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Theoretical Research

Quantum Simulation and Quantum Computing

Principal Investigator: Eliot Kapit

Quantum simulation—the art of arranging collections of simple quantum objects, such as trapped atoms or microscopic superconducting circuits, and tuning their interactions to mimic the behavior of much more complex systems—is a revolutionary new tool for physical inquiry. As an example, current experiments using cold atoms, trapped and cooled to a billionth of a degree above absolute zero, can accurately model the properties of electrons in a material, allowing a host of new experiments (such as instantaneous measurement of all the particles’ positions or momenta) that could never be performed in the original system. Similarly, superconducting device arrays can induce strong interactions between microwave photons trapped within them, generating complex many-body states of light. Most enticingly, quantum simulators can realize phenomena that would never occur naturally, allowing us to engineer and manipulate new quantum states with fascinating properties.

As a theorist, my research goal is to identify new and exotic possible states of matter, and provide simple and concrete blueprints for how to realize them. I am particularly interested in topological quantum states, where information can be encoded in the system such that it is protected against random local disturbances and unwanted operations acting on individual components of the quantum simulator. Due to this protection, these states could be used for quantum computing and quantum memory. An important focus of my recent research has been studying how to generate these states from microwave photons trapped in superconducting circuits. Unlike trapped atoms, photons can be created or destroyed, so when photons are lost to the environment, they can be passively replaced by a suitable circuit. Passive error correction mechanisms for many-body systems (such as the one detailed in arxiv:1402.6847) can automatically repair distortions to a quantum state due to losses and decoherence, without the intervention of an external observer. They could thus make both quantum simulation and quantum computing much easier to achieve in real experiments, and are a major theme of my work. Finally, while much of my work deals with many-body physics in simulated systems of tens or hundreds of qubits, most current experimental work is still done with groups of one to four qubits, as large scale integration remains a technical challenge. As such, I am always interested in simpler applications of my ideas, and I am working with experimental collaborators to develop useful technologies from smaller-scale versions of the concepts considered in my work.

Quantum Chaos and Quantum Information

Principal Investigator: Lev Kaplan

Tulane Group Members: Sicong Chen, Basil Davis, Robert Kramer, Jake Smith, Dmitry Uskov, Yang Zhang

Group Website

Quantum chaos addresses fundamental questions about quantum-classical correspondence and semi-classical methods for generic quantum systems (with non-integrable classical analogues), bringing together methods, insights, and examples from areas as diverse as condensed matter and mesoscopic physics, atomic, optical, molecular, and chemical physics, nuclear physics, microwave physics, nonlinear dynamics, statistical mechanics, and mathematical physics. The goal is to develop a framework and set of techniques relevant to a broad range of complex physical phenomena and transcending the peculiarities of specific physical models.

Specific areas of recent interest have included:

  • Transport in nanostructures and quantum dots
  • Quantum vacuum energy (Casimir forces) in integrable and non-integrable geometries
  • Statistics of extreme ocean waves (rogue waves)
  • Branching for electron and microwave flow in the presence of correlated disorder
  • Statistics of wave functions and transport in the presence of chaos and disorder
  • Superradiance and transport in open quantum systems
  • Wave functions beyond Random Matrix Theory (RMT)
  • Quantum-classical correspondence and the accuracy of semiclassical approximations
  • Electron-electron interactions in chaotic quantum dots (application to statistics of conductance peaks)
  • Quantum computation in linear optics (designing optimal quantum gates)
  • Quantum metrology using coherent photon states
  • Photons carrying orbital angular momentum and their interaction with matter

Theoretical Solid State Physics

Principal Investigator: James MacLaren

This research group is a highly theoretical one working in the art of density functional theory to calculate the Density of States (DOS) or the electronic structure of materials. This all-important aspect of a material lies at the heart of all solid-state physics, by knowing structure of an atom's electronic shell provides the ability to basically describe or predict all other associated properties. The calculation of atoms' electronic structure requires massive computational power and deft approximations for even relatively basic systems, which is why this group utilizes its own Supercomputing Center to perform VASP calculations.

