Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf ·...
Transcript of Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf ·...
![Page 1: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/1.jpg)
January 2013, ScientificAmerican.com 45Illustration by Artist NameIllustration by Artist Name Photograph by Zachary Zavislak
MAGNET is being levitated by an unseen superconductor in which
countless trillions of electrons form a vast inter connected quan-
tum state. Astoundingly, the quantum state of many modern
materials is subtly related to the mathematics of black holes.
sad0113Sach3p.indd 45 11/16/12 6:20 PM
Quantum Entanglement and Superconductivity
Subir Sachdev, Harvard University
![Page 2: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/2.jpg)
January 2013, ScientificAmerican.com 45Illustration by Artist NameIllustration by Artist Name Photograph by Zachary Zavislak
MAGNET is being levitated by an unseen superconductor in which
countless trillions of electrons form a vast inter connected quan-
tum state. Astoundingly, the quantum state of many modern
materials is subtly related to the mathematics of black holes.
sad0113Sach3p.indd 45 11/16/12 6:20 PM
Superconductor, levitated by an unseen magnet, in which countless trillions of electrons form a vast interconnected quantum state.Scientific American, January 2013
Quantum Entanglement and Superconductivity
Subir Sachdev, Harvard University
![Page 3: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/3.jpg)
YBa2Cu3O6+x
High temperature superconductors
![Page 4: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/4.jpg)
Julian Hetel and Nandini Trivedi, Ohio State University
Nd-Fe-B magnets, YBaCuO superconductor
![Page 5: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/5.jpg)
Julian Hetel and Nandini Trivedi, Ohio State University
Nd-Fe-B magnets, YBaCuO superconductor
![Page 6: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/6.jpg)
Efficient Rotating Machines
Power Efficiency/Capacity/Stability Power Bottlenecks Accommodate Renewable Power
Information Technology Next Generation HEP
HE Accelerators Science / Medicine
Ultra-High Magnetic Fields TransportMedical
![Page 7: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/7.jpg)
YBa2Cu3O6+x
High temperature superconductors
![Page 8: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/8.jpg)
YBa2Cu3O6+x
High temperature superconductors
CuO2 plane
Cu
O
![Page 9: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/9.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
![Page 10: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/10.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Superconductor
![Page 11: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/11.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Antiferromagnet
![Page 12: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/12.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Strange metal
![Page 13: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/13.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Strange metal
Can the “long-range quantum entanglement” in the strange metal help us understand high temperature superconductivity ?
![Page 14: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/14.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
![Page 15: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/15.jpg)
Principles of Quantum Mechanics: 1. Quantum Superposition
The double slit experiment
Interference of water waves
![Page 16: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/16.jpg)
The double slit experiment
Send electrons through the slits
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 17: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/17.jpg)
The double slit experiment
Interference of electrons
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 18: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/18.jpg)
The double slit experiment
Interference of electrons
Principles of Quantum Mechanics: 1. Quantum Superposition
Unlike water waves,
electrons arrive one-
by-one
![Page 19: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/19.jpg)
The double slit experiment
Interference of electrons
Principles of Quantum Mechanics: 1. Quantum Superposition
TWO$SLITS$
![Page 20: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/20.jpg)
The double slit experiment
Interference of electrons
Which slit does an electron
pass through ?
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 21: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/21.jpg)
The double slit experiment
Interference of electrons
Which slit does an electron
pass through ?
No interference when you watch the electrons
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 22: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/22.jpg)
The double slit experiment
Interference of electrons
Which slit does an electron
pass through ?
Each electron passes
through both slits !
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 23: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/23.jpg)
Let |L� represent the statewith the electron in the left slit
|L�
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 24: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/24.jpg)
And |R� represents the statewith the electron in the right slit
Let |L� represent the statewith the electron in the left slit
|L� |R�
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 25: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/25.jpg)
And |R� represents the statewith the electron in the right slit
Let |L� represent the statewith the electron in the left slit
|L� |R�
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
Actual state of each electron is
|Li + |Ri
![Page 26: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/26.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
![Page 27: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/27.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Hydrogen atom:
![Page 28: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/28.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Hydrogen atom:
=1⌃2
(|⇥⇤⌅ � |⇤⇥⌅)
Hydrogen molecule:
= _
![Page 29: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/29.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
![Page 30: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/30.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
![Page 31: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/31.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
![Page 32: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/32.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
Einstein-Podolsky-Rosen “paradox”: Measurement of one particle instantaneously
determines the state of the other particle arbitrarily far away
![Page 33: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/33.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
![Page 34: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/34.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
String theory and black holes
Long-range quantum
entanglement of electrons in crystals
![Page 35: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/35.jpg)
Quantum phase transitions
Quantum superposition and
entanglement Long-range quantum
entanglement of electrons in crystals
String theory and black holes
![Page 36: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/36.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Strange metalAntiferromagnet
Superconductor
![Page 37: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/37.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Antiferromagnet
Strange metal
Spins of electrons on Cu sites
![Page 38: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/38.jpg)
Square lattice of Cu sites
![Page 39: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/39.jpg)
Square lattice of Cu sites
Remove density p electrons
![Page 40: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/40.jpg)
Square lattice of Cu sites
Electrons entangle in (“Cooper”) pairs into chemical bonds
= | ⇥⇤⌅ � | ⇤⇥⌅
![Page 41: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/41.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 42: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/42.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 43: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/43.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 44: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/44.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 45: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/45.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 46: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/46.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 47: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/47.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 48: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/48.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 49: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/49.jpg)
Square lattice of Cu sites
Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”
= | ⇥⇤⌅ � | ⇤⇥⌅
Superconductivity !
