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Science in China Series A Mathematics

Coherent states of a time-dependent forced harmonic oscillator and their Aharonov-Anandan phase

Yufeng Liu, Yian Lei, Jinyan Zeng

Published Jun 1, 2000• 2 citations
Publisher
DOI
10.1007/bf02908779

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Beyond the adiabatic limit, the Aharonov-Anandan phase is a generalized description of Berry's phase. In this regime, systems with time-independent Hamiltonians may also acquire observable geometric phases. Here we report on a measurement of the Aharonov-Anandan phase in photonics. Different from previous optical experiments on geometric phases, the implementation is based on light modes confined in evanescently coupled waveguides rather than polarization-like systems, thereby physical models in more than two-dimensional Hilbert spaces are achievable. In a tailored photonic lattice, we realize time-independent quantum-driven harmonic oscillators initially prepared in the vacuum state and achieve a measurement of the Aharonov-Anandan phase via integrated interferometry.