Quantum Entanglement, - Subir Sachdevsachdev.physics.harvard.edu/talks/simons17.pdf · Subir...
Transcript of Quantum Entanglement, - Subir Sachdevsachdev.physics.harvard.edu/talks/simons17.pdf · Subir...
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,Strange metals,and black holes
Subir Sachdev, Harvard University
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,Strange metals,and black holes
Subir Sachdev, Harvard University
Superconductor, levitated by an unseen magnet, in which countless trillions of electrons form a vast interconnected quantum state.Scientific American, January 2013
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.
Quantum phase transitions
Quantum entanglement
The double slit experiment
Interference of water waves
Principles of Quantum Mechanics: 1. Quantum Superposition
TWO$SLITS$
The double slit experiment
Bullets
Principles of Quantum Mechanics: 1. Quantum Superposition
The double slit experiment
Send electrons through the slits
Principles of Quantum Mechanics: 1. Quantum Superposition
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
Interference of electrons
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
Interference of electrons
Is the electron a wave ?
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 ?)
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
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 ?
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 ?
Let |L� represent the statewith the electron in the left slit
|L�
The double slit experiment
Principles of Quantum Mechanics: 1. Quantum Superposition
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
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
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Hydrogen atom:
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
Hydrogen atom:
=1⌃2
(|⇥⇤⌅ � |⇤⇥⌅)
Hydrogen molecule:
= _
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
Quantum Entanglement: quantum superposition with more than one particle
Principles of Quantum Mechanics: 1I. Quantum Entanglement
_
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
Quantum phase transitions
Quantum entanglement
Quantum phase transitions
Quantum entanglement
Black holes
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.
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
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 !
LIGOSeptember 14, 2015
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
_
Quantum Entanglement across a black hole horizon
_
Quantum Entanglement across a black hole horizon
Black hole horizon
_
Black hole horizon
Quantum Entanglement across a black hole horizon
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
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
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)
LIGOSeptember 14, 2015
• The Hawking temperature, TH influences the radiation from theblack hole at the very last stages of the ring-down (not observedso far). The ring-down (approach to thermal equilibrium) hap-
pens very rapidly in a time ⇠ ~kBTK
⇠ 8 milliseconds.
Quantum phase transitions
Quantum entanglement
Black holes
Quantum phase transitions
Strange metals
Quantum entanglement
Black holes
YBa2Cu3O6+x
High temperature superconductors
Julian Hetel and Nandini Trivedi, Ohio State University
Nd-Fe-B magnets, YBaCuO superconductor
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
YBa2Cu3O6+x
High temperature superconductors
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Strange metalAntiferromagnet
Superconductor
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Antiferromagnet
Strange metal
Spins of electrons on Cu sites
Square lattice of Cu sites
Square lattice of Cu sites
Remove density p electrons
Square lattice of Cu sites
Electrons entangle in (“Cooper”) pairs into chemical bonds
= | ⇥⇤⌅ � | ⇤⇥⌅
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
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
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
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
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity !
Electrons entangle by exchanging partners, and there is long-range quantum entanglement in the strange metal.
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
Electrons entangle by exchanging partners, and there is long-range quantum entanglement in the strange metal.
High temperature superconductivity !
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
Electrons entangle by exchanging partners, and there is long-range quantum entanglement in the strange metal.
High temperature superconductivity !
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
Electrons entangle by exchanging partners, and there is long-range quantum entanglement in the strange metal.
High temperature superconductivity !
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity !
Electrons entangle by exchanging partners, and there is long-range quantum entanglement in the strange metal.
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity !
Electrons entangle by exchanging partners, and there is long-range quantum entanglement in the strange metal.
Square lattice of Cu sites
= | ⇥⇤⌅ � | ⇤⇥⌅
High temperature superconductivity !
Electrons entangle by exchanging partners, and there is long-range quantum entanglement in the strange metal.
SM
FL
Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)
Strange metalEntangled
electrons lead to “strange”
temperature dependence of resistivity and
other properties
Almost all many-electron systems are described by the quasiparticle concept: a quasiparticle is an “excited lump” in the many-electron state which responds just like an ordinary particle.
R.D. Mattuck
Almost all many-electron systems are described by the quasiparticle concept: a quasiparticle is an “excited lump” in the many-electron state which responds just like an ordinary particle.
Quasiparticles eventually collide with each other. Such collisions eventually leads to thermal equilibration in a chaotic quantum state, but the equilibration takes a long time.
