Abstract
We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters allowing for the engineered realization of distinct topological phases. The option to directly monitor the walker's probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition. We analytically calculate the probability distribution describing the quantum critical walk in terms of a (time staggered) spin polarization signal and propose a concrete experimental protocol for its measurement. Numerical simulations back the realizability of our blueprint with current date experimental hardware.
Highlights
Low-dimensional disordered quantum systems can escape the common fate of Anderson localization once topology comes into play, as witnessed at the integer quantum Hall plateau transitions [1,2]
We explore a quantum walk operating at a topological Anderson localization transition
Csl is states an additional chiral sym-. This symmetry is visible in the density of states (DoS), as we show in Appendix C
Summary
Low-dimensional disordered quantum systems can escape the common fate of Anderson localization once topology comes into play, as witnessed at the integer quantum Hall plateau transitions [1,2]. The controlled experimental study of a critical state at the Anderson localization transition presents an intriguing challenge. Quantum walks allow for a large tunability of the system parameters and have been used experimentally to observe Anderson localization [23,25,33], dynamical localization [28], and topological effects [34,35,36,37,38,39,40,41]. It is generated by the single time-step evolution U = R T , iteratively acting on a walker with a two-dimensional internal degree of freedom, referred to as spin in the following.
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