Taylors experiment 1909

1
Taylors experiment (1909)
film
slit
needle
diffraction pattern f(y)
Proceedings of the Cambridge philosophical
society. 15 114-115 (1909)
2
Taylors experiment (1909)
Interpretation Classical f(y) ?
ltE2(y)gt Early Quantum (J. J. Thompson) if
photons are localized concentrations of E-M
field, at low photon density there should be too
few to interfere. Modern Quantum f(y) ltn(y)gt
lta(y)a(y)gt ? ltE-(y)E(y)gt E(r) ? a
expi k.r iwt E-(r) ? a exp-i k.r
iwt f(y) same as in classical. Dirac each
photon interferes only with itself.
film
slit
needle
diffraction pattern f(y)
3
Hanbury-Brown and Twiss (1956)
Nature, v.117 p.27
Correlation g(2)
Tube position
I
Detectors see same field
t
I
Detectors see different fields
Signal is g(2) ltI1(t)I2(t)gt / ltI1(t)gtltI2(t)gt
t
4
Hanbury-Brown and Twiss (1956)

• Signal is
• g(2) ltI1I2gt / ltI1gtltI2gt
• lt (ltI1gtdI1) (ltI2gt dI2) gt / ltI1gtltI2gt
• Note ltI1gt dI1 0 ltI2gt dI2 0
  
• ltdI1gt ltdI2gt 0
• g(2) (ltI1gtltI2gtltdI1gtltI2gtltdI2gtltI1gtltdI1dI2gt)/ltI1
  gtltI2gt
• 1 ltdI1dI2gt)/ltI1gtltI2gt
• 1 for uncorrelated ltdI1dI2gt 0
• gt 1 for positive correlation ltdI1dI2gt gt 0
  e.g. dI1dI2
• lt 1 for anti-correlation ltdI1dI2gt lt 0
• Classical optics viewing the same point, the
• intensities must be positively correlated.

