Experimental Geometric State Preparation on the Bloch Sphere Via Linear Mechanical Resonator
Abstract
The Bloch sphere representation, familiar from quantum two-level systems, can also describe classical linear systems whose dynamics are effectively confined to two modes. Here, we experimentally realize this framework in a linear two-mass, three-spring mechanical system by controlling superpositions of its symmetric and antisymmetric eigenmodes. The system is driven from both boundaries at a fixed frequency between the two resonances, so that the steady-state response remains within a two-mode manifold. By independently varying the relative amplitude and phase of the boundary excitations, we generate tunable modal superpositions. Scanning laser vibrometer measurements and frequency-domain analysis are used to extract the complex modal coefficients, which are then normalized and mapped onto Bloch sphere coordinates. This reconstruction reveals planar rotations of the state under phase sweeps and continuous steering between eigenstates under amplitude-ratio tuning. These results provide an experimental validation of Bloch sphere state reconstruction and steady-state geometric state preparation in a minimal linear mass-spring platform, establishing a simple classical testbed for exploring two-mode manifold dynamics.
Related
- Multimode radiation pressure actuation of a mechanical resonator using a spatial mode sorter
- Geometric calibration of central omnidirectional cameras under the unit-viewing sphere model
- Novel 10-dB Directional Coupler for Wireless RF Interrogator of SAW Resonator Sensors: Design, Simulation, and Experimental Investigation
- Geometric decomposition of the d-dimensional hard-sphere partition function
- On Optimal Measurement-State Preparation via Geometric Transport of the Squeezing Ellipse
BibTeX
@misc{faiaz2026experimental,
title = {{Experimental Geometric State Preparation on the Bloch Sphere Via Linear Mechanical Resonator}},
author = {Abrar N-E Faiaz and Donte McMullen and Kazi T Mahmood and M. Arif Hasan and Pierre Deymier and Keith Runge and Joshua A. Levine},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36322},
eprint = {2610.36322},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36322},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Experimental Geometric State Preparation on the Bloch Sphere Via Linear Mechanical Resonator
AU - Abrar N-E Faiaz
AU - Donte McMullen
AU - Kazi T Mahmood
AU - M. Arif Hasan
AU - Pierre Deymier
AU - Keith Runge
AU - Joshua A. Levine
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36322
UR - https://arxiv.org/abs/2610.36322
AB - The Bloch sphere representation, familiar from quantum two-level systems, can also describe classical linear systems whose dynamics are effectively confined to two modes. Here, we experimentally realize this framework in a linear two-mass, three-spring mechanical system by controlling superpositions of its symmetric and antisymmetric eigenmodes. The system is driven from both boundaries at a fixed frequency between the two resonances, so that the steady-state response remains within a two-mode manifold. By independently varying the relative amplitude and phase of the boundary excitations, we generate tunable modal superpositions. Scanning laser vibrometer measurements and frequency-domain analysis are used to extract the complex modal coefficients, which are then normalized and mapped onto Bloch sphere coordinates. This reconstruction reveals planar rotations of the state under phase sweeps and continuous steering between eigenstates under amplitude-ratio tuning. These results provide an experimental validation of Bloch sphere state reconstruction and steady-state geometric state preparation in a minimal linear mass-spring platform, establishing a simple classical testbed for exploring two-mode manifold dynamics.
ER -