Download Taylor`s experiment (1909)

Classic Experiments in Quantum
Optics
Experimental Quantum Optics and Quantum Information
Part II, Photonic Quantum Optics
Morgan W. Mitchell
Spring 2007
ICFO – Institut de Ciencies Fotoniques
Quantum Optics and Quantum Information
Light source
Interesting physics
State of light
Detection
Continuous Variables
← Approach →
Lasers
← Light Source →
Field operators, e.g. E(t)
← Description of light →
Field distributions
← mixed states →
Linear and NL optics, atoms
← Physics →
Homodyne detection
← Detection →
Discrete variables
Lasers
Particles, state vectors | >
Density matrices
Linear and NL optics, atoms
Photon counting
“Squeezing”
Low-noise measurements
(grav-wave detection)
“Hong-Ou-Mandel”
Foundations of physics
(non-locality, Q. meas.)
← Favourite word →
← Classic
→
Applications
Quantum Optics and Quantum Information
Continuous Variables
← Approach →
Lasers
← Light Source →
Field operators, e.g. E(t)
← Description of light →
Field distributions
← mixed states →
Linear and NL optics, atoms
← Physics →
Homodyne detection
← Detection →
Discrete variables
Lasers
Particles, state vectors | >
Density matrices
Linear and NL optics, atoms
Photon counting
“Squeezing”
Low-noise measurements
(grav-wave detection)
“Hong-Ou-Mandel”
Foundations of physics
(non-locality, Q. meas.)
← Favourite word →
← Classic
→
Applications
Continuous Var. QI
Discrete Var. QI
Q. Entanglement
Q. Teleportation
Q. Gates
Q. Memory
Q. Entanglement
Q. Teleportation
Q. Gates
Q. Memory
Schrodinger Kittens / Cats
Loophole free Bell I. tests
Quantum Teleportation
Quantum info output:
3 has state of 1
Joint measurement
Of 1 & 2
Manipulation of
half of entangled
state, 3
Quantum info input:
Unknown state of 1
Quantum resources input:
Entangled state of 2 & 3
Better than measure 1, prepare 3, because of uncertainty principle.
DV Teleportation
Quantum info output:
Unknown state

Joint measurement:
Project onto singlet
state




12
1
  unknown
12


1
 unknown 1  cH H 1  cV V
  unknown
3
Manipulation of
half of entangled
state
Quantum info input:
Unknown state

3



23

23
1
H V  V H

2

1
Quantum resources input:
Entangled state
Bouwmeester, et al. "Experimental Quantum Teleportation," Nature 390, 575, 11 Dec 1997
CV Teleportation
Quantum info output:
Unknown state
Xˆ 3 , Pˆ3  Xˆ 1 , Pˆ1
Joint measurement:
Combined variables
Xˆ 1  Xˆ 2
Pˆ  Pˆ
1
Manipulation of
half of entangled
state
2
Quantum info input:
Unknown state
Xˆ 1 , Pˆ1

Xˆ 3  Xˆ 3  Xˆ 1  Xˆ 2
Pˆ  Pˆ  Pˆ  Pˆ
3
Xˆ 3  Xˆ 2  0
Pˆ  Pˆ  0
3
2
3

1
2

Quantum resources input:
Einstein-Podolsky-Rosen
Entangled state
Furusawa et al. "Unconditional Quantum Teleportation," Science, 282, 706, 23 October 1998

Quantum Optics and Quantum Information
Course Topics
What is quantum light?
• Quantization of the EM Field
• Quantum states of light
How to measure quantum light
• Direct detection
• Homodyne detection
• Correlation functions
• Distribution functions
How to manipulate quantum light
• Linear optics
• Nonlinear optics
How to produce quantum light
• Single photons
• Squeezing
Light – matter interactions
• Single atoms (see JE)
• Atomic ensembles
• Collective variables
• Collective excitations
Theory
Experiment
Taylor 1909
Dirac, 1920s
Glauber, 1960s
Glauber, 1960s
Glauber, 1960s
Glauber, 1960s
Hanbury-Brown
1956
Many: 1980s
And 1990s
Hong, Ou,
Mandel 1987
Many: 1980s
to present
Kimble, Mandel 1977
Slusher, 1985
Many: 2000s
Kuzmich, Mandel 2000
Many, 2005
Optical Quantum Information
Optical Quantum Information
Taylor’s experiment (1909)
film
slit
needle
diffraction pattern f(y)
Proceedings of the Cambridge
philosophical society. 15 114-115
(1909)
Taylor’s experiment (1909)
Interpretation:
Classical: f(y)  <E2(y)>
film
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)>
f(y) same as in classical.
Dirac: “Each photon interferes only with itself.
Interference between two different photons
never occurs.” (not entirely correct, but close).
slit
needle
diffraction pattern f(y)
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
Avalanche Photodiode Mechanism
Many valence electrons,
each with a slightly different
absorption frequency wi.
Broadband detection.
E
conduction
band
(empty)
valence
band
(filled)
possible
transitions
wi = DE/hbar
k
“Classic” Photomultiplier Tube
E
Many valence electrons,
each can be driven into the
continuum wi.
Broadband detection.
Photocathode Response
Broad wavelength range: 120 nm – 900 nm
Lower 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)
Proposal for squeezing (C. Caves, 1981)
C. Caves, “Quantum Mechanical Noise In an Interferometer” Phys. Rev. D 23 1693 1981
Proposal for squeezing (C. Caves, 1981)
C. Caves, “Quantum Mechanical Noise In an Interferometer” Phys. Rev. D 23 1693 1981
Proposal for squeezing (C. Caves, 1981)
C. Caves, “Quantum Mechanical Noise In an Interferometer” Phys. Rev. D 23 1693 1981
Proposal for squeezing (C. Caves, 1981)
EIN
ELO

