Quantum Entanglement, - Harvard Universityqpt.physics.harvard.edu/talks/simons17.pdfThe complex...

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






sad0113Sach3p.indd 45 11/16/12 6:20 PM


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$SLITS$


Bullets



Send electrons through the slits




Interference of electrons




Is the electron a wave ?




TWO$SLITS$ Unlike water waves, electrons arrive

one-by-one (so is it like a particle ?)



But if it is like a

particle, which slit does each

electron pass through ?




No interference when you watch the electrons


But if it is like a





Each electron passes

through both slits !


But if it is like a



Let |L� represent the statewith the electron in the left slit

|L�



And |R� represents the statewith the electron in the right slit


|L� |R�



And |R� represents the statewith the electron in the right slit


|L� |R�



Actual state of each electron is

|Li + |Ri

Quantum Entanglement: quantum superposition with more than one particle

Principles of Quantum Mechanics: 1I. Quantum Entanglement



Hydrogen atom:



Hydrogen atom:

=1⌃2

(|⇥⇤⌅ � |⇤⇥⌅)

Hydrogen molecule:

= _



_



_

Einstein-Podolsky-Rosen “paradox” (1935): Measurement of one particle instantaneously

determines the state of the other particle arbitrarily far away



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

_


Black hole horizon

_

Black hole horizon


Black hole horizon


There is long-range quantum entanglement between the inside

and outside of a black hole

Black hole horizon


Hawking used this to show that black hole horizons have an entropy and a temperature

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.



Black holes


Strange metals


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


Antiferromagnet

Strange metal

Spins of electrons on Cu sites

Square lattice of Cu sites


Remove density p electrons


Electrons entangle in (“Cooper”) pairs into chemical bonds

= | ⇥⇤⌅ � | ⇤⇥⌅


Cooper pairs form quantum superpositions at different locations: “Bose-Einstein condensation” in which all pairs are “everywhere at the same time”

= | ⇥⇤⌅ � | ⇤⇥⌅

Superconductivity


= | ⇥⇤⌅ � | ⇤⇥⌅

High temperature superconductivity !

Electrons entangle by exchanging partners, and there is long-range quantum entanglement in the strange metal.


= | ⇥⇤⌅ � | ⇤⇥⌅



SM

FL


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.


Strange metals


Black holes


Strange metals


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


Entangle electrons pairwise randomly


The SYK model has “nothing but entanglement”


This describes both a strange metal and a black hole!


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”


D-dimensionalspace

Emergent spatial directionof SYK model or string theory

~x

⇣

String theory near a “D-brane”


D-dimensionalspace

Emergent spatial directionof SYK model or string theory

~x

⇣ Quantum entanglementleads to an emergent

spatial dimension


Strange metals


Black holes

A “toy model” which is both a strange metal and a black hole!






sad0113Sach3p.indd 45 11/16/12 6:20 PM


Subir Sachdev, Harvard University and TIFR

Quantum Entanglement, - Harvard Universityqpt.physics.harvard.edu/talks/simons17.pdfThe complex...

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