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The Berry phase, a concept of significant interest in quantum and classical mechanics, illuminates the dynamics of physical systems. Our current study explores this phenomenon within a classical granular network, employing an "elastic bit" that serves as a classical counterpart to the quantum bit. This approach establishes a connection between classical and quantum mechanics. By adjusting external forces, we generate an elastic bit within the granular network and map its behavior onto a Bloch sphere, akin to operating quantum logic gates. Varied manipulations of these external drivers yield a spectrum of Berry phases, from trivial (0) to nontrivial (π), unveiling the topological nature of the elastic bit. Crucially, this topological behavior is governed by external manipulations rather than the material or geometric properties of the medium. The nontrivial Berry phases, in particular, highlight energy localization within the granule vibrations, marking a significant insight into system dynamics. This research bridges the gap between the quantum and classical realms and paves the way for designing novel materials with unique properties.
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Topological insights from state manipulation in a classical elastic system
The exploration of the Berry phase in classical mechanics has opened new frontiers in understanding the dynamics of physical systems, analogous to quantum mechanics. Here, we show controlled accumulation of the Berry phase in a two-level elastic bit, which is a classical counterpart to qubits, achieved by manipulating coupled granules with external drivers. Employing the Bloch sphere representation, the paper demonstrates the manipulation of elastic bit states and the realization of quantum-analog logic gates. A key achievement is the calculation of the Berry phase for various system states, revealing insights into the system’s topological nature. Unique to this study is the use of external parameters to explore topological transitions, contrasting with traditional approaches focusing on internal system modifications. By linking the classical and quantum worlds through the Berry phase of an elastic bit, this work extends the potential applications of topological concepts in designing new materials and computational models.
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- PAR ID:
- 10570190
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- AIP Advances
- Volume:
- 15
- Issue:
- 2
- ISSN:
- 2158-3226
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This study investigates the Berry phase, a key concept in classical and quantum physics, and its manifestation in a classical system. We achieve controlled accumulation of the Berry phase by manipulating the elastic bit (a classical analogue to a quantum bit) in an externally driven, homogeneous, spherical, nonlinear granular network. This is achieved through the classical counterpart of quantum coherent superposition of states. The elastic bit's state vectors are navigated on the Bloch sphere using external drivers' amplitude, phase, and frequency, yielding specific Berry phases. These phases distinguish between trivial and nontrivial topologies of the elastic bit, with the zero Berry phase indicating pure states of the linearized granular system and the nontrivial π phase representing equal superposed states. Other superposed states acquire different Berry phases. Crucially, these phases correlate with the structure's eigenmode vibrations: trivial phases align with distinct, in-phase, or out-of-phase eigenmodes, while nontrivial phases correspond to coupled vibrations where energy is shared among granules, alternating between oscillation and rest. Additionally, we explore Berry's phase generalizations for non-cyclic evolutions. This research paves the way for advanced quantum-inspired sensing and computation applications by utilizing and controlling the Berry phase.more » « less
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