Research topics mainly consist of the extraction of the magnetic properties of solids and their interfaces, including the measurement of materials' anisotropy, magnetization, phase structure and the density of states. The current focus is on the search for a half-metallic material by virtue of a doped metallic semiconductor. These highly exotic materials exist in nature in an anti-ferromagnetic state, and are highly coveted because they play an important role in high temperature superconductors and compressed magnetic storage media. The group is also investigating the phase transitions of certain binary metallic alloys, which are described by the composition of the unit cell, whether it has all of atom A, all of B or a mixture of both. These phases are interpreted through a graphical representation that relates the different phases by the structures thermal energy and its molecular concentration. This is beneficial for devices in the realm of electronics, such as circuit gates, switches, loads, etc. There also exists possibilities elsewhere outside of the computer, common things, such as color changing materials and morphable solids to name a few.

Theoretical Atomic Physics & Quantum Control

Principal Investigators: Jim McGuire (Emeritus) & Khazhgery "Jerry" Shakov

Our group is studying coherent population control of electrons in atoms. We are developing analytic methods to understand how to move electrons from one state to another in an atom when we want, where we want, as completely as we want, as fast as we want, keeping it there as long as we want, using simple mathematics. The trick is to take advantage of degenerate states where quantum energy fluctuations are absent. In this case time correlations are eliminated and the physics and the mathematics both simplify. When non-degeneracy is reintroduced we are able to study quantum time correlations. These effects are observable in some data, e.g. in polarization of light emitted from excited atomic levels. This enables us to understand how time works in quantum mechanical systems.

Current research interests are primarily focused on various aspects of quantum control, concerning a variety of applications ranging from quantum information and quantum computation to modification of paths of chemical reactions. Recent work regarding the development of analytical description of dynamics of N-state quantum systems, especially two-state and three-state systems, is most likely to be used for practical applications (e.g. as a physical realization of a qubit–a quantum version of the classical computer bit). Recent work also concerns the role of time correlation and time ordering in the dynamics of the quantum systems interacting with external fields, under the motivation of understanding reaction dynamics and coherent control in the time domain. In particular, we are interested in the study of observable effects of time ordering, and understanding the related problem of time correlation in few body dynamics, corresponding to a system of a few dynamically coupled qubits. We have used both analytic and numerical solutions to study effects of time ordering in multiply kicked systems.

Condensed Matter and Materials Theory and Computation/Density Functional Theory

Principal Investigators: Jianwei Sun

Tulane Group Members:  Yubo Zhang, James Furness, Jinliang Ning, Manish Kothakonda, Kanun Pokharel

The importance of materials is demonstrated by the names we use to identify human civilizations, from stone to bronze to iron to the modern silicon ages. On the microscopic scale, all materials exist as collections of atoms consisting of nuclei surrounded by much lighter electrons. The behavior of the electrons is governed by quantum mechanics and largely determines properties of materials. The grand challenge of developing the advanced materials that benefit society therefore becomes how to understand and control material processes at the level of electrons.

The high efficiency and useful accuracy of density functional theory (DFT) and its extensions (e.g., time-dependent or TD DFT), have caused them to become the most widely used electronic structure theories in chemistry, materials science, and condensed matter physics. In principle DFT is exact for the ground state energy and electron density, but in practice the exchange-correlation energy as a functional of electron density must be approximated. My research interests are in understanding the fundamental properties of the exchange-correlation energy (or the exchange-correlation potential and kernel in case of TD-DFT), using this understanding to derive more accurate and efficient approximations, and applying the approximations to predict properties and behaviors of materials and computationally design materials that are scientifically, technologically, or economically important.

I have constructed the strongly-constrained and appropriately-normed (SCAN) density functional that is physically justified, non-empirical, efficient, and accurate. SCAN predicts accurate material structures and energies, with improved electronic energy band gaps for diversely-bonded systems (including covalent, metallic, ionic, hydrogen, and van der Waals (vdW) bonds) simultaneously. SCAN significantly and systematically improves over conventional density functionals, and thus greatly advances the development of DFT and its applications in a wide range of materials. My group currently focuses on taking advantage of SCAN for density functional developments and applications, with an emphasis on:

  1. Development of a local hybrid density functional for solving the strong many-electron interaction (SMEI) originating from a degeneracy or near-degeneracy and the self-interaction error (SIE) due to the imperfect cancellation of the spurious classical Coulomb interaction between an electron and itself.
  2. New insights into difficult electron systems, e.g., strongly-correlated electron systems.
  3. Ionic dynamics for realistic modeling of materials, e.g., finite temperature and pressure effects, and for electron-phonon coupling.
  4. Computational design of cheap and environmentally friendly catalysts based on 2D materials for energy applications.
  5. Quantum materials including superconducting and topological materials.

