Effect of Static Disorder in an Electron Fabry – Perot Interferometer with Two Quantum Scattering Centers

The key role that entanglement plays in quantum information processing has been investigated over the past few years [1]. In this framework, the role that it plays in quantum transport in mesoscopic systems has been analyzed [2]. Recently, we have shown a novel way in which entanglement can be used for controlling electron transport in nanostructures [3]. Assume that we have a 1D wire, where two spin–1/2 impurities are embedded at a fixed distance. Such a system can be regarded as the electron analogue of a Fabry–Perot (FP) interferometer, with the impurities playing the role of two mirrors with a spin quantum degree of freedom. Single electrons are injected into the wire and undergo multiple scattering between the two magnetic impurities due to the presence of a contact exchange electron– impurity coupling. At each scattering event, spin-flip may occur and, thus, the transmitted spin state of the overall system will be generally different from the incoming one. The typical behavior shown by electron transmittivity T consists of a loss of electron coherence and, thus, of a resonance condition T = 1, due to the presence of internal spin degrees of freedom of the scattering centers [4]. Such a system is, indeed, the electron analogue of a Fabry–Perot (FP) interferometer, with the impurities playing the role of two mirrors with a spin quantum degree of freedom. However, unlike the standard FP device, where scattering with each mirror introduces a well-fixed phase shift, in the present system , the above phase shifts depend on the electron– impurities spin state and, thus, in general, a resonance condition cannot take place. However, the presence of quantum scatterers allows one to investigate if and to what extent maximally entangled states of the impurity spins can affect electron transmission. Denoting the triplet and singlet maximally entangled spin states of the impurities, respectively, by |Ψ ± 〉 = (|↑↓〉 ± |↓↑〉), we have, thus, found that when |Ψ – 〉 is prepared, a perfect resonance condition T = 1 can be always reached at electron wavevectors fulfilling kx 0 = n π (where n is an integer and x 0 is the distance between the impurities) and regardless of the electron spin state. When this occurs, the incoming spin state of the electron–impuri-ties system is transmitted completely unchanged. Therefore, a sort of perfect " transparency " takes place [3]. Moreover, as illustrated in Fig. 1, electron transmission …