On the entanglement spectrum: From the Levy distribution to the Tracy- Widom by Arul Lakshminarayan

Open Quantum Systems

DATE: 17 July 2017 to 04 August 2017

VENUE: Ramanujan Lecture Hall, ICTS Bangalore

There have been major recent breakthroughs, both experimental and theoretical, in the field of Open Quantum Systems. The aim of this program is to bring together leaders in the Open Quantum Systems community from a range of subfields, such as Mesoscopic Quantum Optics (Quantum Dot Circuit-QED systems), Cavity Optomechanics, Cavity-QED systems and many more. This field of hybrid quantum systems sits perfectly at the interface of condensed matter physics, quantum optics and non-equilibrium physics. Despite remarkable progress, there are still a large number of challenging and important experimental and theoretical questions thereby creating an immediate need for the program that is expected to facilitate vibrant discussions and collaborations among researchers from diverse fields.

The main areas of focus in the program will be

Mesoscopic Quantum Optics
Hamiltonian and Quantum Bath Engineering
Cavity Optomechanics
Quantum Gases in Cavities
Light-matter interactions in 1D continuum
This program will be for active researchers in the areas and is designed to be especially beneficial for advanced graduate students and postdocs.

There will also be some pedagogic lectures on the following topics:

Cavity optomechanics - Aashish Clerk (Theory) - Week 2
Theory of solid-state quantum information processing - Guido Burkard (Theory) - Week 2
Non-Equilibrium physics of polaritons - Jacqueline Bloch (Experiment) - Week 2
Hybrid circuit quantum electrodynamics - Jason Petta (Experiment) - Week 1
Superradiance and the Dicke model - Jonathan Keeling (Theory) - Week 1
Quantum manifolds of steady states in driven, dissipative superconducting circuits - Michel Devoret (Experiment) - Week 2
Non-equilibrium behavior of quantum many-body systems - Stefan Kehrein (Theory) - Week 3
Mesoscopic quantum electrodynamics - Takis Kontos (Experiment) - Week 1

0:00:00 Start
0:00:07 On the entanglement spectrum: From the Levy distribution to the Tracy- Wisdom
0:00:58 Outline
0:01:55 Integrable vs Chaotic: Billiards as examples
0:04:37 Coexistence of regular and chaotic
0:06:27 Eigenfunctions of Chaos: Quantum ergodicity
0:11:14 Introduction
0:14:40 Bipartite pure states: Reduced Density Matrices
0:17:39 Typical entanglement
0:20:55 Applications of typical / random states
0:21:57 Typical entanglement and quantum chaos
0:23:40 Two coupled kicked pendula
0:25:52 Entanglement growth 4
0:27:08 Noninteracting to Interacting entanglement transitions, when all limits are nonintegrable.
0:29:00 Case of coupled kicked rotors vs Theory
0:30:27 Universal entanglement for weakly interacting strongly chaotic systems
0:31:47 Ent. spectrum across the transition
0:32:49 ... and it blows up in our face
0:33:28 Moments tamed
0:34:00 Distributions of X1.2
0:34:05 Distributions of lambda 2: Power laws
0:34:50 Distribution of lambda 1:= Levy distribution
0:36:00 Strong interactions: 1 := Tracy-Widom
0:38:06 Summary
0:41:05 MBL: Ising spins with NNN interactions
0:42:18 Perturbation theory and entanglement
0:43:49 ... and it blows up in our face