Edge Localized Schr\"odinger Cat States in Finite Lattices via Periodic Driving

• URL: http://arxiv.org/abs/2010.00016v1
• Date: Wed, 30 Sep 2020 18:00:02 GMT
• Title: Edge Localized Schr\"odinger Cat States in Finite Lattices via Periodic Driving
• Authors: Asadullah Bhuiyan and Frank Marsiglio
• Abstract summary: Floquet states have been used to describe the impact of periodic driving on lattice systems. We show that edge bands represent Schr"odinger cat-like states with effective tunneling across the entire lattice.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Floquet states have been used to describe the impact of periodic driving on lattice systems, either using a tight-binding model, or by using a continuum model where a Kronig-Penney-like description has been used to model spatially periodic systems in one dimension. A number of these studies have focused on finite systems, and results from these studies are distinct from those of infinite lattice systems as a consequence of boundary effects. In the case of a finite system, there remains a discrepancy in the results between tight-binding descriptions and continuous lattice models. Periodic driving by a time-dependent field in tight-binding models results in a collapse of all quasienergies within a band at special driving amplitudes. In the continuum model, on the other hand, a pair of nearly-degenerate edge bands emerge and remain gapped from the bulk bands as the field amplitude increases. We resolve these discrepancies and explain how these edge bands represent Schr\"odinger cat-like states with effective tunneling across the entire lattice. Moreover, we show that these extended cat-like states become perfectly localized at the edge sites when the external driving amplitude induces a collapse of the bulk bands.

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