Download Quantum Optics and Quantum Engineering for Undergraduates

TEACHING EXPERIMENTS ON
PHOTON QUANTUM MECHANICS
Svetlana Lukishova, Carlos Stroud, Jr, Luke Bissell, Wayne Knox
The Institute of Optics, University of Rochester, Rochester NY
OSA Annual Meeting Special Symposium “Quantum Optics and Quantum
Engineering for Undergraduates , 23 October 2008, Rochester NY
Generation and detection of single and entangled photons using modern
photon counting instrumentation
Photon counting applications
bioluminescence
single molecule
detection
detector
calibration
primary
radiometric
scales
quantum
standards
quantum
cryptography
hyper-spectral
imaging
medical imaging
Metrology
lighting
single photon
sources
photon
count
Electronics
quantum
computing
Quantum
Information
Processing
Biotechnology
displays
quantum
imaging
Medical
Physics
medical / non
interactive
imaging
entertainment
neutrino/
cherenkov/ dark
matter detection
Space
Applications
radioactivity
Military
Meteorology
nuclear
night vision
IR detectors
robust imaging
devices
remote sensing
lidar
environmental monitoring
security
chemical – bio agent detection
Areas of applications of photon counting instrumentation [prepared by organizers of
second international workshop “Single Photon: Sources, Detectors, Applications and
Measurements Methods” (Teddington, UK, 24-26 October 2005)].
Students Anand C. Jha, Laura Elgin, Sean White
contributed to the development of these experiments
and to the alignment of setups
In this talk the results of the following students (Fall 2008) are used:
Kristin Beck, Jacob Mainzer, Mayukh Lahiri, Roger Smith, Carlin
Gettliffe
Teaching course “Quantum Optics and Quantum Information
Laboratory” consists of four experiments:
Lab. 1: Entanglement and Bell inequalities;
Lab. 2: Single-photon interference: Young’s double slit
experiment and Mach-Zehnder interferometer;
Lab. 3: Confocal microscope imaging of single-emitter
fluorescence;
Lab. 4: Hanbury Brown and Twiss setup. Fluorescence
antibunching and fluorescence lifetime
measurement.
Lab 1 is also part of the Advanced Physics Laboratory
course of the Department of Physics and Astronomy
Lab. 1. Entanglement and Bell inequalities
In quantum mechanics, particles are called entangled if their state
cannot be factored into single-particle states.
Entangled
A
B
A
B
Any measurements performed on first particle would change the state
of second particle, no matter how far apart they may be.
This is the standard Copenhagen interpretation of quantum
measurements which suggests nonlocality of the measuring process .
The idea of entanglement was introduced into physics by Einstein-Podolsky-Rosen
GEDANKENEXPERIMENT (Phys. Rev., 47, 777 (1935)).
In the mid-sixties it was realized that the nonlocality of nature was a
testable hypothesis (J. Bell (Physics, 1, 195 (1964)), and subsequent
experiments confirmed the quantum predictions.
1966: Bell Inequalities – John Bell proposed a mathematical theorem
containing certain inequalities. An experimental violation of his
inequalities would suggest the quantum theory is correct.
Lab. 1. Entanglement and Bell inequalities
Creation of Polarization Entangled Photons:
Spontaneous Parametric Down Conversion
Type I BBO crystals
  VsVi
 ei H s Hi
Downconverted light cone with λ = 2 λinc from 2mm thick
type I BBO crystal
Lab. 1. Entanglement and Bell inequalities
  VsVi
 ei H s Hi
Initial experiment of P.G. Kwiat, E. Waks, A.G.
White, I. Appelbaum, P.H. Eberhand, ”Ultrabright
source of polarization-entangled photons”, Phys.
Rev. A. 60, R773 (1999).
1.
2.
D. Dehlinger and M.W.Mitchell, “Entangled Photon Apparatus for the Undergraduate
Laboratory,” Am. J. Phys, 70, 898 (2002).
D. Dehlinger and M.W.Mitchell, “ Entangled Photons, Nonlocality, and Bell
Inequalities in the Undergraduate Laboratory”, Am. J. Phys, 70, 903 (2002).
Experimental Setup
Laser
Quartz Plate
Mirror
BBO Crystals
Experimental Setup
Filters and Lenses
Beam Stop
Polarizers
Dependence of Coincidence Counts on Polarization Angle
The probability P of coincidence detection for the
case of 45o incident polarization and phase
compensated by a quartz plate, depends only on the
relative angle β-α:
P(α, β) ~ cos2 (β-α).
  VsVi
 ei H s Hi
a0
a90
Coincidence Counts
(for 10 seconds)
3000
2500
2000
1500
1000
500
0
0
50
100
150
200
250
b ( in degrees)
300
350
400
Dependence of Coincidence Counts on Polarization Angle
Calculation of Bell’s Inequality
We used Bell’s inequality in the form of Clauser, Horne,
Shimony and Holt, Phys. Rev. Lett., 23, 880 (1969)
Bell’s inequalities define the sum S. A violation of Bell’s
inequalities means that |S|>2.
