排列在正多边形中的相同量子位的完整本征态
Complete eigenstates of identical qubits arranged in regular polygons
摘要：
我们计算了N个量子比特或排列在正多边形顶点上的二能级原子（TLA）阵列的相干单激发和多激发对应的能量本征值和本征态。我们仅假设耦合通过交换相互作用发生，该交换相互作用取决于量子位之间的分离。我们包括了所有量子比特对之间的相互作用，我们的结果对相对于辐射波长的任意距离都有效。为了说明这些状态的有用性，我们绘制了4个量子比特阵列的n=2（双激子）本征态的衰减率的距离依赖性，并将双激子本征值和本征态以及吸收频率、线宽和相对强度制成表格，用于由N=2，.，长波长极限的9个量子比特。
英文摘要：
We calculate the energy eigenvalues and eigenstates corresponding to coherent single and multiple excitations of an array of N identical qubits or two-level atoms (TLA's) arranged on the vertices of a regular polygon. We assume only that the coupling occurs via an exchange interaction which depends on the separation between the qubits. We include the interactions between all pairs of qubits, and our results are valid for arbitrary distances relative to the radiation wavelength. To illustrate the usefulness of these states, we plot the distance dependence of the decay rates of the n=2 (biexciton) eigenstates of an array of 4 qubits, and tabulate the biexciton eigenvalues and eigenstates, and absorption frequencies, line widths, and relative intensities for polygons consisting of N=2,...,9 qubits in the long-wavelength limit.
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