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International Journal of Modern Physics B

SHOT NOISE OF ELECTRON PAIRS IN NONCYCLIC AND NON-ADIABATIC MAGNETIC FIELD

XIAN-JUN YE

Published Jul 10, 2007• 0 citations
Publisher

Abstract

By adding a rotating magnetic field in one incoming lead, we calculate the shot noise with different incident states in a 4-lead beam-splitter. The result shows that the shot noise of singlet and triplet states oscillates with the external magnetic field and depends on the symmetric properties of the incident states. Thus, the singlet, entangled triplet, and polarized states can be distinguished by adjusting the magnetic field.

DOI
10.1142/s0217979207037491

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By adding a rotating magnetic field in one incoming lead, we calculate the shot noise with different incident states in a 4-lead beam-splitter. The result shows that the shot noise of singlet and triplet states oscillates with the external magnetic field and depends on the symmetric properties of the incident states. Thus, the singlet, entangled triplet, and polarized states can be distinguished by adjusting the magnetic field.
We study shot noise for entangled electrons in a 4-lead beam-splitter with one incoming lead driven by adiabatically rotating magnetic fields. We propose a setup of an adiabatically rotating magnetic field which is appropriate for an electron beam to transport through. Using the scattering matrix approach, we find that shot noise for the singlet and that for the entangled triplet oscillates between bunching and antibunching due to the influence of the Berry phase. It provides us with a new approach for testing the Berry phase in electron transport on the basis of entanglement.
We extend our previous work on shot noise for entangled and spin polarized electrons in a beam-splitter geometry with spin-orbit (SO) interaction in one of the incoming leads (lead 1). In addition to accounting for both the Dresselhaus and the Rashba spin-orbit terms, we present general formulas for the shot noise of singlet and triplets states derived within the scattering approach. We determine the full scattering matrix of the system for the case of leads with two orbital channels coupled via weak SO interactions inducing channel anticrossings. We show that this interband coupling coherently transfers electrons between the channels and gives rise to an additional modulation angle---dependent on both the Rashba and Dresselhaus interaction strengths---which allows for further independent coherent control of the electrons traversing the incoming leads. We derive explicit shot noise formulas for a variety of correlated pairs (e.g., Bell states) and lead spin polarizations. Interestingly, the singlet and each of the triplets defined along the quantization axis perpendicular to lead 1 (with the local SO interaction) and in the plane of the beam splitter display distinctive shot noise for injection energies near the channel anticrossings; hence, one can tell apart all the triplets, in addition to the singlet, through noise measurements. We also find that spin-orbit induced backscattering within lead 1 reduces the visibility of the noise oscillations, due to the additional partition noise in this lead. Finally, we consider injection of two-particle wavepackets into leads with multiple discrete states and find that two-particle entanglement can still be observed via noise bunching and antibunching.
We report experimental research into the possibility of using shot noise mea-surements to detect the entangled states of electron spins. The study is part of the effort towards the demonstration of the use of electron spins as quantum bits (qubits) for quantum computing and quantum information processing. Electrons are electrically injected into two neighboring quantum dots and interact with each other through the exchange coupling, after which they tunnel out of the dots and are incident on a beam splitter, which introduces quantum interference between electron states. Depending on the state of the electrons exiting the dots, the outgoing states of electrons scattering off the beam splitter are different, corresponding to different shot noise in the electrical currents flowing into the channels after the beam splitter. Our experimental data is consistent with most theoretical predictions and provides initial evidence of electron spin entanglement. A comprehensive study of the shot noise in mesoscopic semiconductor tunnel barriers is also reported. Besides the theoretically predicted full shot noise, sup-pressed and enhanced shot noise are also observed. Normal conductance measure-ments and numerical simulations are done to understand the shot noise deviation. Our study shows that shot noise in mesoscopic systems is extremely sensitive to the microscopic details, such as potential disorder and impurity configuration.
The correlation and fluctuation of both entangled electrons and spin-polarized pairs affected by two rotating magnetic fields in a setup proposed by J. Carlos Egues etc. (Phys. Rev. Lett. {\bf 89}(2002) 176401) are studied theoretically by using scattering approach. Differing from polarized pair, the entangled electron pairs are shown to behave like a composite particle with the total spins and its zzz components. The singlet and triplet states exhibit different bunching and antibunching features, which can be easily adjusted by the magnetic fields. The correlations and variances can show up distinguish output signals for the four incident states. Our results are expected to be tested by using coincident technique.
We are motivated by a setup proposed by J. Carlos Egues et al . ( Phys. Rev. Lett. , 89 (2002) 176401) to investigate correlations of entangled electron pairs in the presence of two rotating magnetic fields. Using the scattering approach we show that the entangled electron pairs just like a composite particle. The singlet and triplet states show different bunching and anti-bunching behaviors, which can be easily controlled by the magnetic fields. The results can be demonstrated by using a coincident technique. The correlations show up at characteristic output signals for different states.
Addressing the feasibility of quantum communication with entangled electrons in an interacting many-body environment, we propose an interference experiment using a scattering setup with an entangler and a beam splitter. It is shown that, due to electron-electron interaction, the spin correlation of the entangled singlet and triplet states is reduced by zF2{z}_{F}^{2}zF2​ in a conductor described by Fermi liquid theory. We calculate the quasiparticle weight factor zF{z}_{F}zF​ for a two-dimensional electron system. The current noise for electronic singlet states turns out to be enhanced (bunching behavior), while it is reduced for triplet states (antibunching). Within standard scattering theory, we find that the Fano factor (noise-to-current ratio) for singlets is twice as large as for independent classical particles and is reduced to zero for triplets.