Quantum Entanglement and Superconductivity. Subir Sachdev, Perimeter Institute and Harvard University

Transcription

1 Quantum Entanglement and Superconductivity Subir Sachdev, Perimeter Institute and Harvard University

2 Quantum Entanglement and Superconductivity Superconductor, levitated by an unseen magnet, in which countless trillions of electrons form a vast interconnected quantum state. Scientific American, January 2013 Subir Sachdev, Perimeter Institute and Harvard University

3 High temperature superconductors YBa 2 Cu 3 O 6+x

4 Nd-Fe-B magnets, YBaCuO superconductor Julian Hetel and Nandini Trivedi, Ohio State University

5 Nd-Fe-B magnets, YBaCuO superconductor Julian Hetel and Nandini Trivedi, Ohio State University

6 YBCO cables! American Superconductor Corporation

7 High temperature superconductors YBa 2 Cu 3 O 6+x

8 High temperature superconductors Cu O CuO 2 plane YBa 2 Cu 3 O 6+x

9 T. Wu, H. Maya re, S. Kramer, M. Horvatic, C. Berthier, W.N. Hardy, R. Liang, D.A. Bonn, and M.-H. Julien, Nature 477, 191 (2011) Superconducting T (K) Superconductor 40? Field-induced charge order Spin order p (hole/cu)

10 T. Wu, H. Maya re, S. Kramer, M. Horvatic, C. Berthier, W.N. Hardy, R. Liang, D.A. Bonn, and M.-H. Julien, Nature 477, 191 (2011). 120 Antiferromagnet 80 Superconducting T (K) Superconductor 40? Field-induced charge order Spin order p (hole/cu)

11 T. Wu, H. Maya re, S. Kramer, M. Horvatic, C. Berthier, W.N. Hardy, R. Liang, D.A. Bonn, and M.-H. Julien, Nature 477, 191 (2011). 120 Antiferromagnet Strange metal 80 Superconducting T (K) Superconductor 40? Field-induced charge order Spin order p (hole/cu)

12 T. Wu, H. Maya re, S. Kramer, M. Horvatic, C. Berthier, W.N. Hardy, R. Liang, D.A. Bonn, and M.-H. Julien, Nature 477, 191 (2011). 120 Antiferromagnet Quantum critical point Strange metal with T (K) long-range quantum entanglement. Can this help us understand Superconducting high temperature! Superconductor superconductivity? (and the rest of the phase diagram)? Field-induced charge order Spin order p (hole/cu)

13 Quantum superposition and entanglement Quantum phase transitions

14 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Interference of water waves

15 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Send electrons through the slits

16 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Interference of electrons

17 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Unlike water waves, electrons arrive oneby-one Interference of electrons

18 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Which slit does an electron pass through? Interference of electrons

19 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Which slit does an electron pass through? No interference when you watch the electrons Interference of electrons

20 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Which slit does an electron pass through? Each electron passes through both slits! Interference of electrons

21 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment L Let L represent the state with the electron in the left slit

22 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Let L represent the state with the electron in the left slit L R And R represents the state with the electron in the right slit

23 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Let L represent the state with the electron in the left slit L R And R represents the state with the electron in the right slit Actual state of each electron is Li + Ri

24 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle

25 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom:

26 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom: Hydrogen molecule: = _ = 1 2 ( )

27 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle _

28 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle _

29 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle _

30 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle _ Einstein-Podolsky-Rosen paradox : Measurement of one particle instantaneously determines the state of the other particle arbitrarily far away

31 Quantum superposition and entanglement Quantum phase transitions

32 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions

33 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions

34 120 Antiferromagnet Strange metal 80 Superconducting T (K) Superconductor 40? Field-induced charge order Spin order p (hole/cu) Quantum critical point

35 T. Wu, H. Maya re, S. Kramer, M. Horvatic, C. Berthier, W.N. Hardy, R. Liang, D.A. Bonn, and M.-H. Julien, Nature 477, 191 (2011). 120 Antiferromagnet Strange metal 80 Superconducting T (K) Superconductor 40 Spins of electrons on Cu sites? Field-induced charge order Spin order p (hole/cu)

36 Square lattice of Cu sites

37 Square lattice of Cu sites Remove some electrons

38 Square lattice of Cu sites Electrons entangle in ( Cooper ) pairs into chemical bonds =

39 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

40 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

41 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

42 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

43 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

44 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

45 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

46 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

47 Square lattice of Cu sites Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

48 Square lattice of Cu sites High temperature superconductivity? = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time

49 Square lattice of Cu sites High temperature superconductivity? = Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the quantum critical point.

50 Square lattice of Cu sites High temperature superconductivity? = Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the quantum critical point.

51 Square lattice of Cu sites High temperature superconductivity? = Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the quantum critical point.

52 Square lattice of Cu sites High temperature superconductivity? = Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the quantum critical point.

53 Square lattice of Cu sites High temperature superconductivity? = Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the quantum critical point.

54 Square lattice of Cu sites High temperature superconductivity? = Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the quantum critical point.

