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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.
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