UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

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Subject: search.filters.subject.Bose-Einstein condensates

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    How Non-Hermitian Superfluids are Special? Theory and Experiments
    (2024) Tao, Junheng; Spielman, Ian Bairstow; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Ultracold atoms emerge as a promising advanced platform for researching the principles of quantum mechanics. Its development of scientific understanding and technology enriches the toolbox for quantum simulations and quantum computations. In this dissertation work, we describe the methods we applied to build our new high-resolution 87Rb Bose-Einstein condensate (BEC) machine integrated with versatile quantum control and measurement tools. Then we describe the applications of these tools to the research of novel superfluidity and non-Hermitian physics. Superfluids and normal fluids were often studied in the context of Landau’s two-fluid model, where the normal fluid stemmed from thermally excited atoms in a superfluid background. But can there be normal fluids in the ground state of a pure BEC, at near zero temperature? Our work addressed the understanding of this scenario, and then measured the anisotropic superfluid density in a density-modulated BEC, where the result matched the prediction of the Leggett formula proposed for supersolids. We further considered and measured this BEC in rotation and found a non-classical moment of inertia that sometimes turns negative. We distinguished the roles of superfluid and normal fluid flows, and linked some features to the dipolar and spin-orbit coupled supersolids. As a second direction, we describe our capability to create non-Hermiticity with Raman lasers, digital-micromirror device (DMD), and microwave, and present our work in engineering the real space non-Hermitian skin effect with a spin-orbit coupled BEC. By use of a spin-dependent dissipative channel, we realized an imaginary gauge potential which led to nonreciprocal transport in the flat box trap. We studied the system dynamics by quenching the dissipation, and further prepared stationary edge states. We link our discoveries to a non-Hermitian topological class characterized by a quantized winding number. Finally, we discuss the exciting promises of using these tools to study many-body physics open quantum systems.
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    Classical and quantum dynamics of Bose-Einstein condensates
    (2017) Mathew, Ranchu; Tiesinga, Eite; Sau, Jay D; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    After the first experimental realization of a Bose-Einstein condensate (BEC) in 1995, BECs have become a subject of intense experimental and theoretical study. In this dissertation, I present our results on the classical and quantum dynamics of BECs at zero temperature under different scenarios. First, I consider the analog of slow light in the collision of two BECs near a Feshbach resonance. The scattering length then becomes a function of the collision energy. I derive a generalization of the Gross-Pitaevskii equation for incorporating this energy dependence. In certain parameter regimes, the group velocity of a BEC traveling through another BEC decreases. I also study the feasibility of an experimental realization of this phenomena. Second, I analyze an experiment in which a BEC in a ring-shaped trap is stirred by a rotating barrier. The phase drop across and current flow through the barrier is measured from spiral-shaped density profiles created by interfering the BEC in the ring-shaped trap and a concentric reference BEC after release from all trapping potentials. I show that a free-particle expansion is sufficient to explain the origin of the spiral pattern and relate the phase drop to the geometry of a spiral. I also bound the expansion times for which the phase drop can be accurately determined and study the effect of inter-atomic interactions on the expansion time scales. Third, I study the dynamics of few-mode BECs when they become dynamically unstable after preparing an initial state at a saddle point of the Hamiltonian. I study the dynamics within the truncated Wigner approximation (TWA) and find that, due to phase-space mixing, the expectation value of an observable relaxes to a steady-state value. Using the action-angle formalism, we derive analytical expressions for the steady-state value and the time evolution towards this value. I apply these general results to two systems: a condensate in a double-well potential and a spin-1 (spinor) condensate. Finally, I study quantum corrections beyond the TWA in the semiclassical limit. I derive general expressions for the dynamics of an observable by using the van Vleck-Gutzwiller propagator and find that the interference of classical paths leads to non-perturbative corrections. As a case study, I consider a single-mode nonlinear oscillator; this system displays collapse and revival of observables. I find that the interference of classical paths, which is absent in the TWA, leads to revivals.
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    Existence and Stability of Vortex Solutions of Certain Nonlinear Schrodinger Equations
    (2004-05-04) Kollar, Richard; Pego, Robert L; Mathematics
    The nonlinear Schrodinger equation models a wide variety of different physical phenomena ranging from nonlinear optics, water waves, magnetization of ferromagnets to Bose-Einstein condensates (BEC). The structure of the equation supports existence of topologically non-trivial solutions - vortices. Surprisingly, we demonstrate that the Landau-Lifshitz magnetization equation which is formally also a nonlinear Schrodinger equation does not admit such solutions. On the other hand, the contrary is true for the Gross-Pitaevskii equation which describes the mean-field approximation of BEC. We investigate stability of vortex solutions by means of a very reliable, sensitive and robust technique - the Evans function. This method, although limited to two dimensions, allows us to study rotating axisymmetric BEC for large particle numbers which can be unattainable by other means.We found a singly-quantized vortex linearly stable.The linear stability of multi-quantized vortices depends on the diluteness of a condensate, with alternating intervals of stability and instability. This work justifies previous results in the literature obtained by less reliable methods and opens up a few interesting questions.