quantum entanglement and superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf ·...

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 and Superconductivity

Subir Sachdev, Harvard University






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

Superconductor, levitated by an unseen magnet, in which countless trillions of electrons form a vast interconnected quantum state.Scientific American, January 2013



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

YBa2Cu3O6+x


YBa2Cu3O6+x


CuO2 plane

Cu

O

SM

FL

Figure: K. Fujita and J. C. Seamus Davisp (hole/Cu)

SM

FL


Superconductor

SM

FL


Antiferromagnet

SM

FL


Strange metal

SM

FL


Strange metal

Can the “long-range quantum entanglement” in the strange metal help us understand high temperature superconductivity ?

Quantum phase transitions

Quantum superposition and

entanglement

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment

Interference of water waves


Send electrons through the slits



Interference of electrons





Unlike water waves,

electrons arrive one-

by-one




TWO$SLITS$



Which slit does an electron

pass through ?





pass through ?

No interference when you watch the electrons





pass through ?

Each electron passes

through both slits !


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”: Measurement of one particle instantaneously

determines the state of the other particle arbitrarily far away



entanglement



entanglement

String theory and black holes

Long-range quantum

entanglement of electrons in crystals



entanglement Long-range quantum



SM

FL


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 near the strange metal.



= | ⇥⇤⌅ � | ⇤⇥⌅


SM

FL



Superconductor

SM

FL



Superconductor

But can we measure the quantum entanglement of electrons in this crystal ?

SM

FL



Superconductor

But can we measure the quantum entanglement of electrons in this crystal ?

Only indirectly……

SM

FL


Scanning tunneling microscopy

Scanning Tunneling Microscopy

Ultra low vibration cryostat.

to Pumps

Load Lock

Lead Filled Legs

High-field SC Magnet

Lead Filled Table

Turbo Pump

Air Springs

Fridge

Cleaver

L4He

J. C. Davis group, Rev. Sci. Inst. 70, 1459 (1999).SI-STM System

STM Head

•Massive ULV Cryostat •Subkelvin Fridge •STM + High Field Magnet •Sample Exchange from RT •Cryogenic UHV Cleave

to Pumps

Load Lock

Lead Filled Legs

High-field SC Magnet

Turbo Pump

Air Springs

Cleaver

L4He

Sample insert

SI-STM SystemJ. C. Davis group, Rev. Sci. Inst. 70, 1459 (1999).

Y. Kohsaka et al., Science 315, 1380 (2007)

4⇥ 10�10 meters

Y. Kohsaka et al., Science 315, 1380 (2007)

Locationsof Cu atoms !

4⇥ 10�10 meters

Y. Kohsaka et al., Science 315, 1380 (2007) d-form factor density wave order

M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010).S. Sachdev and R. LaPlaca, Phys. Rev. Lett. 111, 027202 (2013).

Y. Kohsaka et al., Science 315, 1380 (2007) d-form factor density wave order

Intricrate pattern of electron density waves (DW) is giving us important information on the nature of

quantum entanglement in neighboring regions

SM

FL


Scanning tunneling microscopy:

leads to indirect signatures of quantum entanglement



entanglement


Long-range quantum



Long-range entanglement has a heierarchical structure: electrons entangle in pairs, pairs entangle with pairs, and so on..…

= | ⇥⇤⌅ � | ⇤⇥⌅


depth ofentanglement

D-dimensionalspace

Representation of hierarchical entanglement at quantum critical point

G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)

String theory

• Allows unification of the standard model of particlephysics with Einstein’s theory of gravitation(general relativity).

• Vibrations of a string (its “musical notes”) corre-spond to quarks, gravitons, the Higgs boson, pho-tons, gluons . . . . . .

• A D-brane is a D-dimensional surface on which strings

can end.

• If we focused only on the blue points on theD-dimensional

surface, they would appear to us to have long-range

quantum entanglement !


D-dimensionalspace


String theory near a D-brane


D-dimensionalspace

Emergent spatial directionof string theory Brian Swingle, arXiv:0905.1317


D-dimensionalspace

Brian Swingle, arXiv:0905.1317

Emergent spatial directionof string theory


States of matter with long-range quantum entanglement

in D dimensions

String theory and Einstein’s General Relativity

in D+1 dimensions

States of matter with long-range quantum entanglement

in D dimensions

String theory and Einstein’s General Relativity

in D+1 dimensions

Are there solutions of Einstein’s General Relativity in D+1 dimensions which have an entanglement structure similar to that of a “strange metal” ?



entanglement


Long-range quantum


Objects so massive that light is gravitationally bound to them.

Black Holes

Horizon radius R =2GM

c2

Objects so massive 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.

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


The Hawking entropy matches the entropy of some simple

strange metal states of electrons(S. Sachdev, 2015)

Black hole horizon


The Hawking entropy matches the entropy of some simple

strange metal states of electrons(S. Sachdev, 2015)

This connection is leading to a better understanding of the observable properties of strange metals in superconductors and other

quantumm materials



entanglement



entanglement


Long-range quantum







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

Superconductor, levitated by an unseen magnet, in which countless trillions of electrons form a vast interconnected quantum state.Scientific American, January 2013



quantum entanglement and superconductivityqpt.physics.harvard.edu/talks/sydneypublic15.pdf ·...

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