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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.
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Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
We first compare the geometric frameworks behind the Uhlmann andBerry phases in a fiber-bundle language and then evaluate the Uhlmannphases of bosonic and fermionic coherent states. The Uhlmann phases ofboth coherent states are shown to carry geometric information anddecrease smoothly with temperature. Importantly, the Uhlmann phasesapproach the corresponding Berry phases as temperature decreases.Together with previous examples in the literature, we propose acorrespondence between the Uhlmann and Berry phases in thezero-temperature limit as a general property except some special casesand present a conditional proof of the correspondence.
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- Award ID(s):
- 2011360
- PAR ID:
- 10439582
- Date Published:
- Journal Name:
- SciPost Physics Core
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2666-9366
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.21468/SciPostPhysCore.6.1.024
