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Topological quantum walk immersed in synthetic non-Abelian gauge fields

Zehai Pang, Omar Abdelghani, Marin Soljacic A, Yi Yang

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We generalize the photonic mesh lattice configuration with polarization multiplexing to achieve a four-dimensional Hilbert space. We introduce synthetic non-Abelian gauge fields to achieve topological quantum walks and study the simulation of entanglement induced by gauge fields.
DOI
10.1364/cleo_fs.2025.ff139_5

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Floquet systems like quantum walks can exhibit anomalous topological boundary modes that have no stationary counterpart. Although the topological properties of synthetic gauge fields have been explored in quantum walks, these studies have so far focused on Abelian gauge fields. We theoretically introduce synthetic non-Abelian gauge fields for topological quantum walks and study their topological consequences. The photonic mesh lattice configuration is generalized with polarization multiplexing to achieve a four-dimensional Hilbert space, based on which we provide photonic building blocks for realizing various quantum walks in non-Abelian gauge fields. It is found that SU(2) gauge fields can lead to Peierls substitution in both momenta and quasienergy. In one and two dimensions, we describe detailed photonic setups to realize topological quantum walk protocols whose Floquet winding numbers and Rudner–Lindner–Berg–Levin invariants can be effectively controlled by the gauge fields. Finally, we show how non-Abelian gauge fields facilitate convenient simulation of entanglement in conjunction with polarization-dependent and spatial-mode-dependent coin operations. Our results shed light on the study of synthetic non-Abelian gauge fields in photonic Floquet systems and hold implications for time-multiplexed optical networks.
We theoretically introduce synthetic non-Abelian gauge fields for topological quantum walks. The photonic mesh lattice configuration is generalized with polarization multiplexing to achieve a four-dimensional Hilbert space, based on which we provide photonic building blocks for realizing various quantum walks in non-Abelian gauge fields. It is found that SU(2) gauge fields can lead to Peierls substitution in both momenta and quasienergy. In one and two dimensions, we describe detailed photonic setups to realize topological quantum walk protocols whose Floquet winding numbers and Rudner-Lindner-Berg-Levin invariants can be effectively controlled by the gauge fields. Finally, we show how non-Abelian gauge fields facilitate convenient simulation of entanglement in conjunction with polarization-dependent and spatial-mode-dependent coin operations. Our results shed light on the study of synthetic non-Abelian gauge fields in photonic Floquet systems.
There is great interest in designing photonic devices capable of disorder-resistant transport and information processing. In this work we propose to exploit three-dimensional integrated photonic circuits in order to realize two-dimensional discrete-time quantum walks in a background synthetic gauge field. The gauge fields are generated by introducing the appropriate phase shifts between waveguides. Polarization-independent phase shifts lead to an Abelian or magnetic field, a case we describe in detail. We find that, in the disordered case, the magnetic field enhances transport due to the presence of topologically protected chiral edge states that do not localize. Polarization-dependent phase shifts lead to effective non-Abelian gauge fields, which could be adopted to realize Rashba-like quantum walks with spin-orbit coupling. Our work introduces a flexible platform for the experimental study of multiparticle quantum walks in the presence of synthetic gauge fields, which paves the way towards topologically robust transport of many-body states of photons.
Temporal multiplexing provides an efficient and scalable approach to realize a quantum random walk with photons that can exhibit topological properties. But two-dimensional time-multiplexed topological quantum walks studied so far have relied on generalizations of the Su-Shreiffer-Heeger model with no synthetic gauge field. In this work, we demonstrate a two-dimensional topological quantum random walk where the nontrivial topology is due to the presence of a synthetic gauge field. We show that the synthetic gauge field leads to the appearance of multiple band gaps and, consequently, a spatial confinement of the quantum walk distribution. Moreover, we demonstrate topological edge states at an interface between domains with opposite synthetic fields. Our results expand the range of Hamiltonians that can be simulated using photonic quantum walks.
The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops.
Abstract The concept of synthetic dimensions works particularly well in atomic physics, quantum optics, and photonics, where the internal degrees of freedom (Zeeman sublevels of the ground state, metastable excited states, or motional states for atoms, and angular momentum states or transverse modes for photons) provide the synthetic space. In this Perspective article we report on recent progress on studies of synthetic dimensions, mostly, but not only, based on the research realized around the Barcelona groups (ICFO, UAB), Donostia (DIPC), Poznan (UAM), Kraków (UJ), and Allahabad (HRI). We describe our attempts to design quantum simulators with synthetic dimensions, to mimic curved spaces, artificial gauge fields, lattice gauge theories, twistronics, quantum random walks, and more.