We propose an approach to the study of open quantum systems based on a parametric representation of the principal system. The representation is obtained introducing generalized coherent states for the environment, and is such that the evolution from a fully quantum environment to a classical one can be inherently followed. The method is applied to the specific case where the principal system is a central qubit and the environment is a surrounding ring of interacting spins, with the overall Hamiltonian being that of the $s=1/2$ Heisenberg star with frustration. In this case the quantum character of the environment, embodied by the total spin $S$ of the ring, can be physically varied by acting on the ratio between the couplings entering the Hamiltonian, and formally followed by increasing $S$. We find that when the star is in any of its eigenstates, the qubit behaves as if it were under the effect of an external magnetic field, whose direction in real space is set by the variables defining the environmental coherent states, and is hence broadened according to their quantum probability distribution. When the quantum character of the environment is reduced, such distribution becomes narrower, finally collapsing into a Dirac-$δ$ as $S\to\infty$. The entanglement between the central qubit and its environment remains well defined even in this limit, where it comes across as the binary entropy of the $2π$-normalized Berry phase characterizing the dynamics of a qubit in an adiabatically precessing magnetic field.
Environment-assisted squeezing in a coherently driven non-Hermitian degenerate parametric oscillator
Adama Science and Technology University（阿达马科学与技术大学）；Khalifa University of Science and Technology（哈利法科学技术大学）；Durban University of Technology（德班理工大学）；Arba Minch University（阿尔巴明奇大学）
Quantum battery optimized by parametric amplification
College of Physics and Electronic Engineering, Northwest Normal University（西北师范大学物理与电子工程学院）；Gansu Provincial Research Center for Basic Disciplines of Quantum Physics（甘肃省量子物理基础学科研究中心）；Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou Center for Theoretical Physics, and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University（兰州大学理论物理省部共建教育部重点实验室、兰州理论物理中心）；Lanzhou University（兰州大学）
