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DTSTART:20240115T090000Z
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TRANSP:OPAQUE
LOCATION:ICFO Auditorium and Online (Teams)
SUMMARY:ICFO | TYMOTEUSZ SALAMON 
CLASS:PUBLIC
DESCRIPTION:Over the past three decades\, optically trapped ultra-cold atom
 s have served as a versatile platform for controlled exploration of numero
 us condensed matter phenomena. The successful fabrication of magic angle t
 wisted bi-layer graphene (MATBG) has introduced a for condensed matter phy
 sicists\, while concurrently posing a novel challenge for the quantum simu
 lation community. This thesis is devoted to addressing this problem\, focu
 sing mainly on the simulation of MATBG structures using ultra-cold atoms w
 ithin its initial three chapters.\nTo overcome the issue of unit cell expa
 nsion resulting from rotation misalignment\, in the first chapter we propo
 se the concept of \"twist-less twistronics&rdquo\; (twistronics\, a term c
 oined from twist and electronics). This innovative notion involves replaci
 ng the physical rotation of one layer with a light-modulated hopping ampli
 tude between the layers. Enabled by the architecture of ultra-cold atoms\,
  this approach yields quasi-flat bands\, a pivotal ingredient for collecti
 ve phenomena observed in Magic-Angle Twisted Bilayer Graphene (MATBG)\, ac
 hieved at significantly reduced unit cell sizes.\nThe opening chapter also
  presents a suitable experimental set-up. Moreover\, it provides a compreh
 ensive theoretical framework\, including tight-binding calculations and ef
 fective models derived from perturbative analysis. The second chapter delv
 es into the topological properties of an analogous system\, emphasizing th
 e energy separation between the quasi-flat bands and the resulting spectru
 m. We demonstrate Quantum Anomalous Hall Effect across diverse parameter r
 egimes\, accompanied by an exhaustive phase diagram with respect to tunabl
 e parameters.\nIn the third chapter\, we extend our investigation to encom
 pass onsite\, density-density attractive interactions between lattice atom
 s. Employing the Hartree-Fock-Bogoliubov mean-field approximation\, we con
 sider all feasible interaction channels within/between layers and spins. T
 his chapter aims to elucidate the relationship between band flattening\, a
  fully controlled parameter in our system\, and the emergence/size of a su
 perconductive gap. Notably\, we uncover a substantial enhancement in the c
 ritical (Kosterlitz-Thouless) temperature within the quasi-flat band regim
 e at quarter filling\, along with a comprehensive diagram illustrating sup
 erconducting order parameters corresponding to each interaction channel.\n
 The fourth chapter marks a departure from condensed matter simulations\, d
 elving into \"special purpose quantum computing\" within the context of qu
 antum batteries. These devices\, analogous to their classical counterparts
 \, store and release energy on demand\, a process inherently governed by t
 he battery Hamiltonian. Our work establishes a novel framework for assessi
 ng quantum battery performance and setting fundamental bounds on two key a
 ttributes: power and capacity. We investigate the essential Hamiltonian te
 rms of a for achieving quantum speed-up in battery charging.\nThe last\, f
 ifth chapter describes the theoretical tools\, that have been used to supp
 ort the first experimental realisation of the Extended Bose Hubbard model 
 with dipolar excitons. We discuss the parameters of interests and importan
 t observables\, such as a structure factor and discuss both the exact diag
 onalization and mean-field methods\, which were necessary to verify the ob
 servation of strongly correlated phases at half and unit filling.\n&nbsp\;
 \nThesis Director: Prof Dr. Maciej Lewenstein &amp\; Dr. Debraj Rakshit\n&
 nbsp\;
DTSTAMP:20260407T070316Z
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