Superconductivity and Quantum Entanglement Subir Sachdev Harvard University sachdev.physics.harvard.edu

Tuesday, April 23, 13

Tuesday, April 23, 13

MAGNET is being levitated by an unseen superconductor in which countless trillions of electrons form a vast interconnected quantum state. Astoundingly, the quantum state of many modern

High temperature superconductors

YBa2 Cu3 O6+x Tuesday, April 23, 13

Key question: Can we use the fundamental principles of quantum mechanics to understand why YBa2Cu3O6 (and not most other combinations of elements) is a high temperature superconductor ? Tuesday, April 23, 13

Demo of levitating superconductor

Tuesday, April 23, 13

Fundamental principles of quantum mechanics 1. A particle is described by its quantum “state”.

Tuesday, April 23, 13

Fundamental principles of quantum mechanics 1. A particle is described by its quantum “state”. 2. Linear superposition: particles can be in the sum or difference of two “states”

Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment

Interference of water waves Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment

Send electrons through the slits Tuesday, April 23, 13

Show video at http://www.youtube.com/watch?v=jvO0P5-SMxk

Tuesday, April 23, 13

Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment

Send electrons through the slits Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment

Interference of electrons Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment Which slit does an electron pass through ?

Interference of electrons Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment Which slit does an electron pass through ?

No interference when you watch the electrons

Interference of electrons Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment Which slit does an electron pass through ?

Each electron passes through both slits !

Interference of electrons Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment Let |L represent the state with the electron in the left slit

|L

Tuesday, April 23, 13

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment Let |L represent the state with the electron in the left slit

|L

Tuesday, April 23, 13

|R

And |R represents the state with the electron in the right slit

Principles of Quantum Mechanics: 1. Quantum Superposition

The double slit experiment Let |L represent the state with the electron in the left slit

|L

|R

And |R represents the state with the electron in the right slit

Actual state of the electron is |L + |R Tuesday, April 23, 13

Fundamental principles of quantum mechanics 1. A particle is described by its quantum “state”. 2. Linear superposition: particles can be in the sum or difference of two “states”

Tuesday, April 23, 13

Fundamental principles of quantum mechanics 1. A particle is described by its quantum “state”. 2. Linear superposition: particles can be in the sum or difference of two “states” 3. Entanglement: state superposition with many particles. Tuesday, April 23, 13

Principles of Quantum Mechanics: 1I. Quantum Entanglement

Quantum Entanglement: quantum superposition with more than one particle

Tuesday, April 23, 13

Principles of Quantum Mechanics: 1I. Quantum Entanglement

Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom:

Tuesday, April 23, 13

Principles of Quantum Mechanics: 1I. Quantum Entanglement

Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom: Hydrogen molecule:

= 1 = ⌃ (|⇥⇤⌅ 2 Tuesday, April 23, 13

_

|⇤⇥⌅)

Principles of Quantum Mechanics: 1I. Quantum Entanglement

Quantum Entanglement: quantum superposition with more than one particle

_

Tuesday, April 23, 13

Principles of Quantum Mechanics: 1I. Quantum Entanglement

Quantum Entanglement: quantum superposition with more than one particle

_

Tuesday, April 23, 13

Principles of Quantum Mechanics: 1I. Quantum Entanglement

Quantum Entanglement: quantum superposition with more than one particle

_

Tuesday, April 23, 13

Principles of Quantum Mechanics: 1I. Quantum Entanglement

Quantum Entanglement: quantum superposition with more than one particle

_

Einstein-Podolsky-Rosen “paradox”: Non-local correlations between observations arbitrarily far apart Tuesday, April 23, 13

High temperature superconductors

YBa2 Cu3 O6+x Tuesday, April 23, 13

Square lattice of Cu sites

Tuesday, April 23, 13

Square lattice of Cu sites 1. Remove some electrons

Tuesday, April 23, 13

Square lattice of Cu sites 1. Remove some electrons 2. Electrons entangle into chemical bonds

Tuesday, April 23, 13

= | ⇥⇤⌅

| ⇤⇥⌅

Square lattice of Cu sites 1. Remove some electrons 2. Electrons entangle into chemical bonds 3. Chemical bonds undergo Bose-Einstein condensation

Tuesday, April 23, 13

= | ⇥⇤⌅

| ⇤⇥⌅

Square lattice of Cu sites 1. Remove some electrons 2. Electrons entangle into chemical bonds 3. Chemical bonds undergo Bose-Einstein condensation

Tuesday, April 23, 13

= | ⇥⇤⌅

| ⇤⇥⌅

Square lattice of Cu sites 1. Remove some electrons 2. Electrons entangle into chemical bonds 3. Chemical bonds undergo Bose-Einstein condensation

Tuesday, April 23, 13

= | ⇥⇤⌅

| ⇤⇥⌅

Square lattice of Cu sites 1. Remove some electrons 2. Electrons entangle into chemical bonds 3. Chemical bonds undergo Bose-Einstein condensation

Tuesday, April 23, 13

= | ⇥⇤⌅

| ⇤⇥⌅