exploring fundamentals of quantum mechanics with optics
TRANSCRIPT
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Exploring Fundamentals of
Quantum Mechanics with Optics
Mark Beck
Department of Physics
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Photon Laboratories
Experiments
• Spontaneous parametric down conversion
• “Proving” light is made of photons
• Single photon interference
▪ Quantum eraser
• Quantum state measurement
• Tests of local realism
▪ Entanglement
• Hong-Ou-Mandel interference
• Entanglement witness
• …
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If a single photon is incident on a
beamsplitter, it can only go one way
•Only one detector will fire
•No coincident detections
"…a single photon can only be detected once!"
- P. Grangier et al.
T
R
“Proving” Photons Exist
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Quantify:
The degree of second-order coherence
T
R
(2)
ˆ ˆ: :(0)
ˆ ˆ
T R
T R
TR
T R
I Ig
I I
P
P P
=
=
0TRP =
(2) (0) 0g = (for a single photon input)
Single Photon on a Beamsplitter
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T
R
(2) (0)T R TR
T R T R
I I Pg
I I P P= =
(2) (0) 1g (for a classical wave)
T I R II I I I= =T R 1+ =T R
2
(2)
2(0)
I
I
Ig
I=
22
I II I (Cauchy-Schwartz inequality)
Classical Wave on a Beamsplitter
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One photon converted into two
wp
Spontaneous Parametric Downconversion
wp=ws+wi
Momentum Conservation
ws~wi~wp/2wi
ws
Energy Conservation
kp=ks+ki
Photons produced at
the same time
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"click"
You know you have a
photon in the other beam
•Spontaneous parametric
downconversion
▪ One photon converted into two
▪ Photons always come in pairs
Making a Single Photon State
wp
wi
ws
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G
R
T
BS
“Proving” Photons Exist
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St. dev. of St. devs.
Violation
0.064 0.008 117
0.109 0.049 18
0.103 0.037 24
0.107 0.006 149
(2) (0)g (2) (0)g
Typical Student Results
(2) (0) 1g (for a classical wave)
(2) (0) 0g = (for a single photon input)
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G
R
T
BS
“Proving” Photons Exist
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G
R
T
Single-Photon Interference
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Coincidence Counts,
Single Photons (V=89%)
Results
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Simultaneously displays
wave-like (interference)
and particle like (g(2)(0)<1)
behavior.
Coincidence Counts,
Single Photons (V=89%)
Results
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Quantum Teleportation
Transmit the quantum state of a particle from one place
to another
• Don’t send the actual particle
• Send information necessary to recreate the state
• No cloning theorem
▪ State of original particle must be destroyed
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Two-Particle States
( )1
0 0 1 12
A B A BAB
+ = +
Bell States
• A basis for 2-particle systems
( )1
0 0 1 12
A B A BAB
− = −
( )1
0 1 1 02
A B A BAB
+ = +
( )1
0 1 1 02
A B A BAB
− = −
0 0A B
1 1A B
0 1A B
1 0A B
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Quantum Teleportation
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Quantum Teleportation
( )
( )
( )
( )
10 1
2
10 1
2
10 1
2
10 1
2
a AB
B BaA
B BaA
B BaA
B BaA
+
+
−
+
−
=
= +
+ −
+ +
+ − +
( )0 1a a a
= +
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Quantum Teleportation
( )' 0 1B B B
= +
'B
( )
( )
( )
( )
10 1
2
10 1
2
10 1
2
10 1
2
a AB
B BaA
B BaA
B BaA
B BaA
+
+
−
+
−
=
= +
+ −
+ +
+ − +
( )0 1a a a
= +
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( )
( )
( )
( )
10 1
2
10 1
2
10 1
2
10 1
2
a AB
B BaA
B BaA
B BaA
B BaA
+
+
−
+
−
=
= +
+ −
+ +
+ − +
Quantum Teleportation
( )' 0 1B B B
= +
( )ˆ ' 0 1B B B B
U = = +
'B
B
( )0 1a a a
= +
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Four-Photon Source
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Four-Photon Source
one photon into two photons
PBS
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Four-Photon Source
One photon into two photons
PBS
Input pulses: 50fs, 80 MHz
Photon pairs: ~10 kHz
Four simultaneous photons: ~1Hz
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Four-Photon Source
One photon into two photons
PBS
Input pulses: 50fs, 80 MHz
Photon pairs: ~10 kHz
Four simultaneous photons: ~1Hz
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Interference of Independent Sources
one photon into two photons
PBS
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Hong-Ou-Mandel Interference
One photon into each arm
Each can either reflect or transmit
Four possibilities
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Hong-Ou-Mandel Interference
Two possibilities to go to opposite detectors
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Hong-Ou-Mandel Interference
Two possibilities to go to opposite detectors: add them
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Hong-Ou-Mandel Interference
Two possibilities to go to opposite detectors: add them
p phase shift on one term
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Hong-Ou-Mandel Interference
Two possibilities to go to opposite detectors: add them
p phase shift on one term
Terms where photons go opposite ways cancel
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Hong-Ou-Mandel Interference
Photons ALWAYS go to the same detector
• No coincidence detections between the two
detectors
Mosley et al., PRL 100, 133601 (2008)
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Research Interests
Quantum tomography
• State preparation and measurement (SPAM)
tomography
Error detection
• Quantum Key Distribution (Cryptography)
Weak and protected measurements
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Summary
Photon Labs
• Explore fundamental quantum mechanics
• Many different experiments
• They work!
The future
• More than two photons
• Quantum teleportation
• Telecom band (1550 nm)
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With lots of help from:
Faculty: R. Davies (Utah St.)
D. Branning (Trinity College)
E. Galvez (Colgate)
Students: J. Thorn, M. Neel, V. Donato, A. Gogo, W.
Snyder, M. Olmstead, J. A. Carlson, J. Lord,
G. Bergreen, E. Dederick, M. N. Beck,
A. Chambliss, E. Eastman, T. McPhee,
J. Cutshall
Support: NSF, Reed College, Whitman College