HANBURY BROWN & TWISS SCATTERING

r

r’ t

t’

S1 S2

D1

P(2,0) P(1,1) P(0,2)

Classical

D2

Bu,ker,Blanter2000

r

r’ t

t’

S1 S2

D1

D2

Bu,ker,Blanter

P(2,0) P(1,1) P(0,2)

Fermions 0 1 0

Fermions:

11

22

ˆ SD

SD

abSab⎛ ⎞⎛ ⎞

= ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

†1 1 1

†2 2 2

ˆ

ˆD D

D D

n b bn b b=

=† † † †

1 2 2 1 1 1 2 2 1 2ˆ ˆ(1,1) 0 0S S D D D D S SP n n a a b b b b a a= Ψ Ψ =

2(1,1) ( ) 1P T R= + =

r

r’ t

t’

S1 S2

D1 P(2,0) P(1,1) P(0,2)

Classical

Bosons

Fermions 0 1 0

D2

Bu,ker,Blanter

“bunching”=enhanced

noise

“an>-bunching”=reducednoise

P(2,0) P(1,1) P(0,2)

Classical RT RT

Bosons

Fermions

2 2R T+2(1 )RT J+ 2(1 )RT J+2 2 22R T RTJ+ −2(1 )RT J−

2(1 )RT J−2 2 22R T RTJ+ +

overlap between (wavepackets) of colliding particles J =

D1

S

BS1 M1

M2 BS2

D2

ΔΦ+=+= ΔΦ→ cos10

2

21212TTerrttT i

BSBSBSBSDS

Mach-Zehnder Photonic Interferometer

0 1 2 3 4 5

0.0

0.5

1.0

inte

nsity

(a.

u.)

phase difference ( π )

D1 D2

D2 S2 S2 D2

S1 D1

S D1

D2

QPC1

QPC2 M

G G2

G3

G1

air bridge

Neder, Heiblum et al

DEPHASING THROUGH MEASUREMENT (which path)

D2 S2

S2 D2

S1 D1

S1 D1

D2 Φ

1

1

tr

02 /1 1 2 1 2

iD t t e r rπψ Φ Φ= +

1 2 1 2

2 0

| |, | |, | |, | | 1 / 21 1 cos(2 / ) 12 2D

t t r r

P visibilityπ

=

= + Φ Φ ⇒ =

0 1 2 3 4 5

0.0

0.5

1.0

inte

nsity

(a.

u.)

phase difference ( π )

D1 D2

S1 D1

D2 Φ

now, adding a detector

STRONG MEASUREMENT

S1 D1

D2 Φ

STRONG MEASUREMENT

detectorsystemr↓ ⊗

detectorsystemr↓ ⊗

detectorsystemt↑ ⊗ detectorsystem

t↑ ⊗+ 02 /ie πΦ Φ

1 0DP const visibility= ⇒ =

“DEPHASING” (loss of coherent interference pattern due to “which path” detection)

QUANTUM ERASURE (Weisz, Heiblum, YG, et al Science 2014)

IV COMPOSITE MEASUREMENT PROTOCOLS: weak value protocol and beyond

WEAK VALUE : Aharonov, Albert, Vaidman, 1988

time

post selection (eigenstate of )

weak measuremet of

preparation

A

B

ˆ ˆ[ , ] 0A B ≠

µ µ| |in inB B= Ψ Ψ =

µ| | |An

A Ain n n inB

Ψ

Ψ Ψ Ψ Ψ =∑ g

||

An inAn in

Ψ Ψ•

Ψ Ψ

µ2| | | | | / |An

A A An in n in n inB

Ψ

Ψ Ψ Ψ Ψ Ψ Ψ∑ g

µweak disturbance

( | ) | | / |An

A A Afin n in n in n inP B

Ψ

= Ψ = Ψ Ψ Ψ Ψ Ψ Ψ∑ g

µµ| |

( | )|A

n

An inA

fin n in An in

BB P

Ψ

Ψ Ψ= Ψ = Ψ Ψ

Ψ Ψ∑ g

µ0

0

select (post-select)

(only "successful" measurements of with subsequent are considered)

A

A

B

Ψ

Ψ

0

0

0

µ0 weakA BΨ

=

µµ

weak

| |

|final

final in

final in

BBΨ

Ψ Ψ=

Ψ Ψ

µµ| |

( | )|A

n

An inA

fin n in An in

BB P

Ψ

Ψ Ψ= Ψ = Ψ Ψ

Ψ Ψ∑ g

same expression through microscopic system-detector analysis

example: Spin 1/2

time

post selection (eigenvalue of )

weak measuremet of

preparation

A

B

12zS = +

12xS = +

x zˆ ˆ(S +S )measuring

2

example: Spin 1/2

x zˆ ˆ1 (S +S ) 1| [ ] |

2 221 1|2 2

x z

x z

S S

S S

= + = +

== + = +

0

0

ˆ| |ˆ|

fin in

weakfin in

BB

Ψ Ψ=

Ψ Ψ

example: Spin 1/2

x zˆ ˆ1 (S +S ) 1| [ ] |

2 221 1|2 2

x z

x z

S S

S S

= + = +

== + = +

1 1 1 1| |1 1 1 1 12 2 2 2

1 1 1 12 22 2 2| |2 2 2 2

x z x z

x z x z

S S S S

S S S S

= + = + = + = ++ = =

= + = + = + = +g g

2 1 1outside [- , ] !!!2 2 2⇒ +

( )P Q

Quantum Point Contact

t

Q I dtΔ

= ⋅∫t

Q I dtΔ

= ⋅∫

( )P Q

HOW CAN IT BE? (physical picture)

I

WHAT ARE WEAK VALUES GOOD FOR? EXOTIC EXPECTATION VALUES ( > largest eigenvalue; total spin=negative; complex) Romito, YG, Blanter PRL 2008, Shpitalnik, Romito, YG, PRL 2008, Williams, Jordan PRL 2008. ULTRA SENSITIVE AMPLIFICATION Dixon et al, PRL 2009; Hosten Kwiat Science 2009 QUANTUM STATE DISCRIMINATION Zilberberg, Romito, Starling, Howland, Howell, YG PRL 2013 OBSERVATION OF VIRTUAL STATES cotunneling: Romito, YG , 2015 QUANTUM ERASURE Weiss, Heiblum, YG et al Science 2014, YG & Romito NON-LOCAL EFFECTS “Elitzur-Vaidman Box” Zilberberg, Romito,YG,PRB 2016 TOPOLOGICAL EXCITATIONS ….

Zilberberg, Romito, YG, 2016

AMPLIFICATION

Measured 560 frad of mirror deflection deflection 2µ<

Dixon et al, PRL 2009

optical Sagnac interferometer polarization rotating

detector

piezo driven mirror

phase shift for V

source

x

Dixon et al PRL 2009

φ

x

Zilberberg, Romito, YG, PRL 2011

optical Sagnac interferometer polarization rotating

detector

piezo driven mirror

phase shift for V

source

optical Sagnac –ultra sensitivity

optical Sagnac –ultra sensitivity

optical Sagnac –ultra sensitivity

optical Sagnac –ultra sensitivity

i pA ikxAe ek p x

λ

λ θ

→

→ ∝ →

θ

Results

φ

Results

WV amplification factors of over 100 Measured 560 frad of mirror deflection which is caused by 20 fm of piezo travel.

The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.