Master of Science, The Ohio State University, 2012, Physics

We show that photon number measurement can be used to detect superfluidity for a two-band Bose-Hubbard model coupled to a cavity field. The atom-photon coupling induces transitions between the two internal atomic levels and results in entangled polaritonic states. In the presence of a cavity field, we find different photon numbers in the Mott-insulating versus superfluid phases, providing a method of distinguishing the atomic phases by photon counting. Furthermore, we examine the dynamics of the photon field after a rapid quench to zero atomic hopping by increasing the well depth. We find a robust correlation between the field's quench dynamics and the initial superfluid order parameter, thereby providing a novel and accurate method of determining the order parameter.

Committee: Nandini Trivedi PhD (Advisor); Louis DiMauro PhD (Committee Member) Subjects: Physics; Quantum Physics

Doctor of Philosophy, The Ohio State University, 2013, 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 w (open full item for complete abstract)

Committee: Nandini Trivedi Ph.D. (Advisor); Tin-Lun Ho Ph.D. (Committee Member); Gregory Lafyatis Ph.D. (Committee Member); Richard Furnstahl Ph.D. (Committee Member) Subjects: Condensed Matter Physics

PhD, University of Cincinnati, 2009, Arts and Sciences : Physics

This work presents extensions of the numerical methods for strongly correlated electron systems. The first part of the thesis discusses extensions and applications of the quantum cluster theories to the systems of classical spins. It is shown that such extensions can provide faster convergence through better estimation of the effects of fluctuations, yet they can also possess shortcomings which limit their application in the studies of the phase transitions. The second part of the thesis is dedicated to the numerical studies of the Hubbard model. Present Quantum Monte Carlo methods are reviewed and relationships among them are elucidated. The final part of the thesis contains the application of the developed numerical methods to investigate the phase diagram of the two-dimensional Hubbard model, especially the evidence of the Quantum Critical Point (QCP) at a finite doping. High accuracy results for thermodynamic quantities are presented in support of the existence of the QCP at a finite doping in two-dimensional Hubbard model. The relation of the QCP to the charge fluctuations is revealed and a mechanism that relates QCP to incipient phase separation is proposed.

Committee: Michael Ma PhD (Committee Chair); Leigh Smith PhD (Committee Member); L.C.R. Wijewardhana PhD (Committee Member); Mark Jarrell PhD (Committee Member) Subjects: Condensation

PhD, University of Cincinnati, 2009, Arts and Sciences : Physics

Many properties of the two-dimensional Hubbard model have been explored for the model parameters appropriate for strongly correlated electronic systems, especially cuprate superconductors. Most of the calculations are done using a well-established dynamical cluster quantum Monte Carlo method. Using this method, we investigate the effect of long-range hoppings on superconductivity with and without the presence of phonons on small clusters. The superconducting transition temperature, Tc, is found to generally decrease with a negative next nearest neighbor hopping, t′. In the presence of the Holstein phonons, a finite t′ enhances Tc in the under-doped region for the hole-doped system, consistent with band structure calculations and experiment. The validity of the spin-susceptibility-mediated pairing in this model is studied and found to yield symmetries other than d-wave when a finite t′ is considered. A new numerical algorithm for solving the embedded cluster problems is introduced, and used to calculate the thermodynamic properties of the model on larger clusters, especially those associated with the quantum critical behavior at finite doping. Our results suggest that the quantum critical point (QCP) which separates the Fermi liquid and pseudogap regions, is the second order terminus of the line of first order phase separation transition in the limit when a positive t′ goes to zero. For small t′, the superconducting dome is centered at the QCP, suggesting that charge fluctuations might have a role in the pairing mechanism in this model.

Committee: Michael Ma (Committee Chair) Subjects:

Doctor of Philosophy (PhD), Ohio University, 2004, Physics (Arts and Sciences)

Physical nanoscale systems have been analyzed both from an electrostatic point of view and quantum mechanically with respect to quantum computation. We introduce an elaborate code for the efficient numerical simulation of nanoscale electrostatics via a higher – order relaxation algorithm with a large variety of boundary conditions which then is applied to a set of physically relevant problems. Great emphasis is put on screening effects as well as capacitive coupling between spatially separated conducting regions. Specifically, we analyze the depletion of a two – dimensional electron gas using different methods. The effect of surface charges due to the pinning of the Fermi level at a semiconductor surface is shown to play an important role in that it can shift the whole system characteristics, underlining the importance of chemical potentials and work functions. The capacitive coupling is further used to model the interactions in an interacting network of quantum dots, and the use of the capacitance formalism in the quantum mechanical context is explicitly justified. Quantum dot arrays are then analyzed on a general footing with respect to quantum computation and charge qubits based on an extended Hubbard Hamiltonian model. For systems with at most two operative electrons, general restrictions apply, introducing certain constraints on what realizations of this type of charge qubit may eventually look like. Furthermore, the interaction of the macroscopic world with the quantum dot network via quantum gates is discussed. Again, general arguments allow us to rule out certain scenarios of quantum gates. For example it turns out that capacitive coupling alone is not sufficient for full single qubit operation. Alternative ways are discussed, and finally, by using an external magnetic field and its resulting Aharonov – Bohm phases on the array, full single qubit operation based on charge is demonstrated.

Committee: Sergio Ulloa (Advisor) Subjects: Physics, Condensed Matter