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Classic Experiments in Quantum Optics. Experimental Quantum Optics and Quantum Information Part II, Photonic Quantum Optics Morgan W. Mitchell Spring 2005 ICFO – Institut de Ciencies Fotoniques. Taylor’s experiment (1909). film. slit. needle. diffraction pattern f(y). - PowerPoint PPT Presentation
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Classic Experiments in Quantum Optics
Experimental Quantum Optics and Quantum Information
Part II, Photonic Quantum Optics
Morgan W. Mitchell
Spring 2005
ICFO – Institut de Ciencies Fotoniques
Taylor’s experiment (1909)
slit
needle
diffraction pattern f(y)
film
Proceedings of the Cambridgephilosophical society. 15 114-115(1909)
Taylor’s experiment (1909)
slit
needle
diffraction pattern f(y)
Interpretation:
Classical: f(y) <E2(y)>
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) = <n(y)> = <a+(y)a(y)> <E-(y)E+(y)>E+(r) = a exp[i k.r – it]E-(r) = a+ exp[-i k.r + it]
f(y) same as in classical.
Dirac: “each photon interferes only with itself.”
film
Hanbury-Brown and Twiss (1956)
Nature, v.117 p.27Correlation g(2)
Tube position
Detectors see same field
Detectors see different fields
I
t
I
t
Signal is:g(2) = <I1(t)I2(t)> / <I1(t)><I2(t)>
Hanbury-Brown and Twiss (1956)
Correlation g(2)
Tube position
I
t
I
t
Signal is:g(2) = I1I2 / <I1><I2>= < (<I1>+I1) (<I2>+ I2) > / <I1><I2>
Note: <I1> + I1≥<I2> + I2 ≥ <I1> = <I2> = 0
g(2) = (<I1><I2>+<I1><I2>+<I2><I1>+<I1I2>)/<I1><I2> = 1 + <I1I2>)/<I1><I2> = 1 for uncorrelated <I1I2> = 0 > 1 for positive correlation I1I2 > 0 e.g. I1I2
< 1 for anti-correlation I1I2 < 0
Classical optics: viewing the same point, the intensities must be positively correlated.
I1= I0/2
I2= I0/2
I0
Detectors see same field
Detectors see different fields
Kimble, Dagenais + Mandel 1977
PRL, v.39 p691
I1= I0/2
I2= I0/2
I0
n1=0 or 1
n2= 1 - n1
n0=1
Classical: correlated
Quantum: can beanti-correlated
Correlation g(2)
t1 - t2Correlation g(2)
t1 - t2
Kimble, Dagenais + Mandel 1977
PRL, v.39 p691
Kimble, Dagenais + Mandel 1977
PRL, v.39 p691
Interpretation:
g(2)() < a+(t)a+(t+)a(t+)a(t)> < E-(t) E-(t+) E+(t+)E+(t)>HI(t) -Ed E+(t) |e><g| + E-(t) |g><e| HI(t) HI(t+) E-(t) E-(t+) |g><e| |g><e| + h.c.
Pe
t time
Kuhn, Hennrich and Rempe 2002
Kuhn, Hennrich and Rempe 2002
Pelton, et al. 2002
Pelton, et al. 2002
fs pulserelax
emit
InAs QD
Pelton, et al. 2002
Goal: make the pure state|> = a+|0> = |1>Accomplished: make the mixed state 0.38 |1><1| + 0.62 |0><0|
Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982
J=0
J=0
J=1
Total angular momentum is zero.
For counter-propagating photonsimplies a singlet polarization state:|> =(|L>|R> - |R>|L>)/2
Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982
Total angular momentum is zero.
For counter-propagating photons,implies a singlet polarization state:|> =(|L>|R> - |R>|L>)/2
|> = 1/2(aL+aR
+ - aR+aL
+)|0> = 1/2(aH
+aV+ - aV
+aH+)|0>
= 1/2(aD+aA
+ - aA+aD
+)|0>
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.
Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982
a
a'b
b'
|SQM| ≤ 22 = 2.828...
