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UnexpectedUnexpectedConnections in Physics:Connections in Physics:

From SuperconductorsFrom Superconductorsto Black Holesto Black Holes

Talk online:

sachdev.physics.harvard.edu



The main unsolved problem intheoretical physics today:

Unification of




Unification of

Quantum theory of electrons,protons, neutron, atoms,

molecules..




Unification of

Quantum theory of electrons,protons, neutron, atoms,

molecules..

Einstein’s theory of General Relativity(ravitation! applied to stars, blac"holes, ala#ies, the universe....

and



$or" over the past %&' years has finallyled to a candidate theory hich unifies

ravitation and the )uantum theory, andhich is internally consistent.





This theory is popularly "non as*strin theory+





$e do not "no yet if strintheory is the correct description

of our universe.

This theory is popularly "non as*strin theory+

Th d i i l f h i



The deepest ne principle of physicsto emere from strin theory is the

e)uivalence beteen

Th d i i l f h i




e)uivalence beteen

the )uantum theory ofravity in space dimensions

Th d i i l f h i




e)uivalence beteen


a theory of special )uantum states ofmatter (electron, photons, )uar"s..!ithout ravity in % space dimensions

and



-dimensional )uantum ravity

can be represented as a*holoram+ in% dimensions



This e)uivalence has led to:




omplete formulations of consistenttheories of )uantum ravity




omplete formulations of consistenttheories of )uantum ravity

/olutions of previously unsolvedproblems in stronly interactin

theories of )uantum matter in %dimensions (ithout ravity!



Quantumsuperposition and

entanlement

Quantum phase transitionsand

Quantum critical points

/uperconductivity

0lac"1oles




entanlement



/uperconductivity

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entanlement



/uperconductivity

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Q



QuantumSuperposition The double slit experiment

Interference of water waves

Q t



The double slit experiment

Interference of electrons

QuantumSuperposition

Q t





Whichslit does

anelectronpass

through


Q t





Whichslit does

anelectronpass

through

!ointerferen

ce whenyou watch

the

electrons


Q t





Whichslit does

anelectronpass

through


"achelectron

passesthrough

both

slits #

Q t





Q t





Quantum "ntanglement: $uantum



Quantum "ntanglement: $uantumsuperposition with more than one

particle




Hydrogen atom:


particle




Hydrogen atom:

Hydrogen molecule:

= _

Superposition of two electron states leads to non-local

correlations between spins


particle




_


particle




_


particle

"instein%&odolsky%'osen (paradox): !on%

local correlations between observations

t l t f h i l b d



Resonance in benzene leads to a symmetric

configuration of chemical bonds

( F. Kekulé, L. Pauling )

ntanglement of chemical bonds

t l t f h i l b d



Resonance in benzene leads to a symmetric

configuration of chemical bonds

( F. Kekulé, L. Pauling )

ntanglement of chemical bonds




entanlement



/uperconductivity

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Q




entanlement



/uperconductivity

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bidi i i



Rubidium atoms in a magnetic trap

and standing wa!es of laser light

"# $reiner% &# "andel% '#

sslinger% '# # Hnsch% and+loch% Nature 415% , (.//.)#

0t !ery low temperatures and for a wea1 laser




light% the Rubidium atoms form a

+ose-instein condensate


sslinger% '# # Hnsch% and+loch% Nature 415% , (.//.)#



* +ose%"instein condensate:*n $uantum superpositionof all the atoms in allpositions

* li$uid which ,ows withoutresistance -a super,uid



* single atom issuperposed between

all positions




all positions



* single atom issuperposed betweenall positions




+ose%"instein condensate:



superposition between all atoms




2arge fluctuations in number of atoms in each site 3

superfluidity (atoms can 4flow5 without dissipation)





y p

light% the Rubidium atoms form a

+ose-instein condensate


sslinger% '# # Hnsch% and

+loch% Nature 415% , (.//.)#





-Strictly speaking: this is notentanglement between the atoms

because the +"/ is a product of simple(wave) states of the atoms

* d t +



* superconductor: a +osecondensate of pairs of electrons in a

(chemical bond) in a metal



Ca1.90

a0.10

Cu!"Cl

" Bi"."Sr1.#Ca0.#$y0."Cu"! y

High temperature superconductors

High temperature



High temperature

superconductors

S6uare lattice of 7u sites




0. 'emovesomeelectrons






1. "lectronsentangle intochemicalbonds







2. /hemicalbondsundergo+ose%"insteincondensation




QuickTime3 and a4otion 5&"6 7pen849 decompressor

are needed to see this picture.

