Quantum Optics Laboratory · 2013. 1. 4. · NV color centre in nano diamond with 5 ns exposure....

Chitraleema Chakraborty Material Science Program, University of Rochester

OPT 453

December 13, 2012

Quantum and Nano Optics Laboratory

Experiments involving the quantum theory of light:

Imaging of Single Photon Emitter Fluorescence and Photon Antibunching

Entanglement and Bell’s Inequalities

Single Photon Interference

Outline Lab 3-4 Lab 1 Lab 2 Reference Acknowledgement

Overview

Introduction Sources of photon that emits one photon at a time: Single Emitter

Antibunching: where all the photons are separated in time

In 1956, Hanbury Brown and Twiss observed the existence of correlation between the outputs of two photoelectric detectors illuminated by partially correlated light waves

For detectors placed at two different points with positions r1 and r2, the joint photo-detection probability at the two detectors, at two different times t and t + τ may be given by


Single Photon Emitter fluorescence and Photon Antibunching

In classical theory of light

In quantum theory of light,

The correlation function can become greater than or equal to one in classical light field (eg thermal or coherent light) and can be lower than one in quantum light field



Antibunching was first observed in two level atoms by Kimble and Mandel.

Experiment :

Single emitters like quantum dots, CNT and Nano-diamond was used

Schematics of our experimental setup



Experiment :



Confocal Microscope



Experiment :



Confocal Microscope

Hanbury Brown and Twiss Setup



Single Photon Emitter fluorescence and Photon Antibunching Result and Analysis : Measurement of Fluorescence Lifetime, τ of the quantum dots

Fluorescence lifetime found by fitting the ln(photon counts) in τ = - (1/slope), in the triple exponential graph on right

0

1000

2000

3000

4000

5000

6000

7000

0 2 4 6 8 10

phot

on co

unts

Time (ns)

7.8

7.9

8

8.1

8.2

8.3

8.4

8.5

8.6

8.7

1.5 3.5 5.5 7.5 9.5

y= -0.1006x + 8.8265, τ = 9.94 ns y=-0.0611x + 8.6523, τ = 16.37 ns y= -0.1873x + 9.8816, τ = 5.34 ns




Single Photon Emitter fluorescence and Photon Antibunching Result and Analysis : Characterization of our samples by measuring their spectrum.

Calibration of the diode pumped solid state laser beam at around 532 nm approx.



Sample 1. SWCNT Characteristic spectrum of single walled CNT with 5 ns exposure



Sample 2. Nano diamond Characteristic spectrum of NV color centre in nano diamond with 5 ns exposure


Sample 3. Gold nanoparticles Characteristic spectrum of gold nanoparticles with 5 ns exposure




Single Photon Emitter fluorescence and Photon Antibunching Result and Analysis : Confocal Microscopy Imaging of Single Emitter Fluorescence


Single Photon Emitter fluorescence and Photon Antibunching Result and Analysis : Confocal Microscopy Imaging of Single Emitter Fluorescence

Confocal microscope fluorescence image from single colour centres in nanodiamond (left) and 10nM of800nm wavelength CdSe quantum dot (right).


Single Photon Emitter fluorescence and Photon Antibunching Result and Analysis : Imaging the emitters by EMCCD camera

Result and Analysis : Photon antibunching measurements:

The zero point delay. The signals that should have arrived at the same time all show up in the same histogram bin at around 62.5 ns.




Left: The streaky nature of the scan is indicative of a blinking quantum dot, because different line scans see different fluorescence intensities. Green pointer is the region of sample which was tested for antibunching. Right: Time trace to show that Q dot blinking




Several histograms were constructed via the Time Harp program for antibunching obtained from different quantum dots. Dip is observed at delay point 62.5 ns.