22.5°
Perkin-Elmer Avalanche Photodiode
thin p region (electrode)
absorption region intrinsic silicon
multiplication regionV positive
V negative
“Geiger mode”: operating pointslightly above breakdown voltage
e- h+
Avalanche Photodiode Mechanism
Many valence electrons, each with a slightly differentabsorption frequency i.Broadband detection.
k
E
valence band(filled)
conduction band (empty)
possible transitions
= E/hbar Di
“Classic” Photomultiplier Tube
Many valence electrons, each can be driven into the continuum i.Broadband detection.
E
Photocathode Response
Broad wavelength range: 120 nm – 900 nmLower efficiency: QE < 30%
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)
Coincidence Detection with Parametric Downconversion
FRIBERG S, HONG CK, MANDEL LMEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 2011-2013 1985
Using MCP PMTs for best time-resolution.CF Disc. = Constant-fraction discriminator: identifies “true” detection pulses, rejects background, maintains timing.TDC = “Time to digital converter”:Measures delay from A detection to B detection.PDP11: Very old (1979) computer from DEC.
Physical Picture of Parametric Downconversion
valence
conduction
Material (KDP) is transparent to both pump (UV) and downconvertedphotons (NIR). Process is “parametric” = no change in state of KDP.This requires energy and momentum conservation: s + i = p ks + ki = kp Even so, can be large uncertainty in s i
Intermediate states (virtual states) don’t even approximately conserve energy.Thus must be very short-lived. Result: signal and idler produced at same time.
k-vector conservationks + ki = kp
collinear
non-collinearor
phase matching
Coincidence Detection with Parametric Downconversion
FRIBERG S, HONG CK, MANDEL LMEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 2011-2013 1985
transit time through KDP~400 ps
Dt < 100 ps
TDC = time-to-digitalconverter. Measuresdelay from A detectionto B detection.
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
Quadrature Detection (Wu, Xiao, Kimble 1985)
WU L-A., Xiao M., KIMBLE H.J.SQUEEZED STATES OF LIGHT FROM AN OPTICAL PARAMETRIC OSCILLATOR JOSA B 4 (10): 1465-1475 OCT 1987
Quadrature Detection Electronics
P
freq
Spectrumanalyzer
environmental noise
measurementfrequency P
time
Slusher, et. al. 1985 Wu, et. al. 1987
Quadrature Detection of Squeezed Vacuum
LO phase
input isvacuum
input issqueezedvacuum
P
D1
D2
LO
in
Di(t)
X2
X1
X2
X1
vacuum squeezedvacuum
63% VRMS
(40% power)
Cauchy Schwarz Inequality Violation
Cauchy Schwarz Inequality Violation
9P
7S
7P
435.8 nm
567.6 nm
202Hg
e- impact
Cauchy Schwarz Inequality Violation
Two-photon diffraction
D’Angelo, Chekhova and Shih, Phys. Rev. Lett. 87 013602 (2001)
Two IR photons (pairs)
One IR photon
Pump
2,0high,low
0,2high,low
Two-photon diffraction
D’Angelo, Chekhova and Shih, Phys. Rev. Lett. 87 013602 (2001)
Two IR photons (pairs)
One IR photon
Two paths to coincidence detection:
Pump
2,0high,low
0,2high,low
'2 rrkie
Not just for photons!
Not just for photons!
g(1) g(2)
Hong-Ou-Mandel effect
Hong, Ou and Mandel, Phys. Rev. Lett. 59 2044 (1987)
2,0high,low
0,2high,low
Hong-Ou-Mandel effect
Hong, Ou and Mandel, Phys. Rev. Lett. 59 2044 (1987)
2,0high,low
0,2high,low
Hong-Ou-Mandel effect with polarization
Sergienko, Shih, and Rubin, JOSA B, 12, 859 (1995)
Single-pass squeezing
Wenger,Tualle-Brouri, and Grangier, Opt. Lett. 29, 1267 (2004)
Single-pass squeezing
Wenger,Tualle-Brouri, and Grangier, Opt. Lett. 29, 1267 (2004)
