Talks

We will present the basic inequalities concerning the classical entropic quantities introduced in the first lecture. We will then proceed to the quantum analogue of Shannon entropy. We will first briefly review pure and mixed states, and their evolution. We will then present Von Neumann entropy, and other related quantum mechanical entropic quantities, study their properties, and present the basic inequalities.

We will see that Shannon entropy arises naturally from the problem of efficiently representing the outcome of a probabilistic experiment as a string of bits. We will review entropic quantities such as relative entropy, conditional entropy and mutual information, and relate them to notions such as the rate of growth of the number of typical sequences and asymptotic limits on the rate of information transmission across a noisy channel.

Kagome materials have emerged as a promising platform to study novel quantum phases of matter that arise from the interplay between lattice geometry, band topology, and electronic correlations. They host a variety of electronic and structural instabilities, with charge density waves being a prominent example.

In this talk, I will describe how first principles calculations can be used to explore the rich physics associated with charge density waves. Using bilayer kagome metal ScV6Sn6 as an illustrative example, I will explore competing charge density waves, the role of anharmonic phonon-phonon interactions in the charge density wave transition, and the control of charge density waves by external parameters such as pressure and doping.

Traditionally, measurements have been synonymous with extracting information from physical systems. Yet, in quantum systems measurement can actively modify and steer quantum states, acting as a quantum chisel to sculpt new patterns of entanglement. I will describe how this power of measurements can be leveraged to efficiently create the long sought after non-Abelian topological phases. Surprisingly, the particular non-Abelian states created in this way are closely related to Galois' characterization of solvable polynomial equations.
Finally, I will describe our recent collaboration with Quantinuum that utilizes this approach. In particular, I will discuss the Borromean braiding of excitations, a signature unique to non Abelian topological order, and its measurement on the Quantinuum platform.

Two dimensional di-chalcogenide materials with Ising spin orbit coupling often show enhanced charge density wave transition temperature and signatures of unconventional superconductivity unlike their three dimensional bulk counterparts. Some of these experiments in monolayer NbSe2 include enhancement of superconducting transition temperature with increasing disorder concentration, observation of two fold symmetric gap in the presence of in plane magnetic field, and observation of Leggett modes in tunnelling experiments.
In this talk, we will first present our calculation of 3Q CDW ordering and role of disorder in normal state of monolayer NbSe2. We will then present our results for the superconducting state assuming a spin fluctuation mediated pairing scenario and explore the dominant gap functions within this theory. Finally, we will discuss the effects of an in-plane Zeeman field on the homogenous superconducting state.
Indian Institute Of Technology Ma