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arXiv:2412.09766 · Physical Review Letters

Synthetic Multidimensional Aharonov-Bohm Cages in Fock State Lattices

Jiajian Zhang, Wenhui Huang, Jiawei Qiu, Jiawei Qiu, Xuandong Sun, Ziyu Tao, Lushuang Zhang, Libo Zhang, Yuxuan Zhou, Yuanzhen Chen, Yang Liu, Song Liu, Youpeng Zhong, Jian-Jian Miao, Jingjing Niu, Dapeng Yu

Published Feb 19, 2025• 18 citations
arXivHTMLPDF

Abstract

Fock-state lattices, composed of photon number states with infinite Hilbert space, have emerged as a promising platform for simulating high-dimensional physics due to their potential to extend into arbitrarily high dimensions. Here, we demonstrate the construction of multidimensional Fock-state lattices using superconducting quantum circuits. By controlling artificial gauge fields within their internal structures, we investigate flux-induced extreme localization dynamics, such as Aharonov-Bohm caging, extending from 2D to 3D. We also explore the coherent interference of quantum superposition states, achieving extreme localization within specific subspaces assisted by quantum entanglement. Our findings pave the way for manipulating the behavior of a broad class of quantum states in higher-dimensional systems.

DOI
10.1103/physrevlett.134.070601

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Fock-state lattices, composed of photon number states with infinite Hilbert space, have emerged as a promising platform for simulating high-dimensional physics due to their potential to extend into arbitrarily high dimensions. Here, we demonstrate the construction of multidimensional Fock-state lattices using superconducting quantum circuits. By controlling artificial gauge fields within their internal structures, we investigate flux-induced extreme localization dynamics, such as Aharonov-Bohm caging, extending from 2D to 3D. We also explore the coherent interference of quantum superposition states, achieving extreme localization within specific subspaces assisted by quantum entanglement. Our findings pave the way for manipulating the behavior of a broad class of quantum states in higher-dimensional systems.
Aharonov-Bohm (AB) caging is a complete localization phenomenon in two-dimensional lattices due to destructive interference induced by the background gauge fields. However, current investigations of AB caging are mostly restricted to the Abelian gauge field case, and the observation of AB caging under non-Abelian gauge fields in a quantum system still remains elusive. Here, we report experimental realization of tunable synthetic non-Abelian SU(2) gauge fields in a rhombic lattice, engineered within the synthetic dimensions of a vibrating trapped ion with multiple levels. We realize AB caging under both Abelian and non-Abelian gauge fields and systematically investigate the distinctive transport properties of the non-Abelian case. In particular, we observe typical emergent quantum dynamics unique to non-Abelian AB caging, including initial-state-dependent dynamics, second-order effects, and asymmetric caging behavior. These observations demonstrate the trapped ion system as a powerful platform for simulating emergent phenomena in high-dimensional quantum systems with exotic synthetic gauge fields.
Aharonov-Bohm (AB) caging is the complete wavefunction localization effect in translational-invariant lattices induced by destructive phase interference. These phases originate from the gauge fields such as the penetrated magnetic fields, which are directly related to several novel topological quantum states of matter. Recently, this effect has shown significant potential for applications in quantum simulation and topological quantum computation. Here, we propose a scalable protocol to derive universal conditions for AB caging with multi-flux. The numerical simulations validate the theoretical predictions by directly observing AB caging phenomena. We also investigate the breakage of the caging effect with onsite detuning, decoherence and non-Hermitian transitions. Our protocol provides an alternative approach for advancing quantum simulation of exotic states of matter.
Synthetic frequency dimension offers a powerful approach to simulate lattice models and control photon dynamics. However, extending this concept into the quantum regime, particularly at the single-photon level, has remained challenging in photonic platforms. Here, we demonstrate quantum-state initialization and detection of single-photon evolutions within a synthetic frequency lattice by integrating a superconducting qubit with a 16-meter aluminum coaxial cable. A tunable superconducting quantum interference device (SQUID)-based modulator is employed to synthesize lattice couplings and artificial gauge fields. We observe single-photon quantum random walks and Bloch oscillations, as well as nonadiabatic, unidirectional frequency conversion under rapid temporal modulation of the lattice Hamiltonian, together with band-structure measurements. The lattice connectivity can be readily reconfigured to construct higher-dimensional lattices using multiple drive tones. Our results establish superconducting quantum circuits as a versatile platform for programmable Hamiltonians and extensible synthetic lattices with flexible single-photon control.
Aharonov-Bohm (AB) caging, a special flat-band localization mechanism, has spurred great interest in different areas of physics. AB caging can be harnessed to explore the rich and exotic physics of quantum transport in flatband systems, where geometric frustration, disorder, and correlations act in a synergetic and distinct way than that in ordinary dispersive band systems. In contrast to the ordinary Anderson localization, where disorder induces localization and prevents transport, in flat band systems disorder can induce mobility, a phenomenon dubbed inverse Anderson transition. Here, we report on the experimental realization of the AB cage using a synthetic lattice in the momentum space of ultracold atoms with tailored gauge fields, and demonstrate the geometric localization due to the flat band and the inverse Anderson transition when correlated binary disorder is added to the system. Our experimental platform in a many-body environment provides a fascinating quantum simulator where the interplay between engineered gauge fields, localization, and topological properties of flat band systems can be finely explored.
Flat bands in condensed matter systems can host emergent states of matter, from insulating states in twisted bilayer graphene to fractionalized excitations in frustrated magnets and quantum Hall materials. A key phenomenon in certain flat-band systems is Aharonov-Bohm caging, where particles become localized due to destructive interference caused by gauge fields. Here we report on the experimental realization of highly tunable flat-band models populated by strongly interacting Rydberg atoms. By employing synthetic dimensions, we engineer a flat-band rhombic lattice with twisted boundaries and explore the control of Aharonov-Bohm caging during non-equilibrium dynamics through a tunable gauge field. Microscopic measurements of Rydberg pairs reveal the interaction-driven breakdown of Aharonov-Bohm caging in the limit of strong dipolar interactions, where lattice bands mix. In the limit of weak interactions, where caging persists, we observe effective magnetism arising from the interaction-driven mixing of degenerate flat-band states. These observations offer insights into emergent phenomena in synthetic quantum materials and expand our understanding of quantum many-body physics in engineered lattice systems.
The manipulation of distinct degrees of freedom of photons plays a critical role in both classical and quantum information processing. While the principles of wave optics provide elegant and scalable control over classical light in spatial and temporal domains, engineering quantum states in Fock space has been largely restricted to few-photon regimes, hindered by the computational and experimental challenges of large Hilbert spaces. Here, we introduce ``Fock-space optics", establishing a conceptual framework of wave propagation in the quantum domain by treating photon number as a synthetic dimension. Using a superconducting microwave resonator, we experimentally demonstrate Fock-space analogues of optical propagation, refraction, lensing, dispersion, and interference with up to 180 photons. These results establish a fundamental correspondence between Schrödinger evolution in a single bosonic mode and classical paraxial wave propagation. By mapping intuitive optical concepts onto high-dimensional quantum state engineering, our work opens a path toward scalable control of large-scale quantum systems with thousands of photons and advanced bosonic information processing.