(ELO+EIN)/√2
(ELO+EIN) ei /√2
(ELO-EIN)/√2
(ELO-EIN)/√2
2 E1 = ELO (1+ei) - EIN (1-ei)
2 E2 = ELO (1-ei ) - EIN (1+ei)
2 E1 = ELO (1+i) - EIN (1-i)
Like homodyne, with LO phase 90°
One quadrature of EIN contributes noise
Squeeze this and make better
interferometers.
2 E2 = ELO (1-i ) - EIN (1+i)
E1 (1+i) / √2 = (iELO - EIN )/ √2
E2 (i-1) / √2 = (iELO + EIN )/ √2
C. Caves, “Quantum Mechanical Noise In an Interferometer” Phys. Rev. D 23 1693 1981
First Squeezed Light Experiment
(Slusher, et. al. 1985)
SLUSHER RE, HOLLBERG LW, YURKE B, et al.
OBSERVATION OF SQUEEZED STATES GENERATED BY 4WAVE MIXING IN AN OPTICAL CAVITY
Phys. Rev. Lett. 55 (22): 2409-2412 1985
Second Squeezed Light Expt. (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
Theorist’s Spectrum Analyzer
band-pass
filter.
V In
V Out
Frequency 
Power meter
Sweep frequency → Power Spectrum |V()|2
Fixed frequency → Power in one freq. component |V()|2(t)
Quadrature Detection Electronics
environmental noise
P
measurement
frequency 
P
freq
Spectrum
analyzer
Slusher, et. al. 1985
time
Wu, et. al. 1987
Quadrature Detection of Squeezed Vacuum
LO
input is
squeezed
vacuum
q
in
D1
Di(t)
input is
vacuum
63% VRMS
(40% power)
D2
LO phase
X2
vacuum
Pn
X2
q
q
X1
X1
squeezed
vacuum
Correlation Functions
CT  C(t )T (t )  C T  0
C (t )T (t   )  [C (t )  C ][T (t   )  T ]
 C (t )T (t   )  C T
Correlation Functions
C(t )T (t   )
, years
Ppm °C
Stellar Interferometry
Robert Hanbury-Brown
Stellar Interferometry
Robert Hanbury-Brown
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) = <I1(t)I2(t)> / <I1(t)><I2(t)>
t
Hanbury-Brown and Twiss (1956)
Signal is:
g(2) = <I1I2 / <I1><I2>
= < (<I1>+I1) (<I2>+ I2) > / <I1><I2>
Note:
Correlation g(2)
<I1> + I1 ≥ 0<I2> + I2 ≥ 0
<I1> = <I2> = 0
g(2) = (<I1><I2>+<I1><I2>+<I2><I1>+<I1I2>)/<I1><I2>
I
= 1 + <I1I2>)/<I1><I2>
= 1 for uncorrelated <I1I2> = 0
> 1 for positive correlation <I1I2 > 0 e.g. I1I2
< 1 for anti-correlation <I1I2 < 0
Classical optics: viewing the same point, the
intensities must be positively correlated.
I0
Tube position
Detectors see same field
t
I Detectors see different fields
I1= I0/2
t
I2= I0/2
Hanbury-Brown and Twiss (1956)
The publication of these results led to much dispute in the scientific community (see for
example 119, p.120). In particular, two independent groups attempted to repeat the
experiment and concluded that Hanbury and Twiss had misinterpreted their data and that
if such a correlation existed, a major revision of fundamental concepts in quantum
mechanics would be required (Ádám, Jánossy & Varga, 1955; Brannen & Ferguson,
1956).
In their response (25) Hanbury and Twiss pointed out that although the experimental
procedure in both cases was beyond reproach, their critics had missed the essential point
that correlation could not be observed in a coincidence counter unless one had an
extremely intense source of light of narrow bandwidth. Hanbury and Twiss had used a
linear multiplier that was counting a million times more photons than the coincidence
system used in their critics' experiments. In fact, they calculated that Brannen and
Ferguson would need to count for 1,000 years before observing the effect and Ádám et al.
for 1011 years.
They also responded (27) to a criticism of their theoretical treatment by Fellgett (1957)
and subsequently, in order to settle all remaining arguments, the laboratory experiment
