quantum entanglement: “spooky action at distance” in the lab,...
TRANSCRIPT
![Page 1: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/1.jpg)
Quantum entanglement: “Spooky action at distance”
in the lab, and in black holes
Tilde Cafe, Branford CTNovember 9, 2019
Subir Sachdev
HARVARD
Talk online: sachdev.physics.harvard.edu
![Page 2: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/2.jpg)
http://nyti.ms/1OIO2WJ
SCIENCE
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 theNetherlands reported that they had conducted an experiment that they say provedone of the most fundamental claims of quantum theory — that objects separated bygreat distance can instantaneously affect each other’s behavior.
The finding is another blow to one of the bedrock principles of standardphysics known as “locality,” which states that an object is directly influenced onlyby its immediate surroundings. The Delft study, published Wednesday in thejournal Nature, lends further credence to an idea that Einstein famously rejected.He said quantum theory necessitated “spooky action at a distance,” and he refusedto accept the notion that the universe could behave in such a strange andapparently random fashion.
In particular, Einstein derided the idea that separate particles could be“entangled” so completely that measuring one particle would instantaneouslyinfluence the other, regardless of the distance separating them.
Einstein was deeply unhappy with the uncertainty introduced by quantumtheory and described its implications as akin to God’s playing dice.
But since the 1970s, a series of precise experiments by physicists are1 of 2
© 2015 The New York Times Company
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.
![Page 3: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/3.jpg)
Quantum phase transitions
Quantum entanglement
![Page 4: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/4.jpg)
The double slit experiment
Interference of water waves
Principles of Quantum Mechanics: 1. Quantum Superposition
TWO$SLITS$
![Page 5: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/5.jpg)
The double slit experiment
Bullets
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 6: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/6.jpg)
The double slit experiment
Send electrons through the slits
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 7: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/7.jpg)
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
Interference of electrons
![Page 8: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/8.jpg)
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
Interference of electrons
Is the electron a wave ?
![Page 9: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/9.jpg)
The double slit experiment
Interference of electrons
Principles of Quantum Mechanics: 1. Quantum Superposition
TWO$SLITS$
Unlike water waves, electrons arrive one-by-one
(so is it like a particle ?)
![Page 10: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/10.jpg)
The double slit experiment
Interference of electrons
But if it is like a
particle, which slit does each
electron pass through ?
Principles of Quantum Mechanics: 1. Quantum Superposition
![Page 11: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/11.jpg)
The double slit experiment
Interference of electrons
No interference when you watch the electrons
Principles of Quantum Mechanics: 1. Quantum Superposition
But if it is like a
particle, which slit does each
electron pass through ?
![Page 12: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/12.jpg)
The double slit experiment
Interference of electrons
Each electron passes
through both slits !
Principles of Quantum Mechanics: 1. Quantum Superposition
But if it is like a
particle, which slit does each
electron pass through ?
![Page 13: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/13.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 14: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/14.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 15: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/15.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 16: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/16.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
![Page 17: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/17.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Hydrogen atom:
![Page 18: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/18.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Hydrogen atom:
=1⌃2
(|⇥⇤⌅ � |⇤⇥⌅)
Hydrogen molecule:
= _
![Page 19: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/19.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
![Page 20: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/20.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
![Page 21: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/21.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
![Page 22: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/22.jpg)
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
Einstein-Podolsky-Rosen “paradox” (1935): Measurement of one particle instantaneously
determines the state of the other particle arbitrarily far away
![Page 23: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/23.jpg)
Quantum phase transitions
Quantum entanglement
![Page 24: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/24.jpg)
Quantum phase transitions
Quantum entanglement
Black holes
![Page 25: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/25.jpg)
Horizon radius R =2GM
c2
Objects so dense 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 26: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/26.jpg)
On September 14, 2015, LIGO detected the merger of two black holes, each weighing about 30 solar masses, with radii of about 100 km, 1.3 billion light years away
![Page 27: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/27.jpg)
On September 14, 2015, LIGO detected the merger of two black holes, each weighing about 30 solar masses, with radii of about 100 km, 1.3 billion light years away
0.1 seconds later !
