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Quantum Phase Transitions in the Bose Hubbard Model and in a Bose-Fermi Mixture

Duchon, Eric Nicholas

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2013, Doctor of Philosophy, Ohio State University, Physics.
Ultracold atomic gases may be the ultimate quantum simulator. These isolated systems have the lowest temperatures in the observable universe, and their properties and interactions can be precisely and accurately tuned across a full spectrum of behaviors, from few-body physics to highly-correlated many-body effects. The ability to impose potentials on and tune interactions within ultracold gases to mimic complex systems mean they could become a theorist's playground. One of their great strengths, however, is also one of the largest obstacles to this dream: isolation. This thesis touches on both of these themes. First, methods to characterize phases and quantum critical points, and to construct finite temperature phase diagrams using experimentally accessible observables in the Bose Hubbard model are discussed. Then, the transition from a weakly to a strongly interacting Bose-Fermi mixture in the continuum is analyzed using zero temperature numerical techniques. Real materials can be emulated by ultracold atomic gases loaded into optical lattice potentials. We discuss the characteristics of a single boson species trapped in an optical lattice (described by the Bose Hubbard model) and the hallmarks of the quantum critical region that separates the superfluid and the Mott insulator ground states. We propose a method to map the quantum critical region using the single, experimentally accessible, local quantity R, the ratio of compressibility to local number fluctuations. The procedure to map a phase diagram with R is easily generalized to inhomogeneous systems and generic many-body Hamiltonians. We illustrate it here using quantum Monte Carlo simulations of the 2D Bose Hubbard model. Secondly, we investigate the transition from a degenerate Fermi gas weakly coupled to a Bose Einstein condensate to the strong coupling limit of composite boson-fermion molecules. We propose a variational wave function to investigate the ground state properties of such a Bose-Fermi mixture with equal population, as a function of increasing attraction between bosons and fermions. The variational wave function captures the weak and the strong coupling limits and at intermediate coupling we make two predictions using zero temperature quantum Monte Carlo methods: (I) a complete destruction of the atomic Fermi surface and emergence of a molecular Fermi sea that coexists with a remnant of the Bose-Einstein condensate, and (II) evidence for enhanced short-ranged fermion-fermion correlations mediated by bosons.
Nandini Trivedi, Ph.D. (Advisor)
Tin-Lun Ho, Ph.D. (Committee Member)
Gregory Lafyatis, Ph.D. (Committee Member)
Richard Furnstahl, Ph.D. (Committee Member)
186 p.

Recommended Citations

Citations

  • Duchon, E. N. (2013). Quantum Phase Transitions in the Bose Hubbard Model and in a Bose-Fermi Mixture [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1386002245

    APA Style (7th edition)

  • Duchon, Eric. Quantum Phase Transitions in the Bose Hubbard Model and in a Bose-Fermi Mixture. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1386002245.

    MLA Style (8th edition)

  • Duchon, Eric. "Quantum Phase Transitions in the Bose Hubbard Model and in a Bose-Fermi Mixture." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1386002245

    Chicago Manual of Style (17th edition)