Nuclear Physics

Principal Investigator: Daniel Purrington

Group Website

This group's research interests have been traditionally focused on the quantum theory of scattering, principally few-body problems, and nuclear structure. In recent years this has evolved into theoretical treatment of classical scattering, mostly in the ocean acoustics context, and primarily involving scattering from randomly rough interfaces, including fractal geometries.

History of Physics

Principal Investigator: Daniel Purrington (Emeritus)

Group Website

Specific scholarship on the history of physics and astronomy in recent years has focused on a number of various topics, including the history of cosmology, the history of physics in the 19th century, and the history of astronomy, principally, archaeoastronomy.

Since 1989, Dr. Purrington has been particularly interested in the scientific revolution, and has just recently completed a monograph project on Robert Hooke and the Royal Society.

Mathematical Physics

Principal Investigator: George Rosensteel

Tulane Group Members: Farren Curtis, Nick Sparks

As one of the original discoverers in the mid 1970's of symplectic dynamical symmetry to describe geometrical collective modes in atomic nuclei and astrophysical systems, this research program encompasses several areas of theoretical and mathematical physics including representations of non-compact Lie groups, geometric quantization, differential geometry of fiber bundles, dynamical systems on co-adjoint orbits, and density functional theory.

Physics Instruction

Tulane Group Members: Khazhgery "Jerry" Shakov, James McGuire

This loosely organized group focuses on techniques and innovations involved in the teaching of physics, primarily at the college level.

Current and ongoing projects include the development of new courses, technological improvements to lecture and lab courses, outreach programs within the community, and the development of classroom demonstrations and techniques.

We are also interested in building effective and productive partnerships with STEM educators at elementary and secondary levels. Some of the projects we have been involved with include professional development for local K-12 STEM teachers (Math & Science Partnership NOLA SMILE, Core Element), as well as our service learning course, Introduction to Physics Pedagogy. In that course, Tulane students experience a technology enabled constructivist approach to Physics education by observing and participating in the teaching of Physics courses with Stephen Collins at Lusher Charter School.

Relativity & Cosmology

Principal Investigator: Frank Tipler

Astrophysical black holes almost certainly exist, but Hawking has shown that if black holes are allowed to exist for unlimited proper time, then they will completely evaporate, and unitarity will be violated. Thus unitarity requires that the universe must cease to exist after finite proper time, which implies that the universe has the spatial topology of a three-sphere. The Second Law of Thermodynamics says the amount of entropy in the universe cannot decrease, but it can be shown that the amount of entropy already in the CBR will eventually contradict the Bekenstein Bound near the final singularity unless there are no event horizons, since in the presence of horizons the Bekenstein Bound implies the universal entropy S is less that a constant times the radius of the universe squared, and general relativity requires the radius to go to zero at the final singularity. The absence of event horizons by definition means that the universe's future c-boundary is a single point, call it the Omega Point. Thus life (which near the final state, is really collectively intelligent computers) almost certainly must be present arbitrarily close to the final singularity in order for the known laws of physics to be mutually consistent at all times. Misner has shown in effect that event horizon elimination requires an infinite number of distinct manipulations, so an infinite amount of information must be processed between now and the final singularity. The amount of information stored at any given time diverges to infinity as the Omega Point is approached, since the entropy diverges to infinity there, implying divergence of the complexity of the system that must be understood to be controlled. Life transferring its information to a medium that can withstand the arbitrarily high temperatures near the final singularity has several implications: first, (Omega-naught - 1) is between a millionth and a thousandth, where Omega-naught is the density parameter, and second, the Standard Model Higgs boson mass must be 220 plus or minus 20 GeV.