Quantum Entanglement and Superconductivity. Subir Sachdev, Perimeter Institute and Harvard University
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1 Quantum Entanglement and Superconductivity Subir Sachdev, Perimeter Institute and Harvard University
2 Sorry, Einstein. Quantum Study Suggests Spooky Action Is Real. By JOHN MARKOFF OCT. 21, 2015 In a landmark study, scientists at Delft University of Technology in the Netherlands reported that they had conducted an experiment that they say proved one of the most fundamental claims of quantum theory that objects separated by great distance can instantaneously affect each other s behavior. Part of the laboratory setup for an experiment at Delft University of Technology, in which two diamonds were set 1.3 kilometers apart, entangled and then shared information.
3 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
4 High temperature superconductors YBa 2 Cu 3 O 6+x
5 Nd-Fe-B magnets, YBaCuO superconductor Julian Hetel and Nandini Trivedi, Ohio State University
6 Slide by J. C. Seamus Davis 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 Quantum superposition and entanglement Quantum phase transitions
8 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment TWO$ SLITS$ Interference of water waves
9 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Interference of water waves
10 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Send electrons through the slits
11 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Interference of electrons
12 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Is the electron a wave? Interference of electrons
13 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment Unlike water waves, electrons arrive one-by-one (so is it like a particle?) Interference of electrons
14 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment TWO$ SLITS$ Unlike water waves, electrons arrive one-by-one (so is it like a particle?) Interference of electrons
15 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment But if it is like a particle, which slit does each electron pass through? Interference of electrons
16 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment But if it is like a particle, which slit does each electron pass through? No interference when you watch the electrons Interference of electrons
17 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment But if it is like a particle, which slit does each electron pass through? Each electron passes through both slits! Interference of electrons
18 Principles of Quantum Mechanics: 1. Quantum Superposition The double slit experiment L Let L represent the state with the electron in the left slit
19 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
20 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
21 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle
22 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom:
23 Principles of Quantum Mechanics: 1I. Quantum Entanglement Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom: Hydrogen molecule: = _ = 1 2 ( )
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 _
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 _ Einstein-Podolsky-Rosen paradox : Measurement of one particle instantaneously determines the state of the other particle arbitrarily far away
28 Quantum superposition and entanglement Quantum phase transitions
29 Quantum superposition and entanglement Long-range quantum entanglement of electrons in matter: (A) superconductors Quantum theory of black holes (B) graphene Quantum phase transitions
30 Quantum superposition and entanglement Long-range quantum entanglement of electrons in matter: (A) superconductors Quantum theory of black holes (B) graphene Quantum phase transitions
31 High temperature superconductors YBa 2 Cu 3 O 6+x
32 Antiferromagnet Strange metal SM Superconductor FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
33 Antiferromagnet Strange metal SM FL Spins of electrons on Cu sites p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
34 Square lattice of Cu sites
35 Square lattice of Cu sites Remove density p electrons
36 Square lattice of Cu sites Electrons entangle in ( Cooper ) pairs into chemical bonds =
37 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
38 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
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 High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
42 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
43 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
44 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
45 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
46 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
47 Square lattice of Cu sites High temperature superconductivity? Electrons entangle by exchanging partners, and there is longrange quantum entanglement near the strange metal. =
48 Antiferromagnet Strange metal SM Superconductor FL p (hole/cu) Figure: K. Fujita and J. C. Seamus Davis
49 Quantum superposition and entanglement Long-range quantum entanglement of electrons in matter: (A) superconductors Quantum theory of black holes (B) graphene Quantum phase transitions
50 Graphene A single layer of carbon atoms in a honeycomb lattice
51 Graphene 600 T (K) 500 Dirac liquid temperature Hole Gas of holes Fermi liquid 1 n (1 + λ ln Λ n ) Electron Gas of particles Fermi liquid n /m 2 density of electrons D. E. Sheehy and J. Schmalian, PRL 99, (2007) M. Müller, L. Fritz, and S. Sachdev, PRB 78, (2008) M. Müller and S. Sachdev, PRB 78, (2008)
52 M. Müller, L. Fritz, and S. Sachdev, PRB 78, (2008) M. Müller and S. Sachdev, PRB 78, (2008) Graphene temperature T (K) Hole Gas of holes Fermi liquid Dirac liquid 1 n (1 + λ ln Λ n ) Electron Gas of particles Fermi liquid density of electrons Predicted (and recently observed) strange metal with long-range quantum entanglement The strange metal is a much better conductor of heat than electricity, when compared to ordinary metals n /m 2 J. Crossno et al. arxiv:
53 Quantum superposition and entanglement Long-range quantum entanglement of electrons in matter: (A) superconductors Quantum theory of black holes (B) graphene Quantum phase transitions
54 Quantum superposition and entanglement Long-range quantum entanglement of electrons in matter: (A) superconductors Quantum theory of black holes (B) graphene Quantum phase transitions
55 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
56 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
57 Quantum Entanglement across a black hole horizon _
58 Quantum Entanglement across a black hole horizon _ Black hole horizon
59 Quantum Entanglement across a black hole horizon _ Black hole horizon
60 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
61 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
62 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
63 Quantum Entanglement across a black hole horizon The Hawking entropy matches the entropy of some simple strange metal states of electrons (S. Sachdev, 2015) The dynamics of black hole horizons has many similarities to strange metals, and this has led us to a better understanding of the observable properties of strange metals in superconductors and other quantum materials Black hole horizon
64 Quantum superposition and entanglement Quantum phase transitions
65 Quantum superposition and entanglement Long-range quantum entanglement of electrons in matter: (A) superconductors Quantum theory of black holes (B) graphene Quantum phase transitions
66 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
Quantum Entanglement, Strange metals, and black holes. Subir Sachdev, Harvard University
Quantum Entanglement, Strange metals, and black holes Subir Sachdev, Harvard University Quantum Entanglement, Strange metals, and black holes Superconductor, levitated by an unseen magnet, in which countless
Quantum Entanglement and Superconductivity. Subir Sachdev, Harvard University
Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University Quantum Entanglement and Superconductivity Superconductor, levitated by an unseen magnet, in which countless trillions of electrons
Quantum Entanglement and Superconductivity. Subir Sachdev, Perimeter Institute and Harvard University
Quantum Entanglement and Superconductivity Subir Sachdev, Perimeter Institute and Harvard University Quantum Entanglement and Superconductivity Superconductor, levitated by an unseen magnet, in which countless
Quantum Entanglement and Superconductivity. Subir Sachdev, Harvard University
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