![Page 28: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/28.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 29: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/29.jpg)
_
Quantum Entanglement across a black hole horizon
![Page 30: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/30.jpg)
_
Quantum Entanglement across a black hole horizon
Black hole horizon
![Page 31: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/31.jpg)
_
Black hole horizon
Quantum Entanglement across a black hole horizon
![Page 32: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/32.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 33: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/33.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 34: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/34.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
(because to an outside observer, the state of the electron inside the black hole is an unknown)
![Page 35: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/35.jpg)
Quantum phase transitions
Quantum entanglement
Black holes
![Page 36: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/36.jpg)
Quantum phase transitions
Superconductors
Quantum entanglement
Black holes
![Page 37: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/37.jpg)
YBa2Cu3O6+x
High temperature superconductors
![Page 38: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/38.jpg)
Julian Hetel and Nandini Trivedi, Ohio State University
Nd-Fe-B magnets, YBaCuO superconductor
![Page 39: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/39.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
Slide by J. C. Seamus Davis
![Page 40: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/40.jpg)
Square lattice of Cu sites
![Page 41: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/41.jpg)
Square lattice of Cu sites
Remove some electrons
![Page 42: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/42.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
Electrons entangle in (“Cooper”) pairs into chemical bonds
![Page 43: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/43.jpg)
Square lattice of Cu sites
Electrons entangle “en masse” by exchanging partners, and there is long-range quantum entanglement
= | ⇥⇤⌅ � | ⇤⇥⌅
![Page 44: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/44.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
Electrons entangle “en masse” by exchanging partners, and there is long-range quantum entanglement
![Page 45: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/45.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
Electrons entangle “en masse” by exchanging partners, and there is long-range quantum entanglement
![Page 46: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/46.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
Electrons entangle “en masse” by exchanging partners, and there is long-range quantum entanglement
![Page 47: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/47.jpg)
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
Electrons entangle “en masse” by exchanging partners, and there is long-range quantum entanglement
![Page 48: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/48.jpg)
Quantum phase transitions
Superconductors
Quantum entanglement
Black holes
![Page 49: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/49.jpg)
Quantum phase transitions
Quantum entanglement
Black holes
A “toy model” which describes both a superconductor and a black hole!
Superconductors
![Page 50: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/50.jpg)
The Sachdev-Ye-Kitaev (SYK) model
Pick a set of random positions
![Page 51: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/51.jpg)
Place electrons randomly on some sites
The SYK model
![Page 52: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/52.jpg)
The SYK model
Place electrons randomly on some sites
![Page 53: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/53.jpg)
Entangle electrons pairwise randomly
The SYK model
![Page 54: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/54.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 55: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/55.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 56: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/56.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 57: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/57.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 58: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/58.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 59: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/59.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 60: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/60.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 61: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/61.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 62: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/62.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 63: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/63.jpg)
The SYK model
Entangle electrons pairwise randomly
![Page 64: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/64.jpg)
The SYK model
This describes both a superconductor and a black hole!
![Page 65: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/65.jpg)
Maxwell’s electromagnetism and Einstein’s general relativity
allow black hole solutions with a net charge
![Page 66: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/66.jpg)
~x⇣
Zooming into the near-horizon region of a
charged black hole at low temperature, yields
a quantum theory in one space ( ) and one
time dimension⇣
Maxwell’s electromagnetism and Einstein’s general relativity
allow black hole solutions with a net charge
![Page 67: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/67.jpg)
~x⇣
The quantum versions of Maxwell’s and
Einstein’s equations in this two-dimensional
spacetime are also the equations describing
electron entanglement in the SYK model
Maxwell’s electromagnetism and Einstein’s general relativity
allow black hole solutions with a net charge
![Page 68: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/68.jpg)
~x⇣
This has led to a deeper understanding
of entanglement in superconductors and
of Hawking’s black hole information “paradox”
Maxwell’s electromagnetism and Einstein’s general relativity
allow black hole solutions with a net charge
![Page 69: Quantum entanglement: “Spooky action at distance” in the lab, …qpt.physics.harvard.edu/talks/branford19.pdf · 2019-11-09 · Quantum entanglement: “Spooky action at distance”](https://reader033.vdocuments.mx/reader033/viewer/2022043009/5f9c1e52657e4b39ce007759/html5/thumbnails/69.jpg)
Quantum entanglement
Black holes
A “toy model” which describes both a superconductor and a black hole!
Superconductors