Temperature-dependent quantum fluctuations of a capacitor with quantum relaxor material included inductor–capacitor circuit
摘要
An quantum electrical circuit consisting of a linear inductor and a parallel-plate nonlinear capacitor (inductor–capacitor (LC) circuit) with a quantum relaxor ferroelectric material is considered. The spacing between energy levels in a nonlinear LC circuit is found to be non-uniform, in contrast with the uniform spacing observed in a linear LC circuit. In this work, the capacitance of the nonlinear capacitor is considered as a function of temperature, which leads to a temperature-dependent resonant frequency of the circuit. The analytical expression for capacitance is derived by simulating its temperature-dependent variations in the nonlinear capacitor, based on the corresponding experimental data. The quantum Hamiltonian of a nonlinear LC circuit is written using the rotating wave approximation. By solving the Schrödinger equation, the spectrum of eigenvalues and eigenfunctions, as well as the quantum fluctuations of charge and current in the nonlinear LC circuit, are obtained as functions of temperature. Plots of wavefunctions and quantum fluctuations show that as temperature increases to a specific point, the fluctuations of charge (current) decrease (increase). Below this point, however, the trend reverses, and the fluctuations begin to increase (decrease). This research, by introducing temperature as a tunable parameter, could offer a novel approach to reduce quantum fluctuations, effectively leading to the generation of squeezed states relevant to quantum information and precision measurement applications. Moreover, the non-uniform spacing between energy levels shows that quantum nonlinear LC circuits can be considered promising candidates for the construction of qubits in quantum computers.