55 120 Antiferromagnet Strange metal 80 Superconducting T (K) Superconductor 40? Field-induced charge order Spin order p (hole/cu) Quantum critical point

56 120 Antiferromagnet Strange metal Scanning tunneling 80 microscopy Superconducting T (K) Superconductor 40? Field-induced charge order Spin order p (hole/cu) Quantum critical point

57 Scanning Tunneling Microscopy

58 SI-STM System J. C. Davis group, Rev. Sci. Inst. 70, 1459 (1999). Turbo Pump Load Lock Ultra low vibration cryostat. to Pumps Lead Filled Table Air Springs L 4 He Fridge Cleaver Lead Filled Legs High-field SC Magnet

59 SI-STM System J. C. Davis group, Rev. Sci. Inst. 70, 1459 (1999). Turbo Pump to Pumps Sample insert Load Lock Air Springs Massive ULV Cryostat Subkelvin Fridge STM + High Field Magnet Sample Exchange from RT Cryogenic UHV Cleave L 4 He Cleaver Lead Filled Legs High-field SC Magnet STM Head

60 y x Y. Kohsaka, C. Taylor, K. Fujita, A. Schmidt, C. Lupien, T. Hanaguri, M. Azuma, M. Takano, H. Eisaki, H. Takagi, S. Uchida, and J. C. Davis, Science 315, 1380 (2007).

61 y x Y. Kohsaka, C. Taylor, K. Fujita, A. Schmidt, C. Lupien, T. Hanaguri, M. Azuma, M. Takano, H. Eisaki, H. Takagi, S. Uchida, and J. C. Davis, Science 315, 1380 (2007).

62 R(r,150mV) Bi2212 UD45K y x

63 R(r,150mV) Bi2212 UD45K Cu sites y x

64 R(r,150mV) Bi2212 UD45K Intricrate pattern of tunneling currents contains signatures of long-range quantum entanglement!!(?) y x

65 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions

66 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions

67 Square lattice of Cu sites High temperature superconductivity? = Long-range entanglement has a heierarchical structure: electrons entangle in pairs, pairs entangle with pairs, and so on..

68 Tensor network representation of hierarchical entanglement at quantum critical point D-dimensional space depth of entanglement G. Vidal, Phys. Rev. Lett. 99, (2007)

69 String theory Allows unification of the standard model of particle physics with Einstein s theory of gravitation (general relativity). Vibrations of a string (its musical notes ) correspond to quarks, gravitons, the Higgs boson, photons, gluons......

70 A D-brane is a D-dimensional surface on which strings can end. If we focused only on the blue points on the D-dimensional surface, they would appear to us to have long-range quantum entanglement!

71 A D-brane is a D-dimensional surface on which strings can end. If we focused only on the blue points on the D-dimensional surface, they would appear to us to have long-range quantum entanglement!

72 Tensor network representation of hierarchical entanglement at quantum critical point D-dimensional space depth of entanglement

73 String theory near a D-brane D-dimensional space Emergent depth of spatial direction entanglement of string theory Brian Swingle, arxiv:

74 Tensor network representation of hierarchical entanglement at quantum critical point D-dimensional space Emergent depth of spatial direction entanglement of string theory Brian Swingle, arxiv:

75 States of matter with long-range quantum entanglement in D dimensions String theory and Einstein s General Relativity in D+1 dimensions

76 States of matter with long-range quantum entanglement in D dimensions Are there solutions of Einstein s General Relativity in D+1 dimensions which correspond to superconductors and strange metals? String theory and Einstein s General Relativity in D+1 dimensions

77 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions

78 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions

79 Black Holes Objects so massive that light is gravitationally bound to them.

80 Black Holes Objects so massive that light is gravitationally bound to them. In Einstein s theory, the region inside the black hole horizon is disconnected from the rest of the universe. Horizon radius R = 2GM c 2

81 Black Holes + Quantum theory Around 1974, Bekenstein and Hawking showed that the application of the quantum theory across a black hole horizon led to many astonishing conclusions

82 Quantum Entanglement across a black hole horizon _

83 Quantum Entanglement across a black hole horizon _

84 Quantum Entanglement across a black hole horizon _ Black hole horizon

85 Quantum Entanglement across a black hole horizon _ Black hole horizon

86 Quantum Entanglement across a black hole horizon There is long-range quantum entanglement between the inside and outside of a black hole Black hole horizon

87 Quantum Entanglement across a black hole horizon There are special black hole solutions which mimic strange metals and superconductors! Black hole horizon

88 Quantum Entanglement across a black hole horizon There are special black hole solutions which mimic strange metals and superconductors! These black hole states of General Relativity in D+1 dimensions correspond to (and allow us to compute the properties of) superconductors and strange metals in D dimensions Black hole horizon

89 Quantum superposition and entanglement Quantum phase transitions

90 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions

91 Quantum Entanglement and Superconductivity Superconductor, levitated by an unseen magnet, in which countless trillions of electrons form a vast interconnected quantum state. Scientific American, January 2013 Subir Sachdev, Perimeter Institute and Harvard University