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arXiv 1504.00752cond-mat.mes-hallquant-ph
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微波通过一维量子比特链传输的非厄米哈密顿方法

Non-Hermitian Hamiltonian approach to the microwave transmission through one- dimensional qubit chain

Ya. S. Greenberg, A. A. Shtygashev

摘要:

研究了微波光子在一维开放波导中与多个人工原子(量子比特)相互作用的传播。在投影算符和非厄米哈密顿方法的基础上,我们发展了一个单光子近似方案,用于计算微波信号在含有任意数量\emph{N}的非相互作用量子比特的波导中的透射和反射因子.我们详细考虑了链中两个和三个量子比特的共振和光子介导的纠缠。我们证明了在非马尔可夫情形下,定义纠缠态衰变率的共振宽度可以比单个量子比特的衰变宽度小得多。研究还表明,对于相同的量子比特,在长波长极限下,相干超辐射态的宽度等于\emph{N}单个量子比特自发跃迁宽度之和.本文所得到的结果具有普遍性,可以应用于任何类型的量子比特。量子比特的具体属性仅编码在两个参数中:量子比特能量$Ω$和自发发射率$Γ$。

英文摘要:

We investigate the propagation of microwave photons in a one-dimensional open waveguide interacting with a number of artificial atoms (qubits). Within the formalism of projection operators and non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme for the calculation of the transmission and reflection factors of the microwave signal in a waveguide which contains an arbitrary number \emph{N} of non-interacting qubits. We considered in detail the resonances and photon mediated entanglement for two and three qubits in a chain. We showed that in non Markovian case the resonance widths, which define the decay rates of the entangled state, can be much smaller than the decay width of individual qubit. It is also shown that for identical qubits in the long wavelength limit a coherent superradiant state is formed with the width being equal to the sum of the widths of spontaneous transitions of \emph{N} individual qubits. The results obtained in the paper are of general nature and can be applied to any type of qubits. The specific properties of the qubit are only encoded in the two parameters: the qubit energy $Ω$ and the rate of spontaneous emission $Γ$.

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