8ulian Hetel and 9andini 'ri!edi% &hio State ni!ersity

!d%e%+ magnets; <+a/u7 superconductor



Quantumentanlement

Quantum phase transitions

andQuantum critical points

/uperconductivity

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Quantumentanlement



/uperconductivity

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hat is a 4phase transition5 ;



hat is a phase transition ;

0 change in the collecti!e properties of a

macroscopic number of atoms

hat is a 4quantum phase transition5 ;



hat is a quantum phase transition ;

7hange in the nature of

6uantum superposition in amacroscopic 6uantum system#

>uantum 7riticality



'he comple< and non-localentanglement at the critical point

between two 6uantum phases#'here is entanglement between

electronsatoms at all distance scales#

Rubidium atoms in a magnetic trap



g p

and standing wa!es of laser light



+loch% Nature 415% , (.//.)#

*ncrease the intensity of laser light



y g



+loch% Nature 415% , (.//.)#

*ncrease the intensity of laser light





+loch% Nature 415% , (.//.)#

y g




sslinger% '# # Hnsch% and *#

+loch% Nature 415% , (.//.)#

Strong laser light



4ggs in an egg carton5

Strong laser light




Strong laser light




Super,uid Insulator



Intensity of laserlightQuantum critical

point

Super,uid Insulator

Super,uid Insulator



Intensity of laserlight"ntanglement

between atoms at

Super,uid Insulator

Superfluid-insulator 6uantum phase transition



"# $reiner% &# "andel% '# sslinger% '# # Hnsch% and *# +loch% Nature 415% , (.//.)#

>uantum 7riticality



'he comple< and non-localentanglement at the critical point

between two 6uantum phases#'here is entanglement between

electronsatoms at all distance scales#



Quantumentanlement



/uperconductivity

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Quantumentanlement



/uperconductivity

0lac"1oles

+lac1 Holes



&b?ects so massi!e that light isgra!itationally bound to them#

+lac1 Holes



&b?ects so massi!e that light isgra!itationally bound to them#

In "instein=s theory; theregion inside the black

hole hori>on is

disconnected from therest of the universe.

+lac1 Holes @ >uantum theory



*round 0?@A; +ekenstein andBawking showed that the

application of the $uantumtheory across a black holehori>on led to many

astonishing conclusions

Quantum "ntanglement across a blackhole hori>on



_

hole hori>on




_

hole hori>on

Black hole

horizon




_

Black hole

horizon

hole hori>on




Black hole

horizon

hole hori>on

There is a non%local

$uantum entanglementbetween the inside and

outside of a black hole




Black hole

horizon

hole hori>on



outside of a black hole




hole hori>on



outside of a black hole This entanglement leads toa

black hole temperature-the Bawking temperatureand a black hole entropy

Q t



Quantumentanlement



/uperconductivity

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Q t



9

9

Quantumentanlement



/uperconductivity

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hole hori>on


$uantum entanglementbetween the inside andoutside of a black hole




hole hori>on


$uantum entanglementbetween the inside andoutside of a black hole

In anti%de Sitter -*dS space;this entanglement is

e$uivalent to that of a$uantum critical point of

$uantum matter in 1

The $uantum theory of a black hole in a 2C0%dimensional negatively curved *dS universe is



dimensional negatively curved *dS universe isholographically represented by the theory of a

$uantum critical point in 1C0 dimensions

"aldacena% $ubser% Alebano!% Bolya1o!% itten

3+1 dimensional

d! spa"e





3+1 dimensional

d! spa"e 0 .@C

dimensionalsystem at its

6uantum

critical point







3+1 dimensional

d! spa"e >uantum

criticality in.@C

dimensions0lac" holetemperature

2temperatureof )uantumcriticality





5. 4c6reevy

9ength%scale of

entanglementrepresents (extra)

third dimension




3+1 dimensional

d! spa"e >uantum

criticality in.@C

dimensionsQuantumcritical

dynamics 2aves incurved space







3+1 dimensional

d! spa"e >uantum

criticality in.@C

dimensions3riction of)uantum

criticality 2aves fallininto blac"

hole

Ao!tun% Bolicastro% Son



Super,uid Insulator



Intensity of laserlightQuantum critical

point



Quantum critical

point

Intensity of laserlight

riction of atom ,owdescribed by waves near a



Quantum critical

point

Intensity of laserlight

described by waves near ablack hole hori>on #






Question: if you lived in this world;would you think you lived in 1 or 2

spatial dimensions







spatial dimensions

*nswer: it

depends......







spatial dimensions *nswer: for some values of theparameters in the theory; the world

would appear 2 dimensional; whilefor other parameters; it wouldappear 1 dimensional; and there

many theories which would appear




ye)uivalence beteen


a theory of special )uantum states ofmatter (electron, photons, )uar"s..!ithout ravity in % space dimensions

and




superposition andentanlement



/uperconductivity

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superposition andentanlement



/uperconductivity

0lac"

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