Correlation g(2)
Tube position
I
Detectors see same field
t
I
Detectors see different fields
I1 I0/2
I0
t
I2 I0/2
5
Kimble, Dagenais Mandel 1977
PRL, v.39 p691
Correlation g(2)
I1 I0/2
Classical correlated
I0
I2 I0/2
t1 - t2
Correlation g(2)
Quantum can be anti-correlated
n10 or 1
n01
n2 1 - n1
t1 - t2
6
Kimble, Dagenais Mandel 1977
PRL, v.39 p691
7
Kimble, Dagenais Mandel 1977
PRL, v.39 p691
Interpretation g(2)(t) ? lt a(t)a(tt)a(tt)a(t
)gt ? lt E-(t) E-(tt) E(tt)E(t)gt HI(t)
?? -E??d ? E(t) egtltg E-(t) ggtlte HI(t)
HI(tt) ? E-(t) E-(tt) ggtlte ggtlte h.c.
Pe
time
t
8
Kuhn, Hennrich and Rempe 2002
9
Kuhn, Hennrich and Rempe 2002
10
Pelton, et al. 2002
11
Pelton, et al. 2002
InAs QD
relax
fs pulse
emit
12
Pelton, et al. 2002
Goal make the pure state ??gt a0gt
1gt Accomplished make the mixed state r ? 0.38
1gtlt1 0.62 0gtlt0
13
Holt Pipkin / Clauser Freedman / Aspect,
Grangier Roger 1973-1982
J0
J1
J0
Total angular momentum is zero. For
counter-propagating photons implies a singlet
polarization state ??gt (LgtRgt - RgtLgt)/?2
14
Holt Pipkin / Clauser Freedman / Aspect,
Grangier Roger 1973-1982
Total angular momentum is zero. For
counter-propagating photons, implies a singlet
polarization state ??gt (LgtRgt -
RgtLgt)/?2 ??gt 1/?2(aLaR - aRaL)0gt
1/?2(aHaV - aVaH)0gt 1/?2(aDaA
- aAaD)0gt Detect photon 1 in any polarization
basis (pA,pB), detect pA, photon 2 collapses to
pB, or vice versa. If you have classical
correlations, you arrive at the Bell
inequality -2 S 2.
15
Holt Pipkin / Clauser Freedman / Aspect,
Grangier Roger 1973-1982
a
b
a'
22.5
b'
SQM 2?2 2.828...
16
Perkin-Elmer Avalanche Photodiode
V negative
thin p region (electrode)
absorption region intrinsic silicon
e-
h
multiplication region
V positive
Geiger mode operating point slightly above
breakdown voltage
17
Avalanche Photodiode Mechanism
Many valence electrons, each with a slightly
different absorption frequency wi. Broadband
detection.
18
Classic Photomultiplier Tube
E
Many valence electrons, each can be driven into
the continuum wi. Broadband detection.
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Photocathode Response
Broad wavelength range 120 nm 900 nm Lower
efficiency QE lt 30
20
Microchannel Plate Photomultiplier Tube
For light, use same photocathode materials, same
Q. Eff. and same wavelength ranges. Much
faster response down to 25 ps jitter (TTS
Transit time spread)
21
Coincidence Detection with Parametric
Downconversion
Using MCP PMTs for best time-resolution. CF Disc.
Constant-fraction discriminator identifies
true detection pulses, rejects background,
maintains timing. TDC Time to digital
converterMeasures delay from A detection to B
detection. PDP11 Very old (1979) computer from
DEC.
FRIBERG S, HONG CK, MANDEL LMEASUREMENT OF TIME
DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON
PAIRS Phys. Rev. Lett. 54 (18) 2011-2013 1985
22
Physical Picture of Parametric Downconversion
phase matching
conduction
collinear
non-collinear
or
k-vector conservation ks ki kp
valence
Material (KDP) is transparent to both pump (UV)
and downconverted photons (NIR). Process is
parametric no change in state of KDP. This
requires energy and momentum conservation ws
wi wp ks ki kp Even so, can be
large uncertainty in ws - wi Intermediate
states (virtual states) dont even approximately
conserve energy. Thus must be very short-lived.
Result signal and idler produced at same time.
23
Coincidence Detection with Parametric
Downconversion
TDC time-to-digital converter. Measures delay
from A detection to B detection.
transit time through KDP 400 ps
Dt lt 100 ps
FRIBERG S, HONG CK, MANDEL LMEASUREMENT OF TIME
DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON
PAIRS Phys. Rev. Lett. 54 (18) 2011-2013 1985
24
Quadrature Detection of Squeezed Light (Slusher,
et. al. 1985)
SLUSHER RE, HOLLBERG LW, YURKE B, et
al. OBSERVATION OF SQUEEZED STATES GENERATED BY
4-WAVE MIXING IN AN OPTICAL CAVITY Phys. Rev.
Lett. 55 (22) 2409-2412 1985
25
Quadrature Detection (Wu, Xiao, Kimble 1985)
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Quadrature Detection Electronics
environmental noise
P
measurement frequency n
Pn
freq
Spectrum analyzer
time
Wu, et. al. 1987
Slusher, et. al. 1985
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Quadrature Detection of Squeezed Vacuum
?Pn
input is squeezed vacuum
input is vacuum
63 VRMS (40 power)
LO phase
X2
X2
q
q
X1
X1
squeezed vacuum
vacuum
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Cauchy Schwarz Inequality Violation
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Cauchy Schwarz Inequality Violation
202Hg
9P
567.6 nm
7S
e- impact
435.8 nm
7P
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Cauchy Schwarz Inequality Violation
32
Two-photon diffraction
Two IR photons (pairs)
One IR photon
Pump
DAngelo, Chekhova and Shih, Phys. Rev. Lett. 87
013602 (2001)
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Two-photon diffraction
Two IR photons (pairs)
Two paths to coincidence detection
One IR photon
Pump
DAngelo, Chekhova and Shih, Phys. Rev. Lett. 87
013602 (2001)
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Not just for photons!
35
Not just for photons!
g(1)
g(2)
36
Hong-Ou-Mandel effect
Hong, Ou and Mandel, Phys. Rev. Lett. 59 2044
(1987)
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Hong-Ou-Mandel effect
Hong, Ou and Mandel, Phys. Rev. Lett. 59 2044
(1987)