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Floquet Engineering of Quantum Scars by Krishnendu Sengupta

International Centre for Theoretical Sciences via YouTube

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Overview

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This course focuses on the Floquet engineering of quantum scars, covering topics such as Eigenstate Thermalization Hypothesis, violation of ETH, classical and quantum scars, scars in quantum many-body Hamiltonians, and quantum dynamics with scars. The course teaches the realization of states with broken Zn symmetries with Rydberg atoms, the dipole model, effective dipole Hamiltonian, and periodic drive with Magnus expansion. The teaching method includes analytical calculations, derivation of Floquet Hamiltonian, and discussions on the dynamics of correlation functions. This course is intended for theorists and experimentalists working in the areas of topological order in condensed matter systems, symmetry protected topological phases, and superconductivity in twisted bilayer graphene.

Syllabus

Floquet engineering of quantum scars
Outline
Eigenstate Thermalization Hypothesis
Violation of ETH
Classical and Quantum Scars
Scars in Quantum Many-body Hamiltonians
Quantum Dynamics with scars
Realization of states with broken Zn symmetries n=2,3,4 with Rydberg atoms
The dipole model
Effective dipole Hamiltonian
The model has a straightforward representation in terms of Ising spins
Periodic drive and Magnus expansion
We study a simple square pulse protocol
Analytical calculation of HF: Magnus expansion
Derivation of Ow Floquet Hamiltonian
Dynamics of the Correlation function
High frequency regime: Lambda/Omega 1
Intermediate frequency regime Lambda/Omega 01
Phase diagram for the periodically driven Rydberg chain
Noisy dynamics
Square pulses with random drive period
The leading term of the commutator C = [U+, U_] may vanish at special drive frequencies
Analytical prediction of regions where random drive would lead to coherent oscillations
Dynamics around Gamma ~ Pi
Noise induced coherent dynamics around dT/T=1/4, 3/4.
Dynamics around Gamma ~ 2Pi
Conclusion
Q&A

Taught by

International Centre for Theoretical Sciences

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