A. Ramšak* J. Mravlje R. Žitko J. Bonča* T. Rejec* The Kondo effect in multiple quantum dot systems Department of Physics Faculty of Mathematics and Physics University of Ljubljana *
Outline (1) Kondo (2) Multiple quantum dot systems (3) Entanglement
Conductance
Conductance
Conductance of non-interacting systems : U=0
Anderson model : U > 0
Kondo effect in a quantum dot
Test: single quantum dot
“Anderson model” with negative-U decrease
J. Mravlje, A. Ramšak, and T. Rejec, Phys. Rev. B 72, (R) (2005)
Double quantum dot
J. Mravlje, A. Ramšak, and T. Rejec, Phys. Rev. B 73, (R) (2006)
Double quantum dot 2 Kondo AFM 1 Kondo t t
Double quantum dot 2 Kondo AFM 1 Kondo t t
Double quantum dot 2 Kondo AFM 1 Kondo t t
Triple quantum dot
Entanglement in double quantum dots (concurrence) A B
Concurrence A B
A B
A B
A B......
Concurrence A B
Double quantum dots: entanglement versus the Kondo effect
Thermal equilibrium A-B entanglement
Zero magnetic field, thermal equilibrium A B
A B
A B
A B
A B
Double quantum dots: entanglement versus the Kondo effect
A. Ramšak, J. Mravlje, R. Žitko, and J. Bonča, quant-ph/ Double quantum dots: entanglement versus the Kondo effect