UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
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Item The complexity of simulating quantum physics: dynamics and equilibrium(2021) Deshpande, Abhinav; Gorshkov, Alexey V; Fefferman, Bill; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum computing is the offspring of quantum mechanics and computer science, two great scientific fields founded in the 20th century. Quantum computing is a relatively young field and is recognized as having the potential to revolutionize science and technology in the coming century. The primary question in this field is essentially to ask which problems are feasible with potential quantum computers and which are not. In this dissertation, we study this question with a physical bent of mind. We apply tools from computer science and mathematical physics to study the complexity of simulating quantum systems. In general, our goal is to identify parameter regimes under which simulating quantum systems is easy (efficiently solvable) or hard (not efficiently solvable). This study leads to an understanding of the features that make certain problems easy or hard to solve. We also get physical insight into the behavior of the system being simulated. In the first part of this dissertation, we study the classical complexity of simulating quantum dynamics. In general, the systems we study transition from being easy to simulate at short times to being harder to simulate at later times. We argue that the transition timescale is a useful measure for various Hamiltonians and is indicative of the physics behind the change in complexity. We illustrate this idea for a specific bosonic system, obtaining a complexity phase diagram that delineates the system into easy or hard for simulation. We also prove that the phase diagram is robust, supporting our statement that the phase diagram is indicative of the underlying physics. In the next part, we study open quantum systems from the point of view of their potential to encode hard computational problems. We study a class of fermionic Hamiltonians subject to Markovian noise described by Lindblad jump operators and illustrate how, sometimes, certain Lindblad operators can induce computational complexity into the problem. Specifically, we show that these operators can implement entangling gates, which can be used for universal quantum computation. We also study a system of bosons with Gaussian initial states subject to photon loss and detected using photon-number-resolving measurements. We show that such systems can remain hard to simulate exactly and retain a relic of the "quantumness" present in the lossless system. Finally, in the last part of this dissertation, we study the complexity of simulating a class of equilibrium states, namely ground states. We give complexity-theoretic evidence to identify two structural properties that can make ground states easier to simulate. These are the existence of a spectral gap and the existence of a classical description of the ground state. Our findings complement and guide efforts in the search for efficient algorithms.Item Cosmological Phase Transition of Composite Higgs Confinement(2021) Ekhterachian, Majid; Agashe, Kaustubh; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We study the cosmological confinement-deconfinement phase transition (PT) of nearly conformal, strongly coupled large N field theories, applicable to composite Higgs models. We find that despite strong coupling, aspects of the PT can be analyzed when the confinement is predominantly spontaneous. In this scenario, the leading contribution to the transition rate can be computed within effective field theory of dilaton-- the pseudo Nambu-Goldstone boson associated with the spontaneous breaking of conformal symmetry. We then show how the holographic dual formulation in terms of 5D warped compactifications allows for qualitative understanding of the missing pieces of the earlier described 4D picture and a quantitative improvement of the calculations. In this description the PT is from a high-temperature black-brane phase to the low-temperature Randall-Sundrum I phase, and the transition proceeds by percolation of bubbles of IR-brane nucleating from the black-brane horizon. We show that the bubble configuration interpolating between the two phases can be smooth enough to be described within 5D effective field theory. We find that cosmological PT in the minimal models can complete only after a large period of supercooling, potentially resulting in excessive dilution of primordial matter abundances. We then show how generic modifications of the minimal models can result in a much faster completion of the PT. We also study the stochastic gravitational wave background produced by the violent bubble dynamics and discuss the implications of the PT for baryogenesis.Item Quantum coherent phenomena in superconducting circuits and ultracold atoms(2010) Mitra, Kaushik; Lobb, Chris J; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis consists of theoretical studies of superconducting qubits, and trapped bosons and fermions at ultracold temperature. In superconducting qubits I analyze the resonant properties and decoherence behavior of dc SQUID phase qubits, in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias lead. Typically qubit states in phase qubits are detected by tunneling it to the voltage state. I