並列タイトル等シュウィンガー-ケルディッシュ形式の非摂動論的完全計数統計理論に基づいたオーミック散逸を持つ極微細個体量子もつれ構造における電流雑音の交差相関のバンチング性に関する研究
一般注記type:Thesis
In this thesis, we propose the the non-perturbative theory for full counting statistics (FCS) in solid state entangler (SSE) based on Nambu-Gor'kov and Schwinger-Keldysh field theoretical non-equilibrium method. Based on the theory we study the currents and cross correlation of the current noise of SSE to get the further understanding of physics of quantum entanglement. The theory can be applicable to the transport properties in the region where Coulomb blockade and Andreev reflection coexist, since tunneling processes are taken into account non-perturbatively in the presence of arbitrarily large charging effect as well as electromagnetic environment effect. Concerning the latter, we treat SSE with ohmic resistance phenomenologically in the spirit of Caldeira-Leggett theory. The SSE considered is a coupled ultra-small double tunnel junction, structure of which consists of a common superconducting electrode/normalconducting left and right ultra-small central electrodes (islands)/normalconducting left and right drains. Each of islands are capacitively coupled with gate electrodes to control tunneling. We call the SSE double S/N/N capacitively coupled single electron transistors (double S/N/N C-SET). This kind of SSE is called the Cooper pair splitter (CPS) in general. Based on the theory, we derive explicit expression for cumulant generating function (CGF) for FCS. Explicit expressions for the currents and cross correlation of current noise for the double S/N/N C-SET are obtained as the first and second cumulants from CGF, respectively. Since we are interested in extracting and controlling quantum entanglement information by the charging effect, we mainly focus our attention on the study of SSE with U < Δ (U: charging energy, Δ: energy gap of superconductor) so that sufficiently wide superconducting subgap region can be expected. We show that, in the subgap region there are three kinds of currents due to the direct Andreev reflection (dAR), crossed Andreev reflection (cAR) and elastic cotunneling (EC). Each of the currents show Coulomb blockade related phenomena (Coulomb gaps, Coulomb staircases, and Coulomb oscillations) due to the charging effect. Since contribution to the cross correlation of current noise SLR(0) comes from currents due to cAR and EC in subgap region, SLR(0) is strongly influenced by the charging effect. It is shown that SLR(0) is always positive (bunching correlation) if two C-SETs are biased symmetrically. The bunching correlation is not genuine one (antibunching correlation) peculiar to the normal fermion flow. It is the direct consequence of the fermion flow with quantum entanglement. SLR(0) also shows bunching-antibunching crossover followed by restoration of bunching correlation as bias voltage increases; i.e., SLR(0) becomes negative only in a narrow window of bias voltage as far as bias condition for two C-SETs is not so asymmetric enough. As the asymmetry in bias condition becomes sizable, SLR(0) shows bunching-antibunching crossover only and never shows the restoration of bunching correlation. We also show that the ohmic resistance strongly influences on SLR(0), partly because of increase in Coulomb Gap of cAR current, and partly because of decrease in magnitude of cAR current due to the de-coherence by ohmic dissipation. We propose the method of extraction and control of quantum entanglement information by the ferromagnetic ordering. We consider double S/F/N C-SET, structure of which is the one with the nonmagnetic islands of double S/N/N C-SET is replaced by ferromagnetic islands. It is shown that only cAR current (EC current) contributes to SLR(0) if the half metal ferromagnetic islands are employed as anti-parallel (parallel) alignment. Theoretical predictions stated above are made for the first time in this study and the results lead us to the new stage of the study on bunching-antibunching nature of current noise cross correlation in the presence of quantum entanglement.
連携機関・データベース国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）