Browsing by Author "Hazzard, Kaden R. A."

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    Computational dynamics of fermion and spin systems
    (2020-04-23) White, Ian G; Hazzard, Kaden R. A.
    The study of quantum dynamics is an increasingly important aspect of atomic, molecular and optical physics, as well as condensed-matter physics and other disciplines. It is essential in order to understand non-equilibrium phenomena which do not fit within the framework of equilibrium thermodynamics, such as many-body localization, dynamical quantum phase transitions, and non-equilibrium steady states in driven-dissipative systems. However, the exact calculation of dynamical observables is extremely difficult in general for several reasons, which makes it challenging for theoretical predictions and analyses to keep pace with rapidly advancing experiments. In this thesis I use and develop several computational methods to investigate the dynamics of quantum many-body systems, with the two goals of better understanding the evolution of local observables and correlation functions in spin and Fermion systems as well as creating and testing more effective numerical methods for solving quantum dynamics problems. I explore quantum dynamics by using Hamiltonian parameter quenches in several commonly-used models in AMO physics and elsewhere: the Fermi-Hubbard model, the XXZ model, and the transverse-Ising model. The first represents a system of short-range interacting Fermions, while the latter two represent spin systems with different spin-spin couplings and magnetic field terms. All of these models can be realized in current experiments. First, I derive an exact solution for an extreme interaction quench in the Fermi-Hubbard model, from a strongly-interacting initial state to a noninteracting final Hamiltonian. From this result I show that there are nontrivial transient connected correlations, despite the fact that the system has very high temperature and a noninteracting Hamiltonian. Those features would suppress such correlations in equilibrium, but the dynamical correlations are still significant. Then, I develop and examine two numerical methods for solving dynamics of the spin expectation values and correlation functions in the transverse-Ising and XXZ models. Both methods rely on approximating a thermodynamically large system with a much smaller and more computationally tractable cluster of lattice sites, or a series of clusters. The first method is a dynamical numerical linked cluster expansion (NLCE). NLCEs have already been used successfully on systems in thermodynamic equilibrium, and I extended the technique to directly compute the dynamics of an observable after a quantum quench. I review the general NLCE method, describe my dynamical variant of it, and compute the quench dynamics of spin and correlation observables in the transverse-Ising and XXZ models. The second method, which I term the adaptive-boundary cluster method, relies on recently refined bounds on information propagation in quantum systems to choose a cluster of lattice sites that minimizes the finite size error bound of a dynamical computation. I briefly review these bounds, and describe a new algorithm which uses them to construct a cluster whose boundary is chosen according to a related error estimate. Such an adaptive-boundary cluster has the property that there exists a computable upper bound on the finite size error of observables measured at the cluster center, and this error bound is nearly minimal when compared to that of other clusters of the same size. I then compute the quench dynamics of spin and correlation observables in the transverse-Ising model using the adaptive boundary clusters. I apply this method to both uniform and strongly disordered systems. To evaluate the effectiveness of both dynamical NLCE and adaptive-boundary clusters, I compare the results obtained using them to results from a standard and general purpose numerical method: exact solvers applied a rectangular cluster with periodic boundary conditions. Both of the new methods usually converge faster and are more accurate than the standard method for comparable cluster sizes. This thesis illustrates that choosing numerical methods which take advantage of the geometric and entanglement structure of the initial state and Hamiltonian can substantially enhance our ability to study quantum dynamics, by reducing the computational cost of numerically exact solutions. I conclude with a discussion of various avenues for future research to build on this work.
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    Mesoscale Models for the Study of Emergent Behaviors Arising from Protein Interactions
    (2022-11-28) Bueno Basurco, Carlos Andres; Wolynes, Peter G.; Onuchic, Jose N.; Hazzard, Kaden R. A.
    Proteins are versatile biopolymers in living systems; they exhibit a great diversity of functions depending on the order in which their amino acids are arranged. Most protein functions, like mechanical or regulatory functions, only emerge from the interactions with other proteins and macromolecules. This dissertation describes how we have developed and adapted new computational models to investigate emergent structural and dynamic properties of protein interactions. Chapter 1 presents a review of the two systems of interest to be explored in successive chapters: the regulation of the actin cytoskeleton and the control of DNA transcription by the nuclear factor kappa B (NF-κB). It also introduces some models developed to study the interactions of proteins with actin filaments and with DNA. Chapters 2 and 3 focus on protein interactions in the actin cytoskeleton network. Chapter 2 describes how we have estimated the mechanical and dynamical properties of actin networks using polymer theory. We developed a simplified mathematical mean-field model of F-actin polymerization, cross-linking, and branching based on mass action kinetics. Then we obtained an analytical solution to the connectivity, rigidity, and force percolation transitions using a generalized version of the Flory-Stockmayer theory. Chapter 3 describes how we used a computational mechano-chemical model to simulate the conditions where the actin networks exhibit rare sudden movements. We show that actin networks containing Arp2/3 undergo sudden releases of strain known as “cytoquakes”. Chapters 4 and 5 focus on DNA-protein interactions. Chapter 4 describes a new implementation to simulate protein and DNA dynamics for large systems that we developed. This new procedure retains the accuracy of previous methods our group developed with a 30-fold speedup and eases the introduction of new potential energy terms. Chapter 5 describes how we used this protein a
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    Second-scale rotational coherence and dipolar interactions in a gas of ultracold polar molecules
    (Springer Nature, 2024) Gregory, Philip D.; Fernley, Luke M.; Tao, Albert Li; Bromley, Sarah L.; Stepp, Jonathan; Zhang, Zewen; Kotochigova, Svetlana; Hazzard, Kaden R. A.; Cornish, Simon L.; Rice Center for Quantum Materials
    Ultracold polar molecules combine a rich structure of long-lived internal states with access to controllable long-range anisotropic dipole–dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous differential light shifts. Here we demonstrate a rotationally magic optical trap for 87Rb133Cs molecules that supports a Ramsey coherence time of 0.78(4) s in the absence of dipole–dipole interactions. This is estimated to extend to >1.4 s at the 95% confidence level using a single spin-echo pulse. In our trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation.
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    Strongly interacting Rydberg atoms in synthetic dimensions with a magnetic flux
    (Springer Nature, 2024) Chen, Tao; Huang, Chenxi; Velkovsky, Ivan; Hazzard, Kaden R. A.; Covey, Jacob P.; Gadway, Bryce; Rice Center for Quantum Materials
    Synthetic dimensions, wherein dynamics occurs in a set of internal states, have found great success in recent years in exploring topological effects in cold atoms and photonics. However, the phenomena thus far explored have largely been restricted to the non-interacting or weakly interacting regimes. Here, we extend the synthetic dimensions playbook to strongly interacting systems of Rydberg atoms prepared in optical tweezer arrays. We use precise control over driving microwave fields to introduce a tunable U(1) flux in a four-site lattice of coupled Rydberg levels. We find highly coherent dynamics, in good agreement with theory. Single atoms show oscillatory dynamics controllable by the gauge field. Small arrays of interacting atoms exhibit behavior suggestive of the emergence of ergodic and arrested dynamics in the regimes of intermediate and strong interactions, respectively. These demonstrations pave the way for future explorations of strongly interacting dynamics and many-body phases in Rydberg synthetic lattices.