![Page 50: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/50.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity ?
Electrons entangle by exchanging partners, and there is long-range quantum entanglement near the strange metal.
![Page 51: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/51.jpg)
Square lattice of Cu sites
Electrons entangle by exchanging partners, and there is long-range quantum entanglement near the strange metal.
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity ?
![Page 52: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/52.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity ?
Electrons entangle by exchanging partners, and there is long-range quantum entanglement near the strange metal.
![Page 53: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/53.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity ?
Electrons entangle by exchanging partners, and there is long-range quantum entanglement near the strange metal.
![Page 54: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/54.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity ?
Electrons entangle by exchanging partners, and there is long-range quantum entanglement near the strange metal.
![Page 55: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/55.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity ?
Electrons entangle by exchanging partners, and there is long-range quantum entanglement near the strange metal.
![Page 56: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/56.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity ?
Electrons entangle by exchanging partners, and there is long-range quantum entanglement near the strange metal.
![Page 57: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/57.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Strange metalAntiferromagnet
Superconductor
![Page 58: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/58.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Strange metalAntiferromagnet
Superconductor
But can we measure the quantum entanglement of electrons in this crystal ?
![Page 59: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/59.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Strange metalAntiferromagnet
Superconductor
But can we measure the quantum entanglement of electrons in this crystal ?
Only indirectly……
![Page 60: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/60.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Scanning tunneling microscopy
![Page 61: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/61.jpg)
Scanning Tunneling Microscopy
![Page 62: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/62.jpg)
Ultra low vibration cryostat.
to Pumps
Load Lock
Lead Filled Legs
High-field SC Magnet
Lead Filled Table
Turbo Pump
Air Springs
Fridge
Cleaver
L4He
J. C. Davis group, Rev. Sci. Inst. 70, 1459 (1999).SI-STM System
![Page 63: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/63.jpg)
STM Head
•Massive ULV Cryostat •Subkelvin Fridge •STM + High Field Magnet •Sample Exchange from RT •Cryogenic UHV Cleave
to Pumps
Load Lock
Lead Filled Legs
High-field SC Magnet
Turbo Pump
Air Springs
Cleaver
L4He
Sample insert
SI-STM SystemJ. C. Davis group, Rev. Sci. Inst. 70, 1459 (1999).
![Page 64: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/64.jpg)
![Page 65: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/65.jpg)
![Page 66: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/66.jpg)
Y. Kohsaka et al., Science 315, 1380 (2007)
4⇥ 10�10 meters
![Page 67: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/67.jpg)
Y. Kohsaka et al., Science 315, 1380 (2007)
Locationsof Cu atoms !
4⇥ 10�10 meters
![Page 68: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/68.jpg)
Y. Kohsaka et al., Science 315, 1380 (2007) d-form factor density wave order
M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010).S. Sachdev and R. LaPlaca, Phys. Rev. Lett. 111, 027202 (2013).
![Page 69: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/69.jpg)
Y. Kohsaka et al., Science 315, 1380 (2007) d-form factor density wave order
M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010).S. Sachdev and R. LaPlaca, Phys. Rev. Lett. 111, 027202 (2013).
![Page 70: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/70.jpg)
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
![Page 71: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/71.jpg)
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Scanning tunneling microscopy:
leads to indirect signatures of quantum entanglement
![Page 72: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/72.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
String theory and black holes
Long-range quantum
entanglement of electrons in crystals
![Page 73: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/73.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
String theory and black holes
Long-range quantum
entanglement of electrons in crystals
![Page 74: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/74.jpg)
Square lattice of Cu sites
Long-range entanglement has a heierarchical structure: electrons entangle in pairs, pairs entangle with pairs, and so on..…
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity ?