was repeated using the coincidence counting system of Brannen and Ferguson but with
an intense narrow-band isotope light source with which they observed the expected
correlation in a series of twenty-minute runs. With the isotope light source replaced by a
tungsten filament lamp, no correlation could be found (29).
Not just for photons!
Not just for photons!
g(1)
g(2)
Smithey, Beck, Raymer and Faridani 1993
Smithey, Beck, Raymer and Faridani 1993
Neergaard-Nielsen, Nielsen, Hettich, Molmer and Polzik
2006 (arxiv)
Neergaard-Nielsen, Nielsen, Hettich, Molmer and Polzik
2006
Neergaard-Nielsen, Nielsen, Hettich, Molmer and Polzik
2006
Kimble, Dagenais + Mandel 1977
PRL, v.39 p691
Correlation g(2)
I0
I1= I0/2
Classical:
correlated
I2= I0/2
Correlation g(2)
n0=1
t1 - t 2
n1=0 or 1 Quantum:
can be
n2= 1 - n1
anti-correlated
t1 - t 2
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)  -Ed  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
InAs QD
relax
fs pulse
emit
Pelton, et al. 2002
Goal: make the pure state
|> = a+|0> = |1>
Accomplished: make the mixed state
r  0.38 |1><1| + 0.62 |0><0|
Holt + Pipkin / Clauser + Freedman /
Aspect, Grangier + Roger 1973-1982
J=0
J=1
J=0
Total angular momentum is zero.
For counter-propagating photons
implies 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
22.5°
b
a'
b'
|SQM| ≤ 22 = 2.828...
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 converter”:Measures delay
from A detection to B detection.
PDP11: Very old (1979) computer from DEC.
FRIBERG S, HONG CK, MANDEL L
MEASUREMENT OF TIME DELAYS IN THE
PARAMETRIC PRODUCTION OF PHOTON
PAIRS
Phys. Rev. Lett. 54 (18): 2011-2013 1985
Physical Picture of Parametric Downconversion
phase matching
conduction
collinear
non-collinear
or
valence
k-vector conservation
ks + ki = kp
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) don’t even approximately conserve energy.
Thus must be very short-lived. Result: signal and idler produced at same time.
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 < 100 ps
FRIBERG S, HONG CK, MANDEL L
MEASUREMENT OF TIME DELAYS IN THE
PARAMETRIC PRODUCTION OF PHOTON
PAIRS
Phys. Rev. Lett. 54 (18): 2011-2013 1985
Cauchy Schwarz Inequality Violation
Cauchy Schwarz Inequality Violation
202Hg
9P
567.6 nm
7S
e- impact
435.8 nm
7P
Cauchy Schwarz Inequality Violation
First observation of optical frequency conversion
ruby laser
(694 nm)
quartz crystal
chi-2 medium
prism
film
Position-momentum entanglement
Howell, Bennink, Bentley and Boyd, Phys. Rev. Lett. 92 210403 (2004)
Position-momentum
entanglement
Howell, Bennink, Bentley and Boyd, Phys. Rev. Lett. 92 210403 (2004)
Two-photon diffraction
Two IR photons (pairs)
One IR photon
2,0
Pump
high,low
 0,2
high,low
D’Angelo, Chekhova and Shih, Phys. Rev. Lett. 87 013602 (2001)

Two-photon diffraction
Two paths to coincidence detection:
e
Two IR photons (pairs)
i 2k r r '
One IR photon
2,0
Pump
high,low
 0,2
high,low
D’Angelo, Chekhova and Shih, Phys. Rev. Lett. 87 013602 (2001)

Hong-Ou-Mandel effect
2,0
Hong, Ou and Mandel, Phys. Rev. Lett. 59 2044 (1987)
high,low
 0,2
high,low
Hong-Ou-Mandel effect
2,0
Hong, Ou and Mandel, Phys. Rev. Lett. 59 2044 (1987)

high,low
 0,2
high,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)
Correlation Function of Castelldefels
Correlation Function of Pedralbes
N
Z
P
R
Spectrum Analyzer
Log amp
Mixer
Out
In
Band-pass.
“Resolution
Bandwidth”
Local Oscillator
Peak
detector
Low-pass.
“Video
Bandwidth”