propose an alternate non-destructive readout mechanism which relies on the difference in the magnetic flux through the SQUID loop due to state of the qubit. I also study decoherence effects in a dc SQUID phase qubit caused by the isolation circuit. When the frequency of the qubit is at least two times larger than the resonance frequency of the isolation circuit, I find that the decoherence time of the qubit is two orders of magnitude larger than the typical ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the isolation circuit. This theory is extended to other similar superconducting quantum devices and has been applied to experiments from the group at the University of Maryland. I also demonstrate, theoretically, vacuum Rabi oscillations, analogous to circuit-QED, in superconducting qubits coupled to an environment with resonance. The result obtained gives an exact analytical expression for coherent oscillation of state between the system (the qubit) and the environment with resonance. Next I investigate ultracold atoms in harmonically confined optical lattices. They exhibit a `wedding cake structure' of alternating Mott shells with different number of bosons per site. In regions between the Mott shells, a superfluid phase emerges at low temperatures which at higher temperatures becomes a normal Bose liquid. Using finite-temperature quantum field theoretic techniques, I find analytically the properties of the superfluid, Bose liquid, and Mott insulating regions. This includes the finite temperature order parameter equation for the superfluid phase, excitation spectrum, Berezinskii-Kosterlitz-Thouless transition temperature and vortex-antivortex pair formation (in the two dimensional case), finite temperature compressibility and density - density correlation function. I also study interacting mixtures of ultracold bosonic and fermionic atoms in harmonically confined optical lattices. For a suitable choice of parameters I find emergence of superfluid and Fermi liquid (non-insulating) regions out of Bose-Mott and Fermi-band insulators, due to finite boson and fermion hopping. I also propose a possible experiment for the detection of superfluid and Fermi liquid shells through the use of Gauss-Laguerre and Gaussian beams followed by Bragg spectroscopy. Another area I explore is ultracold heteronuclear molecules such as KRb, RbCs and NaCs. I obtain the finite and zero-temperature phase diagram of bosons interacting via short range repulsive interactions and long-ranged isotropic dipolar interactions in two-dimensions. I build an analytical model for such systems that describes a first order quantum phase transition at zero temperature from a triangular crystalline phase (analogous to Wigner crystal phase of electrons) to superfluid phase. At finite temperature the crystalline phase melts, due to topological defects, to a hexatic phase where translational order is destroyed but hexagonal orientational order is preserved. Further temperature increase leads to the melting of the hexatic phase into a normal dipolar Bose liquid.Item Phase transitions of high-temperature superconductors(2007-07-30) Li, Su; Lobb, Christopher J; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis phase transitions of the high temperature superconductor YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) have been investigated in both zero and non-zero magnetic field. Current-Voltage characteristics of thin films and single crystals have been studied to determine the transition temperature and critical exponents. We optimized our film samples to ensure that they are of single phase, $c$-axis oriented and homogeneous. High-quality crystal samples were provided by Dr.~Kouji Segawa and Dr.~Yoichi Ando. In the zero-field transition, finite-size effects, which can obscure the phase transition by introducing ohmic tails below the transition temperature, are observed in the current-voltage curves of even the thickest film (2400 \AA) at low currents. The data at high currents are not affected by finite-size effects so that we can use derivative plots to determine $T_c$ and the dynamic critical exponent $z$. The current-voltage curves of crystals' data, however, are not affected by finite-size effects even in the lowest current measured as expected. $z$ determined from YBCO crystals are consistent with the one determined from YBCO films: $z=1.5 \pm 0.2$. This is a strong evidence that the dynamic universality class of high-temperature superconductors belongs to model-E dynamics in zero field. The static critical exponent $\nu$ determined from %the ohmic tails above $T_c$ is $0.85\pm 0.2$ for the melting line $(T_c-T_{g(m)})\sim H^{1/2\nu_0}$ is $0.68 \pm 0.1$ for crystal and $0.62\pm 0.1$ for thin films. The phase transitions in the mixed state (non-zero field) are more complicated. In the phase transition of YBCO thin films in field, finite-size effects are again observed. The presence of magnetic field leads to anisotropic vortex loops so that finite-size effects are enhanced. We observe a magnetic field $H$ dependence of the crossover current density $J_{min}$ as well as the exponent $z$. At $H>1$ T, $J_{min}$ and $z$ stay relatively constant. $z\simeq 2$ at high field implies a crossover from model-E dynamics to model-A dynamics. Finally, we will discuss $E-J$ characteristics of the first-order melting transition of untwinned YBCO single crystals.