The complex quantum entanglement in the strange metal does not allow for any quasiparticle excitations.
Quantum matter without quasiparticles
The complex quantum entanglement in the strange metal does not allow for any quasiparticle excitations.
Quantum matter without quasiparticles
• Systems without quasiparticles, like the strange metal,
reach quantum chaos much more quickly than those with-
out quasiparticles.
• There is an lower bound on the phase coherence time (⌧'),and the time to many-body quantum chaos (⌧L) in all
many-body quantum systems:
⌧' � C~
kBT(SS, 1999)
⌧L � ~2⇡kBT
(Maldacena, Shenker, Stanford, 2015)
• In the strange metal the above inequalities become equal-
ities as T ! 0.
The complex quantum entanglement in the strange metal does not allow for any quasiparticle excitations.
Quantum matter without quasiparticles
• Systems without quasiparticles, like the strange metal,
reach quantum chaos much more quickly than those with-
out quasiparticles.
• There is an lower bound on the phase coherence time (⌧'),and the time to many-body quantum chaos (⌧L) in all
many-body quantum systems:
⌧' � C~
kBT(SS, 1999)
⌧L � ~2⇡kBT
(Maldacena, Shenker, Stanford, 2015)
• In the strange metal the above inequalities become equal-
ities as T ! 0.
The complex quantum entanglement in the strange metal does not allow for any quasiparticle excitations.
Quantum matter without quasiparticles
• Systems without quasiparticles, like the strange metal,
reach quantum chaos much more quickly than those with-
out quasiparticles.
• There is an lower bound on the phase coherence time (⌧'),and the time to many-body quantum chaos (⌧L) in all
many-body quantum systems:
⌧' � C~
kBT(SS, 1999)
⌧L � ~2⇡kBT
(Maldacena, Shenker, Stanford, 2015)
• In the strange metal the above inequalities become equal-
ities as T ! 0.
Quantum phase transitions
Strange metals
Quantum entanglement
Black holes
Quantum phase transitions
Strange metals
Quantum entanglement
Black holes
A “toy model” which is both a strange metal and a black hole!
The Sachdev-Ye-Kitaev (SYK) model
Pick a set of random positions
Place electrons randomly on some sites
The Sachdev-Ye-Kitaev (SYK) model
Entangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) model
Entangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) model
Entangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) model
Entangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) model
Entangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) model
Entangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) model
The SYK model has “nothing but entanglement”
The Sachdev-Ye-Kitaev (SYK) model
This describes both a strange metal and a black hole!
The Sachdev-Ye-Kitaev (SYK) model
H =1
(2N)3/2
NX
i,j,k,`=1
Jij;k` c†i c
†jckc` � µ
X
i
c†i ci
cicj + cjci = 0 , cic†j + c†jci = �ij
Q =1
N
X
i
c†i ci
A. Kitaev, (2015) ; SS 2015
SS and J. Ye 1993
Jij;k` are independent random variables with Jij;k` = 0 and |Jij;k`|2 = J2
N ! 1 yields critical strange metal.
SYK model
~x
SYK and black holes
⇣~x
SYK and black holes
The SYK model has “dual” description
in which an extra spatial dimension, ⇣, emerges.
The curvature of this “emergent” spacetime is described
by Einstein’s theory of general relativity
Black holehorizon
⇣~x
SYK and black holes
Black holehorizon
An extra spatial dimension emerges from quantum entanglement!
SS 2010; A. Kitaev, 2015
⇣~x
SYK and black holes
Black holehorizon
Both the SYK model
and the theory of gravity
have a time to quantum chaos =
~2⇡kBT
A. Kitaev, 2015 Maldacena, Stanford 2016
depth ofentanglement
D-dimensionalspace
Tensor network of hierarchical entanglement
~x
⇣
String theory near a “D-brane”
depth ofentanglement
D-dimensionalspace
Emergent spatial directionof SYK model or string theory
~x
⇣
String theory near a “D-brane”
depth ofentanglement
D-dimensionalspace
Emergent spatial directionof SYK model or string theory
~x
⇣ Quantum entanglementleads to an emergent
spatial dimension
Quantum phase transitions
Strange metals
Quantum entanglement
Black holes
A “toy model” which is both a strange metal and a black hole!
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,Strange metals,and black holes
Subir Sachdev, Harvard University and TIFR