Conclusion:

Obtained quantum dot fluorescence image using confocal microscope

Characterized sample by calculating fluorescence lifetime and its spectrum

Observed antibunching from quantum dots

Thus proved that quantum emitters like quantum dots can emit single photons

Introduction Test violation of Bell's inequalities by using photons whose polarization states are entangled . Entangled photons produced by Spontaneous Parametric Down Conversion (SPDC)

Entanglement: Two entangled particles share a single wave function that is not separable into distinct wave functions for each particle

Bell’s inequalities are simple classical identities predicting the maximum value of a sum of probabilities


Entanglement and Bell’s inequalities

Background EPR paradox: Quantum Mechanics (QM) was incomplete because there existed so called "Hidden Variables" which must explain at least some of the uncertainty inherent in QM

Bell's Theorem is based on EPR

‘Inequality of Bell’s type have got nothing to do with quantum theory’ [3]. They are based on trivial mathematical relation: |a+b+c| ≦ |a|+|b|+|c|

We use the Clauser-Horne-Shimony-Holt (CHSH) version of Bell’s inequality in this experiment . The entangled form of the SPDC state is



Where V and H refer to rotated vertical and horizontal polarization and s and i are the historical way to label

photons produced by spontaneous parametric down-conversion.

Producing entangled photons: BBO is a negative uniaxial nonlinear crystal

For type 1 crystal cut, horizontally polarized photon comes out as 2 vertically polarized photon and vice versa with double wavelength

A 45 degree polarized photon can be considered half vertical and half horizontal producing entangled photon



Experimental scheme Argon laser with λ=363.8nm

The beam is passed through a blue filter and quartz plate, redirected by a mirror and sent through our BBO crystals.

The down-converted photons are then sent to the two detectors. The detectors for the lab are Avalanche Photodiodes (APD), which are capable of counting single-photons.

Rotating polarizer are placed in front of the APDs and beam stop between them to block unnecessary beam.



Theory Measuring the polarization of these photons

PVV (α, β) = ½ cos2(α - β) (5) PHH (α, β) = ½ cos2(α - β) PVH (α, β) = ½ sin2(α - β) PHV (α, β) = ½ sin2(α - β)

The correlation function, E(α, β) = PVV + PHH – PVH - PHV

= cos 2 (α - β) With this quantity, define S,

CHSH states that

But For certain polarizer angle, the inequality is violated



Procedure : Producing polarization-entangled photon pairs by SPDC

Imaging the down-converted light cone by EM-CCD camera Camera gain 255 and exposure time 0.5 sec

Aligning the quartz plate



Coincidence counts while varying the horizontal (left) and vertical (right) angle of wave plate

Test of Entanglement : The angle of polarizer A, α is kept fixed twice and the angle of B, β is varied from 0º to 360º and vice versa.

The cosine squared dependence of the coincidence counts with the angle of polarizer.

This shows that the photons are polarization entangled.



Polarizer B

Determination of fringe visibility, V:

The fringe visibility for polarizer angle 90 as obtained , V= 0.81 which is >0.71 This can be used to see if Bell’s inequality is violated



Polarizer B

Nmax and Nmin are the maximum and minimum count for a particular cosine graph.

Violation of Bell’s Inequality: To show |S|> 2

Set of angles for which S is calculated:

Data showing violation of Bell’s inequalities for standard set of polarizer A and B angles with laser power = 60mW, Current= 56A, Acquisition Time = 1 second. Correlation function is calculated from the net coincidence count obtained by subtracting accidental coincidence



E(α,β) 0.761

S = 2.4

> 2

E(α’,β’) 0.672

E(α’,β) 0.472

E(α,β’) -0.503

Violation of Bell’s Inequality:



Violation of Bells inequalities were not observed from random set of polarization angles. Laser power = 60mW, Current= 56A, Acquisition Time = 1 second

Polarizer A Polarizer B Singles A Singles B Accidental

coincidence

Average

Coincidence

Net

Coincidence 35 15 3650 2979 0.282707 29.33333333 29.05063 35 100 3902 3269 0.331647 14 13.66835 35 -15 3888 2869 0.290021 17.33333333 17.04331 35 30 3942 3079 0.315573 39.33333333 39.01776

180 30 3666 3145 0.299769 21.66666667 21.3669 180 60 3645 3256 0.308571 16 15.69143

