2. A. Ramšak* J. Mravlje R. Žitko J. Bonča* T. Rejec* The Kondo effect in multiple quantum dot systems http://gawain.elte.hu/mcrtn/ Department of Physics Faculty of Mathematics and Physics University of Ljubljana *

3. Outline (1) Kondo (2) Multiple quantum dot systems (3) Entanglement

4. Conductance

5. Conductance

6. Conductance of non-interacting systems : U=0

8. Anderson model : U > 0

12. Kondo effect in a quantum dot

30. Test: single quantum dot

31. “Anderson model” with negative-U decrease

32. J. Mravlje, A. Ramšak, and T. Rejec, Phys. Rev. B 72, 121403(R) (2005)

33. Double quantum dot

36. J. Mravlje, A. Ramšak, and T. Rejec, Phys. Rev. B 73, 241305(R) (2006)

38. Double quantum dot 2 Kondo AFM 1 Kondo t t

39. Double quantum dot 2 Kondo AFM 1 Kondo t t

40. Double quantum dot 2 Kondo AFM 1 Kondo t t

41. Triple quantum dot

52. Entanglement in double quantum dots (concurrence) A B

53. Concurrence A B

54. A B

55. A B

56. A B......

57. Concurrence A B

58. Double quantum dots: entanglement versus the Kondo effect

59. Thermal equilibrium A-B entanglement

60. Zero magnetic field, thermal equilibrium A B

61. A B

62. A B

63. A B

64. A B

65. Double quantum dots: entanglement versus the Kondo effect

66. A. Ramšak, J. Mravlje, R. Žitko, and J. Bonča, quant-ph/0608065. Double quantum dots: entanglement versus the Kondo effect