| Project Detail |
Understanding interacting many-body systems is vital to many areas of science and technology, including developing materials with new functionalities, quantum information, and energy applications. A major component of this project will be developing a general set of analytical and numerical methods to efficiently and accurately describe equilibrium properties and dynamics of stongly interacting many-body systems. Examples of systems that will be studied include quantum materials with strong electron-electron and electron-phonon couplings, systems of ultracold atoms, two dimensional electron gases close to the quantum critical point between the Fermi liquid and Wigner crystal phases, systems with strong coherent light-matter coupling. The first goal of this proposal is theoretical analysis of many-body systems with strong electron-electron and electron-phonon coupling with an emphasis on non-equilibrium dynamics. I plan to focus on the following types of experiments: pump and probe experiments, including time resolved ARPES and optical probes of photoinduced superconductivity, and resonant xray scattering. Microscopic models similar to electron-phonon models are also relevant for Bose-Fermi mixtures of ultracold atoms, magnetic polarons in the Fermi Hubbard model, and exciton/electron systems in transition metal dichalcogenides. I will use theoretical approaches developed in the context of electron-phonon systems to analyze these systems as well. The second class of problems that I will explore is systems with strong coherent light matter coupling, such as quantum materials interacting with terahertz cavities. Systems in which light controls matter hold the promise for realizing novel types of quantum many-body states and creating devices with new capabilities. In most cases this functionality is achieved using external radiation applied to atomic ensembles or solid state systems. Prominent examples include Floquet engineering of electronic band structures, modifying quasiparticle distributions to enhance the order parameter in the superconducting state, using optical pumping to create long-lived metastable states. An alternative route toward light induced changes in matter is to use quantum fluctuations of electro-magnetic fields. Terahertz cavities provide a particularly promising direction in this line of research because many collective excitations in solids can be found in this frequency range, including phonons, magnons, and Josephson plasmons. Furthermore, THz cavities have smaller spatial dimensions than the corresponding wavelength in vacuum, which means that electro-magnetic energy of cavity photons is strongly localized spatially. My group will investigate how THz cavities can be used to control phase transitions in electron systems, in particular, whether they can be used to enhance ferroelectric, magnetic, and superconducting transitions. Our goal is creation of {/it equilibrium} phases of matter, where cavities facilitate formation of infinitely long lived states without the need for external pumping. This should be contrasted to the previously studied light induced phases of matter in which strong external radiation is used to achieve an interesting transient state. As part of this thrust I will develop new theoretical approaches for analyzing cavity quantum electrodynamics at ultrastrong coupling, when traditional approaches based on perturbation theory fail. The third class of systems that I plan to explore in this project is Wigner crystal states in two dimensional electron gases, especially in the vicinity of the liquid to crystal transition. This investigation is motivated by recent experimental observations of Wigner crystal states in transition metal dichalcogenids. Transition between the Fermi liquid and Wigner crystal phases has long been one of the most enigmatic quantum phase transitions. In spite of considerable theoretical work on these systems in the past, there are many open questions regarding the possibility of the intermediate “quantum emulsion” phase between the liquid and crystal states, the possibility of spin liquid states in Wigner crystals close to the transition point arising from strong ring exchange interactions, and the role of disorder on the crystallization transition. My goal is to resolve open questions about Wigner crystals and quantum liquid to solid transition by solving the problem via unbiased numerical calculation. We will not only perform accurate numerical calculations with a goal of understanding the phase diagram, but also identify experimental probes, which can provide smoking gun signatures of different phases. The fourth class of systems that I will study in this project will be quantum simulators based on ultracold atoms. Quantum simulators provide accurate realizations of paradigmatic models of many-body quantum physics. In particular, Quantum Gas Microscopes use ultracold fermionic atoms in an optical lattice to create an accurate emulator of the Fermi-Hubbard model. A particular strength of these experimental systems is that all particles in the system can be measured simultaneously, providing snapshots of many-body states. This is as close as we can come experimentally to complete characterization of the many-body quantum system. By combining tools of quantum many-body physics and classical data science I plan to identify theoretical models that provide the most accurate description of experimental data. I also plan to address a bigger problem of developing new theoretical tools for extracting information from this new and unique type of data. My general philosophy of theoretical investigations is to pursue three interconnected objectives: i) developing new theoretical methods for analyzing strongly correlated many-body systems in and out of equilibrium; ii) analyzing concrete experimental systems including collaborations with experimental groups; iii) identifying general paradigms and principles starting from analysis of concrete systems.
Grant number
212899
Funding scheme
Project funding
Call
Project funding in Mathematics, Natural sciences and Engineering (division II) 2022 April
Approved amount
997,662 CHF |
