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Experiments with Single Photons: Existence Proof and Interference (and Entanglement of 2 Photons)
Mark BeckDept. of Physics, Whitman College
With lots of help from:
Faculty: Robert Davies (Seattle U)Students: Jeremy Thorn (U of O), Matthew Neel,
Vinsunt Donato, Geoffrey BergreenSupport: NSF, Whitman College
Quantum Mechanics
Quantum information is changing how we think about quantum systems.
• Convey this to studentsMany experiments involve photons
• Doable by undergraduatesWhich experiment should undergraduates perform first?
• Proof of the existence of photons!
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Experiment Proving Photons Exist
1) Should be conceptually simple2) Should display the "granular" nature of
individual photons3) Necessary to treat the field quantum
mechanically• Not explainable using classical waves
Proving Photons Exist
Photoelectric Effect?• Satisfies criteria 1) & 2)
– detector "clicks" are granular
• Does NOT satisfy criterion 3)– Does not require photons (i.e. a quantum field)
for its explanation– Can be explained using a semiclassical theory
(detector atoms quantized, field is a classical wave)
Grangier Experiment• P. Grangier, G. Roger, and A. Aspect, Europhys.
Lett. 1, 173-179 (1986).
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Single Photon on a Beamsplitter
If a single photon is incident on a beamsplitter, what do we know about "clicks" at output detectors?
• Only one detector will fire• No coincidence detections
"…a single photon can only be detected once!"- Grangier et al.
T
R
Single Photon on a Beamsplitter
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
PP P
=
=
0TRP =
(2) (0) 0g∴ = (for a single photon input)
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Classical Wave on a BeamsplitterT
R
(2) (0) T R TR
T R T R
I I PgI 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=
22I II I≥ (Cauchy-Schwartz inequality)
Distinguishing Classical and Quantum Fields
Classical waves:
Therefore, any field withcannot be described classically, and is inherently quantum mechanical.
Single photon state:
T
R
(2) (0) 1g ≥
(2) (0) 1g <
(2) (0) 0g =
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Making a Single-Photon State
"click"
You know you have a photon in the other beam
ωω/2
ω/2
Spontaneous parametric downconversion• One photon converted into two• Photons always come in pairs
In 1986 Grangier et al. used a cascade decay in Ca as a photon pair source.
Our Experiment Look for coincidences between T and R, conditioned on a detection at G.
G
R
TEverything is conditioned on a detection at G:
(2) (0) GTR
GT GR
PgP P
=
GTRGTR
G
NPN
=
GRGR
G
NPN
=
GTGT
G
NPN
= (2) (0) GTR G
GT GR
N NgN N
=
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More Details
λ/2
G
R
T
PBS409 nm20 mW
818 nm
BBOType I3mm thick3o cone angle
Detectors have RG780 filters
100,000 cpsGN > 8,000 cpsGT GRN N+ >
Experimental Setup
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Collection Optics
Results
~ 40 min.
~ 20 min.
~ 10 min.
~ 5 min.
Total acq. time
0.00260.017710023.4 s
0.00350.019110311.7 s
0.00410.01801085.4 s
0.00670.01881102.7 s
St. dev. ofNumber of pts.
Integration time per pt.
(2) (0)g (2) (0)g
In 5 minutes of counting we violate the classical inequalityby 146 standard deviations.(2) (0) 1g ≥
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Why not 0?
Perfect single photons have g(2)(0) = 0.• i.e., we expect no coincidences between T
and RWhy do we measure g(2)(0) = 0.0177 + 0.0026?
• Accidental coincidences– Due to finite coincidence window (2.5 ns)
Expected accidental coincidence rate explains difference from 0.
Single Photon Interference
λ/2
G
R
T
PBS
Insert interferometerhere
Insert interference filter (10nm bandpass) here
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BDP λ/2
PBS
BDP
λ/2
λ/2
Polarization Interferometer
R
T
• Easy to align– equal pathlengths
• EXTREMELY stable
φ
BDP λ/2
PBS
BDP
λ/2
λ/2
No Polarization Interferometer
R
T
• Remove interferometer by rotating waveplate
• Switch between Grangier expt. and interference expt.
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Results — Equal Pathlengths
Raw singles counts, not coincidences.
"White-light" fringes.
Results — Equal Pathlengths
Coincidence counts.
True single photon interference.
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Results — Equal Pathlengths
Simultaneously displays wave-like (interference) and particle like (g(2)(0)<1) behavior.
Unequal PathlengthsG
R
TMake pathlength difference longer than the coherence length
Interference filter
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Results — Unequal Pathlengths
Pathlength difference is larger than the coherence length of light in the interferometer.
Why do we still see interference in coincidence?
EntanglementG
R
TIncreases the coherence length of coincident photons in this beam
Inserting interference filter to decrease bandwidth of this beam
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Entanglement
Frequencies of the two beams are entangled
p G Iω = ω +ω
frequency of pump
(blue) beampω ⇒
, frequencies of gate and interferometer beams
G Iω ω ⇒
In coincidence, narrowing the distribution of ωG
narrows the distribution of ωI.
Conclusions
• We have performed an experiment that proves that light is made of photons
• We have demonstrated single-photon interference
• We have demonstrated frequency entanglement of two photons
• Experiments were performed by undergraduates, and are suitable for undergraduate teaching labs
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Whole Table
http://www.whitman.edu/~beckmk/QM/