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Springer eBooks

Experimental Detection of Geometric Phases I: Quantum Systems in Classical Environments

Arno Böhm, Ali Mostafazadeh, Hiroyasu Koizumi, Qian Niu, Joseph Zwanziger

Published Jan 1, 2003• 1 citation
Publisher
DOI
10.1007/978-3-662-10333-3_10

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We study the role of driving in a two-level system evolving under the presence of a structured environment in different regimes. We find that adding a periodic modulation to the two-level system can greatly enhance the survival of the geometric phase for many time periods in an intermediate coupling to the environment. In this regime, where there are some non-Markovian features characterizing the dynamics, we note that adding driving to the system leads to a suppression of non-Markovianity altogether, allowing for a smooth dynamical evolution and an enhancement of the robustness condition of the geometric phase. As the model studied herein is the one used to model experimental situations such as hybrid quantum classical systems feasible with current technologies, this knowledge can aid the search for physical setups that best retain quantum properties under dissipative dynamics.
We present a unified view of the Berry phase of a quantum system and its entanglement with surroundings. The former reflects the nonseparability between a system and a classical environment as the latter for a quantum environment, and the concept of geometric time-energy uncertainty can be adopted as a signature of the nonseparability. Based on this viewpoint, we study their relationship in the quantum-classical transition of the environment, with the aid of a spin-half particle (qubit) model exposed to a quantum-classical hybrid field. In the quantum-classical transition, the Berry phase has a similar connection with the time-energy uncertainty as the case with only a classical field, whereas the geometric phase for the mixed state of the qubit exhibits a complementary relationship with the entanglement. Namely, for a fixed time-energy uncertainty, the entanglement is gradually replaced by the mixed geometric phase as the quantum field vanishes. And the mixed geometric phase becomes the Berry phase in the classical limit. The same results can be draw out from a displaced harmonic oscillator model.