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Springer proceedings in physics

Entropy and Information Measures of an Anharmonic Oscillator

Mariyah Ughradar, Vikash Kumar Ojha, Ramkumar Radhakrishnan, Siddharth Kumar Tiwari

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.1007/978-981-95-1513-4_113

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We explore quantitatively the fundamental connection between the entropy and local uncertainty product as an entanglement measure within the lowest energy eigenstate of a class of two-coupled anharmonic oscillator systems. We find that these two quantum aspects approach a unique relation as the entanglement between the oscillators becomes large if the potential of the first collective mode displays a generic single-well potential structure. This implies that the uncertainty product can be a good choice for the characterization of entanglement when the entropy is sufficiently large. Interestingly, although this relation is robust against the anharmonic perturbation, we find that it can be altered effectively by a quantum catastrophe.
Abstract We study the decoherence of an anisotropic anharmonic oscillator in a magnetic field, coupled to a bath of harmonic oscillators at high and low temperatures. We solve the anharmonic oscillator problem using perturbative techniques and derive the non-Markovian master equation in the weak coupling limit. The anharmonicity parameter α enhances decoherence due to the deconfining effect of anharmonicity. The oscillatory nature of the time evolution of heating function indicates information backflow. The von-Neumann entropy is also calculated for the system, which increases with α , consistent with the deconfining effect noted in the decoherence analysis. We have also proposed a cold ion experimental set up for testing our theoretical predictions. The study is of relevance to the domain of quantum technology where decoherence significantly affects the performance of a quantum computer.
The dependence of decoherence on chirp is investigated in an open one-dimensional chirped-driven anharmonic oscillator. The latter is perturbed by an Ohmic environment and the decoherence of the system is measured by the linear entropy. The entropy growth is found to be significantly dependent on the value of the chirp. Especially, the curve of the entropy growth versus the chirp value has a remarkable peak, near which the decoherence of the is greatly amplified. Further analyses shows that the enhancement of the entropy growth by the chirp is closely related to the influences of the chirped drive on the energy levels participating in the quantum evolution. This can be confirmed by the correspondence between the chirp dependence of the entropy growth, the quantum spectrum and the classical squared amplitude.