superconductivity and quantum...
TRANSCRIPT
![Page 1: Superconductivity and Quantum Entanglementqpt.physics.harvard.edu/talks/Sachdev_Science_Cafe_13.pdfSuperconductivity and Quantum Entanglement Subir Sachdev Harvard University sachdev.physics.harvard.edu](https://reader033.vdocument.in/reader033/viewer/2022042212/5eb5d4763cf2503c0620da89/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
Superconductivityand
Quantum Entanglement
Subir SachdevHarvard University
sachdev.physics.harvard.edu
Tuesday, April 23, 13
![Page 2: Superconductivity and Quantum Entanglementqpt.physics.harvard.edu/talks/Sachdev_Science_Cafe_13.pdfSuperconductivity and Quantum Entanglement Subir Sachdev Harvard University sachdev.physics.harvard.edu](https://reader033.vdocument.in/reader033/viewer/2022042212/5eb5d4763cf2503c0620da89/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
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
Tuesday, April 23, 13
![Page 3: Superconductivity and Quantum Entanglementqpt.physics.harvard.edu/talks/Sachdev_Science_Cafe_13.pdfSuperconductivity and Quantum Entanglement Subir Sachdev Harvard University sachdev.physics.harvard.edu](https://reader033.vdocument.in/reader033/viewer/2022042212/5eb5d4763cf2503c0620da89/html5/thumbnails/3.jpg)
YBa2Cu3O6+x
High temperature superconductors
Tuesday, April 23, 13
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Key question:
Can we use the fundamental principles of quantum mechanics to understand why YBa2Cu3O6
(and not most other combinations of elements) is a high temperature
superconductor ?
Tuesday, April 23, 13
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Demo of levitating superconductor
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Fundamental principles of quantum mechanics
1. A particle is described by its quantum “state”.
Tuesday, April 23, 13
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Fundamental principles of quantum mechanics
1. A particle is described by its quantum “state”.2. Linear superposition: particles can be in the sum or difference of two “states”
Tuesday, April 23, 13
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Principles of Quantum Mechanics: 1. Quantum Superposition
The double slit experiment
Interference of water wavesTuesday, April 23, 13
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The double slit experiment
Send electrons through the slits
Principles of Quantum Mechanics: 1. Quantum Superposition
Tuesday, April 23, 13
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Show video at http://www.youtube.com/watch?v=jvO0P5-SMxk
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Tuesday, April 23, 13
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The double slit experiment
Send electrons through the slits
Principles of Quantum Mechanics: 1. Quantum Superposition
Tuesday, April 23, 13
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The double slit experiment
Interference of electrons
Principles of Quantum Mechanics: 1. Quantum Superposition
Tuesday, April 23, 13
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The double slit experiment
Interference of electrons
Which slit does an electron
pass through ?
Principles of Quantum Mechanics: 1. Quantum Superposition
Tuesday, April 23, 13
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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
Tuesday, April 23, 13
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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
Tuesday, April 23, 13
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Let |L� represent the statewith the electron in the left slit
|L�
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
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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
Tuesday, April 23, 13
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And |R� represents the statewith the electron in the right slit
Let |L� represent the statewith the electron in the left slit
Actual state of the electron is|L� + |R�
|L� |R�
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
Tuesday, April 23, 13
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Fundamental principles of quantum mechanics
1. A particle is described by its quantum “state”.2. Linear superposition: particles can be in the sum or difference of two “states”
Tuesday, April 23, 13
![Page 21: Superconductivity and Quantum Entanglementqpt.physics.harvard.edu/talks/Sachdev_Science_Cafe_13.pdfSuperconductivity and Quantum Entanglement Subir Sachdev Harvard University sachdev.physics.harvard.edu](https://reader033.vdocument.in/reader033/viewer/2022042212/5eb5d4763cf2503c0620da89/html5/thumbnails/21.jpg)
Fundamental principles of quantum mechanics
1. A particle is described by its quantum “state”.2. Linear superposition: particles can be in the sum or difference of two “states”3. Entanglement: state superposition with many particles.
Tuesday, April 23, 13
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Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Tuesday, April 23, 13
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Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Hydrogen atom:
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Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Hydrogen atom:
=1⌃2
(|⇥⇤⌅ � |⇤⇥⌅)
Hydrogen molecule:
= _
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Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
Tuesday, April 23, 13
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Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
Tuesday, April 23, 13
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Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
Tuesday, April 23, 13
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Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
Einstein-Podolsky-Rosen “paradox”: Non-local correlations between observations arbitrarily far apart
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YBa2Cu3O6+x
High temperature superconductors
Tuesday, April 23, 13
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Square lattice of Cu sites
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Square lattice of Cu sites
1. Remove some electrons
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Square lattice of Cu sites
1. Remove some electrons
2. Electrons entangle into chemical bonds
= | ⇥⇤⌅ � | ⇤⇥⌅Tuesday, April 23, 13
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Square lattice of Cu sites
1. Remove some electrons
2. Electrons entangle into chemical bonds
3. Chemical bonds undergo Bose-Einstein condensation
= | ⇥⇤⌅ � | ⇤⇥⌅Tuesday, April 23, 13
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Square lattice of Cu sites
1. Remove some electrons
2. Electrons entangle into chemical bonds
3. Chemical bonds undergo Bose-Einstein condensation
= | ⇥⇤⌅ � | ⇤⇥⌅Tuesday, April 23, 13
![Page 35: Superconductivity and Quantum Entanglementqpt.physics.harvard.edu/talks/Sachdev_Science_Cafe_13.pdfSuperconductivity and Quantum Entanglement Subir Sachdev Harvard University sachdev.physics.harvard.edu](https://reader033.vdocument.in/reader033/viewer/2022042212/5eb5d4763cf2503c0620da89/html5/thumbnails/35.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
1. Remove some electrons
2. Electrons entangle into chemical bonds
3. Chemical bonds undergo Bose-Einstein condensation
Tuesday, April 23, 13
![Page 36: Superconductivity and Quantum Entanglementqpt.physics.harvard.edu/talks/Sachdev_Science_Cafe_13.pdfSuperconductivity and Quantum Entanglement Subir Sachdev Harvard University sachdev.physics.harvard.edu](https://reader033.vdocument.in/reader033/viewer/2022042212/5eb5d4763cf2503c0620da89/html5/thumbnails/36.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
1. Remove some electrons
2. Electrons entangle into chemical bonds
3. Chemical bonds undergo Bose-Einstein condensation
Tuesday, April 23, 13