![Page 75: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/75.jpg)
depth ofentanglement
D-dimensionalspace
Representation of hierarchical entanglement at quantum critical point
G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)
![Page 76: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/76.jpg)
String theory
• Allows unification of the standard model of particlephysics with Einstein’s theory of gravitation(general relativity).
• Vibrations of a string (its “musical notes”) corre-spond to quarks, gravitons, the Higgs boson, pho-tons, gluons . . . . . .
![Page 77: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/77.jpg)
• A D-brane is a D-dimensional surface on which strings
can end.
• If we focused only on the blue points on theD-dimensional
surface, they would appear to us to have long-range
quantum entanglement !
![Page 78: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/78.jpg)
• A D-brane is a D-dimensional surface on which strings
can end.
• If we focused only on the blue points on theD-dimensional
surface, they would appear to us to have long-range
quantum entanglement !
![Page 79: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/79.jpg)
depth ofentanglement
D-dimensionalspace
Representation of hierarchical entanglement at quantum critical point
![Page 80: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/80.jpg)
String theory near a D-brane
depth ofentanglement
D-dimensionalspace
Emergent spatial directionof string theory Brian Swingle, arXiv:0905.1317
![Page 81: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/81.jpg)
depth ofentanglement
D-dimensionalspace
Brian Swingle, arXiv:0905.1317
Emergent spatial directionof string theory
Representation of hierarchical entanglement at quantum critical point
![Page 82: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/82.jpg)
States of matter with long-range quantum entanglement
in D dimensions
String theory and Einstein’s General Relativity
in D+1 dimensions
![Page 83: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/83.jpg)
States of matter with long-range quantum entanglement
in D dimensions
String theory and Einstein’s General Relativity
in D+1 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” ?
![Page 84: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/84.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
String theory and black holes
Long-range quantum
entanglement of electrons in crystals
![Page 85: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/85.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
String theory and black holes
Long-range quantum
entanglement of electrons in crystals
![Page 86: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/86.jpg)
Objects so massive that light is gravitationally bound to them.
Black Holes
![Page 87: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/87.jpg)
Horizon radius R =2GM
c2
Objects so massive that light is gravitationally bound to them.
Black Holes
In Einstein’s theory, the region inside the black hole horizon is disconnected from
the rest of the universe.
![Page 88: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/88.jpg)
Around 1974, Bekenstein and Hawking showed that the application of the
quantum theory across a black hole horizon led to many astonishing
conclusions
Black Holes + Quantum theory
![Page 89: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/89.jpg)
_
Quantum Entanglement across a black hole horizon
![Page 90: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/90.jpg)
_
Quantum Entanglement across a black hole horizon
![Page 91: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/91.jpg)
_
Quantum Entanglement across a black hole horizon
Black hole horizon
![Page 92: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/92.jpg)
_
Black hole horizon
Quantum Entanglement across a black hole horizon
![Page 93: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/93.jpg)
Black hole horizon
Quantum Entanglement across a black hole horizon
There is long-range quantum entanglement between the inside
and outside of a black hole
![Page 94: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/94.jpg)
Black hole horizon
Quantum Entanglement across a black hole horizon
Hawking used this to show that black hole horizons have an entropy and a temperature
![Page 95: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/95.jpg)
Black hole horizon
Quantum Entanglement across a black hole horizon
The Hawking entropy matches the entropy of some simple
strange metal states of electrons(S. Sachdev, 2015)
![Page 96: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/96.jpg)
Black hole horizon
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
![Page 97: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/97.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
![Page 98: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/98.jpg)
Quantum phase transitions
Quantum superposition and
entanglement
String theory and black holes
Long-range quantum
entanglement of electrons in crystals
![Page 99: Quantum Entanglement and Superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf · 2015-09-01 · Quantum Entanglement and Superconductivity Subir Sachdev, Harvard University.](https://reader030.fdocuments.net/reader030/viewer/2022041009/5eb5dc8294c7ea1dad77aea8/html5/thumbnails/99.jpg)
January 2013, ScientificAmerican.com 45Illustration by Artist NameIllustration by Artist Name Photograph by Zachary Zavislak
MAGNET is being levitated by an unseen superconductor in which
countless trillions of electrons form a vast inter connected quan-
tum state. Astoundingly, the quantum state of many modern
materials is subtly related to the mathematics of black holes.
sad0113Sach3p.indd 45 11/16/12 6:20 PM
Superconductor, levitated by an unseen magnet, in which countless trillions of electrons form a vast interconnected quantum state.Scientific American, January 2013
Quantum Entanglement and Superconductivity
Subir Sachdev, Harvard University