, where:
The above calculation of S requires a total of sixteen coincidence
measurements (N), at polarization angles α and β:
α
β
α
β
α
β
α
β
-45
-45
-45
-45
-22.5
22.5
67.5
112.5
0
0
0
0
-22.5
22.5
67.5
112.5
45
45
45
45
-22.5
22.5
67.5
112.5
90
90
90
90
-22.5
22.5
67.5
112.5
Entanglement and Bell’s inequalities
QUEST = QUantum
Entanglement in Space
ExperimenTs (ESA)
A. Zeilinger. Oct. 20, 2008. “Photonic Entanglement and Quantum
Information” Plenary Talk at OSA FiO/DLS XXIV 2008, Rochester, NY.
Lab. 2. Single-photon interference
Concepts addressed:
• Interference by single photons
• “Which-path” measurements
• Wave-particle duality
M.B. Schneider and I.A. LaPuma, Am. J. Phys., 70, 266 (2002).
Lab. 2. Single-photon interference
Mach-Zehnder interferometer
NPBS Polarizer D
mirror
|V>
Polarizer C
screen
Path 2
Polarizer A
Path 1
laser
Spatial filter
|H>
PBS
mirror
Polarizer B
Polarizer D, absent
Polarizer D at 45
No Fringes
Fringes
Photograph of Mach-Zehnder Interferometer Setup
Single-photon Interference Fringes
Polarizer D at 45 deg
Polarizer D absent
Counts for 10 Seconds
600000
500000
400000
300000
200000
100000
0
10
11
12
13
Position of Detector (mm)
14
15
Young’s Double Slit Experiment
with Electron Multiplying CCD iXon
Camera of Andor Technologies
0.5 s
1s
2s
3s
4s
5s
10 s
20 s
Labs 3-4: Single-photon Source
Lab. 3. Confocal fluorescence
microscopy of single-emitter
532 nm/1064 nm,
8 ps, ~100 MHz
laser
Sample with
single emitters
Objective
Interference
filter
Fiber
To Hanbury Brown –
Dichroic
Twiss setup
mirror Fluorescence
PZT stage
light
Lab. 4. Hanbury Brown and Twiss
setup. Fluorescence antibunching
Start
Single photon
counting avalanche
photodiode modules
Fluorescent
light
Nonpolarizing
beamsplitter
Stop
PC data
acquisition card
Single-photon Source (Labs 3-4)
•
Efficiently
produces
photons
antibunching characteristics;
•
Key hardware element
communication technology
pho
Single
in
quantum
ton
Bob
Alice
Eva
with
To produce single photons, a laser beam is tightly
focused into a sample area containing a very low
concentration of emitters, so that only one
emitter becomes excited. It emits only one
photon at a time.
To enhance single photon efficiency a cavity should be used
Confocal fluorescence microscope
and Hanbury Brown and Twiss setup
76 MHz repetition rate, ~6 ps pulsed-laser excitation at 532 nm
We are using cholesteric liquid crystal
1-D photonic bandgap microcavity
o= navPo,  = on/nav ,
Planar-aligned
cholesteric
Po
Transmitted
LH light
Reflected
RH light
Incident unpolarized light
where pitch Po = 2a
(a is a period of the structure);
nav= (ne + no)/2; n = ne - no .
Selective reflection curves of 1-D photonic bandgap
planar-aligned dye-doped cholesteric layers
(mixtures of E7 and CB15)
Blinking of single colloidal quantum dots
in photonic bandgap liquid crystal host (video)
Confocal microscope raster
scan images of single colloidal
quantum dot fluorescence in a
1-D photonic bandgap liquid
crystal host
Histogram
showing
fluorescence
antibunching (dip in the histogram)
Antibunching is a proof of a singlephoton nature of a light source.
Values of a second order correlation function g(2)(0)
1.2
1
g2(t)
0.8
g(2)(0) = 0.18 ± 0.03
0.6
0.4
0.2
0
-60
-40
-20
0
20
40
60
80
interphoton times (ns)
1.4
1.2
g2(t)
1
g(2)(0) = 0.11 ±0.06
0.8
0.6
0.4
0.2
0
-200
-160
-120
-80
-40
interphoton times (ns)
0
40
80
Future plans for new teaching experiments
•
Using a new UV argon ion laser we are planning to make
some new experiments on entangled photon generation in a
spontaneous parametric down conversion process
•
Development of the experiments on spectroscopy and
fluorescence lifetime measurements of colloidal quantum dots
in microcavities for single-photon source applications.
•
Development of a simple single-photon source setup
Acknowledgements
By courtesy of S. Trpkovski (QCV)
The authors
acknowledge the support by the National Science
Foundation Awards DUE-0633621, ECS-0420888, the University of
Rochester Kauffman Foundation Initiative, and the Spectra-Physics
division of Newport Corporation. The authors thank L. Novotny, A.
Lieb, J. Howell, T. Brown, R. Boyd, P. Adamson for advice and help,
and students A. Jha, L. Elgin and S. White for assistance.