Quantum Entanglement and Superconductivity. Subir Sachdev, Harvard University
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1 Quantum Entanglement and Superconductivity Subir Sachdev, 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, 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 BaFe2 As2
8 Resistivity 0 + AT BaFe 2 (As 1-x P x ) 2 T 0 T SD T c α " 2.0 SDW 1.0 Superconductivity 0 S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, (2010)
9 Resistivity 0 + AT BaFe 2 (As 1-x P x ) 2 T 0 T SD T c α " 2.0 SDW 1.0 Superconductivity 0 S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, (2010) Ordinary metal
10 Resistivity 0 + AT Strange Metal BaFe 2 (As 1-x P x ) 2 T 0 T SD T c α " 2.0 SDW 1.0 Superconductivity 0 S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, (2010) Ordinary metal
11 Resistivity 0 + AT Strange Metal BaFe 2 (As 1-x P x ) 2 T 0 T SD T c α " 2.0 SDW Antiferromagnet Superconductivity S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, (2010) Ordinary metal
12 Quantum critical point Strange Metal with BaFe 2 (As 1-x P x ) 2 Resistivity 0 + AT long-range quantum entanglement.! T 0 T SD T c SDW Antiferromagnet Can this help us understand high temperature superconductivity? (and the rest of the phase diagram) Superconductivity α " S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, (2010) Ordinary metal
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 Which slit does an electron pass through? Interference of electrons
18 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
19 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
20 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment L Let L represent the state with the electron in the left slit
21 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
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 Actual state of each electron is Li + Ri
23 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle
24 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom:
25 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom: Hydrogen molecule: = _ = 1 2 ( )
26 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle _
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 _ Einstein-Podolsky-Rosen paradox : Measurement of one particle instantaneously determines the state of the other particle arbitrarily far away
30 Quantum superposition and entanglement Quantum phase transitions
31 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes 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 Resistivity 0 + AT Strange Metal BaFe 2 (As 1-x P x ) 2 T 0 T SD T c α " 2.0 SDW Antiferromagnet Superconductivity S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, (2010) Ordinary metal
34 Electrons pair to form Cooper pairs which are bosons.! BaFe 2 (As 1-x P x ) 2 Bosons do not obey the exclusion principle. So all the Cooper Metal pairs occupy the lowest energy state, and we obtain a Bose-Einstein condensate.! This condensate is responsible for superconductivity. Strange Resistivity 0 + AT T 0 T SD T c α " 2.0 SDW Antiferromagnet Superconductivity S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, (2010) Ordinary metal
35 Resistivity 0 + AT Strange Metal BaFe 2 (As 1-x P x ) 2 T 0 T SD T c α " 2.0 SDW Antiferromagnet Spins of electrons on Fe sites 1.0 Superconductivity 0 S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, (2010) Ordinary metal
36 Spins of electrons on Fe sites
37 = 1 2 ( ) As we increase x, the electron spins entangle in pairs
38 = 1 2 ( ) As we increase x, the electron spins entangle in pairs
39 = 1 2 ( ) As we increase x, the electron spins entangle in pairs
40 = 1 2 ( ) As we increase x, the electron spins entangle in pairs
41 = 1 2 ( ) As we increase x, the electron spins entangle in pairs
42 = 1 2 ( ) As we increase x, the electron spins entangle in pairs
43 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
44 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
45 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
46 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
47 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
48 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
49 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
50 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
51 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other.
52 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other. And then pairs of pairs entangle, and so on.
53 = 1 2 ( ) As we increase x, the electron spins entangle in pairs. And then the pairs entangle with each other. And then pairs of pairs entangle, and so on. This goes on ad-infinitum at the quantum critical point, leading to long-range quantum entanglement
54 Tensor network representation of entanglement at quantum critical point D-dimensional space depth of entanglement G. Vidal, Phys. Rev. Lett. 99, (2007)
55 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions
56 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions
57 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......
58 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!
59 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!
60 Tensor network representation of entanglement at quantum critical point D-dimensional space depth of entanglement
61 String theory near a D-brane D-dimensional space Emergent depth of spatial direction entanglement of string theory Brian Swingle, arxiv:
62 Tensor network representation of entanglement at quantum critical point D-dimensional space Emergent depth of spatial direction entanglement of string theory Brian Swingle, arxiv:
63 States of matter with long-range quantum entanglement in D dimensions String theory and Einstein s General Relativity in D+1 dimensions
64 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
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 Black Holes Objects so massive that light is gravitationally bound to them.
68 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
69 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
70 Quantum Entanglement across a black hole horizon _
71 Quantum Entanglement across a black hole horizon _
72 Quantum Entanglement across a black hole horizon _ Black hole horizon
73 Quantum Entanglement across a black hole horizon _ Black hole horizon
74 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
75 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
76 Quantum Entanglement across a black hole horizon There is long-range quantum entanglement between the inside and outside of a black hole This entanglement leads to a black hole temperature (the Hawking temperature) and a black hole entropy (the Bekenstein entropy)
77 States of quantum matter and black holes Add electrical charge to a black hole in a curved spacetime: initially the charges fall past the horizon into the black hole
78 States of quantum matter and black holes However, eventually there is a balance between the gravitational forces pulling the charges into the black hole, and the repulsive electrical forces which push them out, and a stable state is obtained
79 States of quantum matter and black holes However, eventually there is a balance between the gravitational forces pulling the charges into the black hole, and the repulsive electrical forces which push them out, and a stable state is obtained 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
80 Quantum superposition and entanglement Quantum phase transitions
81 Quantum superposition and entanglement Quantum critical points and long-range entanglement of electrons String theory in crystals and black holes Quantum phase transitions
82 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, Harvard University
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