum gases. In the first part, a variational many-body theory is used to explain a Bragg scattering experiment carried out on a bosonic quantum gas [S.B. Papp et al. Bragg Spectroscopy of a Strongly Interacting 85Rb Bose-Einstein Condensate. Phys. Rev. Lett. 101, 135301 (2008)]. A key feature in the experiment was the use of a Feshbach resonance, which made large values of the scattering length accessible. Due to the large values of the scattering length, existing models such as the Beliaev model could not be used to explain the observations, and therefore the experiment was a particularly interesting one to analyze. In our first approach, we constructed ad hoc potentials that fitted the observed excitation spectrum, and later we improved our approach by using T-matrix formalism to describe the Feshbach resonant system. All in all, the phenomenological model we developed fits the observed excitation spectrum and yields correct molecular Feshbach resonance state energies in certain cases. The second part of this thesis studies fermionic quantum gases. We focus on studying a gas of spin-1/2 particles confined to a spin-dependent optical lattice. The lattice geometry is such that the up-spin component is loaded in a honeycomb lattice, and the down-spin component is confined to the underlying triangular lattice. We considered attractive on-site and nearest-neighbor interactions, and formulated the nearest-neighbor interaction term in such a way that it takes into account the possibility of spontaneous time-reversal symmetry breaking. Furthermore, we took into account the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which breaks spatial symmetry. Within a mean-field approximation, we showed that the FFLO state is the ground state of the system in many instances. In addition, we found out that the system spontaneously breaks time-reversal symmetry if the nearest-neighbor interaction strength is large. Due to the time-reversal symmetry breaking, the system has topologically non-trivial phases characterized by nonzero Chern numbers. Finally, there were also cases where the time-reversal symmetry was broken in the FFLO phase, and thus we found a phase where spatial and time-reversal symmetries are simultaneously broken.
Translated title of the contributionLarge scattering lengths and long-range interactions in ultracold atomic gases
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Törmä, Päivi, Supervising Professor
  • Törmä, Päivi, Thesis Advisor
Print ISBNs978-952-60-6121-4
Electronic ISBNs978-952-60-6122-1
Publication statusPublished - 2015
MoE publication typeG5 Doctoral dissertation (article)


  • quantum gases
  • Bose-Einstein condensate
  • Feshbach resonance
  • optical lattice
  • superfluidity
  • FFLO
  • topological phases


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