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 Power Efficiency/Capacity/Stability Power Bottlenecks Efficient Rotating Machines Information Technology HE Accelerators Ultra-High Magnetic Fields Accommodate Renewable Power Next Generation HEP Science / Medicine Medical Transport
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 SM FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
10 SM Superconductor FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
11 Antiferromagnet SM FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
12 Strange metal SM FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
13 Strange metal SM FL Can the long-range quantum entanglement in the strange metal help us understand high temperature superconductivity? p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
14 Quantum superposition and entanglement Quantum phase transitions
15 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Interference of water waves
16 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Send electrons through the slits
17 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Interference of electrons
18 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Unlike water waves, electrons arrive oneby-one Interference of electrons
19 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment TWO$ SLITS$ Interference of electrons
20 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Which slit does an electron pass through? Interference of electrons
21 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
22 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
23 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment L Let L represent the state with the electron in the left slit
24 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
25 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
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 Hydrogen atom:
28 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom: Hydrogen molecule: = _ = 1 2 ( )
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 _
31 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle _
32 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
33 Quantum superposition and entanglement Quantum phase transitions
34 Quantum superposition and entanglement Long-range quantum entanglement of electrons String theory in crystals and black holes Quantum phase transitions
35 Quantum superposition and entanglement Long-range quantum entanglement of electrons String theory in crystals and black holes Quantum phase transitions
36 Antiferromagnet Strange metal SM Superconductor FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
37 Antiferromagnet Strange metal SM FL Spins of electrons on Cu sites p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
38 Square lattice of Cu sites
39 Square lattice of Cu sites Remove density p electrons
40 Square lattice of Cu sites Electrons entangle in ( Cooper ) pairs into chemical bonds =
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 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 Superconductivity! = Cooper pairs form quantum superpositions at different locations: Bose-Einstein condensation in which all pairs are everywhere at the same time
50 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
51 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
52 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
53 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
54 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
55 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
56 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
57 Antiferromagnet Strange metal SM Superconductor FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
58 Antiferromagnet Strange metal But can we measure the quantum entanglement of electrons in this crystal? SM Superconductor FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
59 Antiferromagnet Strange metal But can we measure the quantum entanglement of electrons in this crystal? SM Only indirectly Superconductor FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
60 Scanning tunneling microscopy SM FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
61 Scanning Tunneling Microscopy
62 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
63 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
64
65
66 meters Y. Kohsaka et al., Science 315, 1380 (2007)
67 Locations of Cu atoms! meters Y. Kohsaka et al., Science 315, 1380 (2007)
68 Y. Kohsaka et al., Science 315, 1380 (2007) d-form factor density wave order M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, (2010). S. Sachdev and R. LaPlaca, Phys. Rev. Lett. 111, (2013).
69 Y. Kohsaka et al., Science 315, 1380 (2007) d-form factor density wave order M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, (2010). S. Sachdev and R. LaPlaca, Phys. Rev. Lett. 111, (2013).
70 Y. Kohsaka et al., Science 315, 1380 (2007) d-form factor density wave order Intricrate pattern of electron density waves (DW) is giving us important information on the nature of quantum entanglement in neighboring regions
71 Scanning tunneling microscopy: leads to indirect signatures of quantum entanglement SM FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
72 Quantum superposition and entanglement Long-range quantum entanglement of electrons String theory in crystals and black holes Quantum phase transitions
73 Quantum superposition and entanglement Long-range quantum entanglement of electrons String theory in crystals and black holes Quantum phase transitions
74 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..
75 Representation of hierarchical entanglement at quantum critical point D-dimensional space depth of entanglement G. Vidal, Phys. Rev. Lett. 99, (2007)
76 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......
77 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!
78 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!
79 Representation of hierarchical entanglement at quantum critical point D-dimensional space depth of entanglement
80 String theory near a D-brane D-dimensional space Emergent depth of spatial direction entanglement of string theory Brian Swingle, arxiv:
81 Representation of hierarchical entanglement at quantum critical point D-dimensional space Emergent depth of spatial direction entanglement of string theory Brian Swingle, arxiv:
82 States of matter with long-range quantum entanglement in D dimensions String theory and Einstein s General Relativity in D+1 dimensions
83 States of matter with long-range quantum entanglement in D dimensions Are there solutions of Einstein s General Relativity in D+1 dimensions which have an entanglement structure similar to that of a strange metal? String theory and Einstein s General Relativity in D+1 dimensions
84 Quantum superposition and entanglement Long-range quantum entanglement of electrons String theory in crystals and black holes Quantum phase transitions
85 Quantum superposition and entanglement Long-range quantum entanglement of electrons String theory in crystals and black holes Quantum phase transitions
86 Black Holes Objects so massive that light is gravitationally bound to them.
87 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
88 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
89 Quantum Entanglement across a black hole horizon _
90 Quantum Entanglement across a black hole horizon _
91 Quantum Entanglement across a black hole horizon _ Black hole horizon
92 Quantum Entanglement across a black hole horizon _ Black hole horizon
93 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
94 Quantum Entanglement across a black hole horizon Hawking used this to show that black hole horizons have an entropy and a temperature Black hole horizon
95 Quantum Entanglement across a black hole horizon The Hawking entropy matches the entropy of some simple strange metal states of electrons (S. Sachdev, 2015) Black hole horizon
96 Quantum Entanglement across a black hole horizon The Hawking entropy matches the entropy of some simple strange metal states of electrons (S. Sachdev, 2015) This connection is leading to a better understanding of the observable properties of strange metals in superconductors and other quantumm materials Black hole horizon
97 Quantum superposition and entanglement Quantum phase transitions
98 Quantum superposition and entanglement Long-range quantum entanglement of electrons String theory in crystals and black holes Quantum phase transitions
99 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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