No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Analytical solution of the time evolution of an entangled electron spin pair in a double quantum dot nanostructure
1.See, e.g., K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1996), and references therein.
2.P. Meystre and M. Sargent, Elements of Quantum Optics (Springer, New York, 1999).
8.Condensed-matter systems such as the one considered here are particularly strongly affected by decoherence due to the strong interaction between the system and its environment. But, decoherence and dissipation are also relevant for other quantum systems which may serve as qubits, such as cold atoms [see, e.g., C. F. Roos, G. P. T. Lancaster, M. Riebe, H. Häffner, W. Hänsel, S. Gulde, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, Phys. Rev. Lett. 92, 220402 (2004)].
10.For a review on quantum dots, see L. P. Kouwenhoven, C. M. Marcus, P. L. McEuen, S. Tarucha, R. M. Westervelt, and N. S. Wingreen, in Proceedings of the Advanced Study Institute on Mesoscopic Electron Transport, edited by L. P. Kouwenhoven, G. Schön, and L. L. Sohn (Kluwer, Dordrecht, 1997).
11.Controlling the number of electrons in a lateral quantum dot down to one or zero has recently been achieved; see M. Ciorga, A. S. Sachrajda, P. Hawrylak, C. Gould, P. Zawadzki, S. Jullian, Y. Feng, and Z. Wasilewski, Phys. Rev. B 61, R16315 (2000);
11.J. M. Elzerman, R. Hanson, J. S. Greidanus, L. H. Willems van Beveren, S. De Franceschi, L. M. K. Vandersypen, S. Tarucha, and L. P. Kouwenhoven, Phys. Rev. B 67, 161308 (2003);
12.Up to parallel magnetic fields of at least the singlet state is the ground state of a doubly occupied quantum dot; see R. Hanson, L. M. K. Vandersypen, L. H. Willems van Beveren, J. M. Elzerman, I. T. Vink, and L. P. Kouwenhoven, Phys. Rev. B 70, 241304 (2004).
16.For the same reason tunneling of an electron from dot to channel—which is an incoherent process and may involve inelastic scattering from one orbital to another—does not affect the spin coherence of the entangled pair.
17.Assuming the same decoherence rate for both dots is not a crucial assumption and Eqs. (8) can straightforwardly be solved for different decoherence rates in the left and right dot. The resulting solution is qualitatively of the same form as Eqs. (9) and (10), only with more lengthy expressions.
18.The RWA approximation (Ref. 2) is not essential and one can solve Eqs. (8) without it, which results in a solution that is qualitatively similar. Since in our system (Ref. 9), where is the time required to rotate one spin, the RWA is an excellent approximation in practice.
19.J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, Nature (London) 430, 431 (2004).
22.See the calculation of and in Ref. 9.
23.For the general case the expressions are rather lengthy, but not qualitatively different.
24.The solutions for and given here are valid for , i.e., assuming the W's to be zero is not necessary.
Article metrics loading...
Full text loading...
Most read this month