Chapter 20 Fractional Quantum Dynamics

Vasilij E. Tarasov

Longzhao Lu, Xiangyang Yu

Arthur L. Smirl

The studies described in this chapter convince the reader that time-resolved polarimetry is an extremely sensitive way to study many body effects. The vectorial dynamics contain useful information about many-body effects, quantum interference and optical anisotropies that would be difficult to obtain in any other way. The chapter begins with a brief review of some of the four-wave-mixing (FWM) techniques that have been most commonly used to measure the coherent emission from multiple quantum wells (MQWs). The ellipticity and the fraction of unpolarised light are both significantly smaller for the negative delay. These features provide additional tests for any proposed model that purports to describe coherent excitonic dynamics in MQWs. The chapter discusses the treatment of excitons in semiconductors as two-level systems, and follows with a detailed review of the solutions to the density matrix equations for two independent two-level systems, with an emphasis on the vectorial nature of the FWM emission from such systems.

Shubhayu Chatterjee

This thesis is devoted to the study of strongly correlated phases of quantum matter in two spatial dimensions. In presence of strong interactions, the electron can split up into separate spin and charge degrees of freedom. The diagnosis of such fractionalized excitations in recent experiments, as well as finding new probes for their detection, comprise the two major themes of this thesis.\nThe first part of the thesis, comprising chapters 2-6, discusses the relevance of fractionalization to the pseudogap phase of the underdoped high Tc cuprate superconductors. This is motivated by transport experiments that show a violation of Luttinger's theorem, possible only in the presence of topological order that can arise naturally as a consequence of fractionalization. Chapters 2 and 3 focus on phenomenological models with bosonic charge carriers and fermionic spin carriers, and investigate transport properties as well as various confinement transitions to symmetry broken phases. Chapters 4, 5 and 6 deal with a different framework of electron fractionalization, where the charge carriers are fermionic and spin carriers are bosonic. We find that these models can better explain the thermal and electrical transport properties in chapter 5. In chapters 6 and 7, we show how such models arise naturally from quantum fluctuations of antiferromagnetism, and can simultaneously intertwine the anti-nodal spectral gap with the discrete broken symmetries that are observed in the cuprates. \nThe second part of the thesis, comprising chapters 7 and 8, proposes new experimental probes to study the behavior of insulating two dimensional quantum magnets. Aided by geometric frustration and strong quantum fluctuations, they may realize a spin liquid ground state which can be extremely difficult to detect via conventional probes. Chapter 7 discusses how novel spin-transport probes from the spintronics community can be used to detect fractionalized excitations in a quantum spin liquid. Chapter 8 studies how the temperature dependent anisotropy of in-plane versus out-of-plane thermal conductivities can serve as an explicit signature of fractionalization in layered two-dimensional materials.

Alexander Iomin