0 60 3743 3319 0.322998 10.33333333 10.01033 0 0 3794 3301 0.325624 32 31.67438 0 90 3797 3516 0.347107 5.333333333 4.986227

70 90 4155 3660 0.39539 50.33333333 49.93794 70 270 4139 3612 0.388702 44 43.6113 50 100 4091 3366 0.358028 28.33333333 27.97531 50 5 4051 3219 0.339044 23.66666667 23.32762

135 5 3084 2669 0.214011 13 12.78599 135 0 3020 2762 0.216872 15 14.78313 135 -10 3092 2629 0.211351 23 22.78865

E(α,β) 0.535

S = 0.93

< 2

E(α’,β’) -0.072

E(α’,β) 0.040

E(α,β’) -0.362

Violation of Bell’s Inequality:



Violation of Bells inequalities was also observed for different setting of quartz wave plate

Data showing violation of Bell’s inequalities for Horizontal angle = 5º and Vertical angle = 34º of wave plate with laser power = 100mW, Current= 57A, Acquisition Time = 1 second.

Visibility Data:

E(α,β) 0.77552

S = 2.15

> 2

E(α’,β’) 0.362012

E(α’,β) 0.306288

E(α,β’) -0.70521

Polarizer A Polarizer B Coincidence Count Visibility (V)

0 0 53.000 0.66 for (0,0) and (0.90)

V < 0.71 0 90 10.667

45 45 20.333 0.94 for (45,45) and (45,135)

V >0.71 45 135 0.667

Conclusion:



Violation of Bells inequalities was observed for the 16 standard values of polarizer angle

With random polarizer angles, we did not violate Bell’s inequalities

Bell’s Inequalities were also violate with slightly different changes of wave plate horizontal angle. However it was not violated when both the vertical and horizontal angles were changed.

Introduction

Exploring wave-particle duality of single photon Idea of duality originated in a debate when competing theories of light were proposed by



Isaac Newton Christian Huygens

Light

WAVES OR PARTICLES

Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa)

http://en.wikipedia.org/wiki/File:Christiaan_Huygens.jpg

http://en.wikipedia.org/wiki/File:GodfreyKneller-IsaacNewton-1689.jpg

Introduction In 1803, Thomas Young showed that light is composed of waves, by means of a double-slit experiment

While in about 1905, Einstein explained photoelectric effect with the concept of energy quanta hypothesized by Planck which proved the presence of light quanta

In 1924 De Broglie hypothesized the wave-particle duality of light

Feynman put forward his view that when an object behaves like a wave, it should produce interference fringes in a Young's double slit experiment and when it behaves like a particle, it will produce no fringe in the same experiment



Experiment We used 5 mW He-Ne laser of 633 nm wavelength

The laser was collimated and a non-polarizing beam splitter divided the laser to 2 setups

Young’s Double Slit Interferometer



Experiment We used 5 mW He-Ne laser of 633 nm wavelength

The laser was collimated and a non-polarizing beam splitter divided the laser to 2 setups

Mach Zehnder Interferometer



Young’s Double Slit Interference : Laser not attenuated Alignment of spatial filter and laser beam to obtain sharpest intensity patterns

Interference pattern obtained in a Young's double-slit experiment performed with laser light not attenuated to single photon level, i.e., attenuation of only 3 orders of magnitude.



Young’s Double Slit Interference : Laser attenuated Attenuation to single photon level required filter with 10-7 transmittance N(photons/m) = N(photons/s)/c = Pλ/hc2 P = power of laser, λ= wavelength, h = Planck’s constant, c= speed of light Bright spots which suggests the particle theory of light (left) and interference fringes which suggest the wave theory of light (right)



Acquisition time 0.1s and 255 camera gain Acquisition time 1s and 255 camera gain

Young’s Double Slit Interference : Laser attenuated Attenuation to single photon level required filter with 10-7 transmittance of 1.26 microwatt laser Acquisition time is 0.1s, gain 255 Adjacent graphs to image show visibility data. Visibility increases as accumulation is increased



Accumulation is 20, Visibility around 15% Accumulation is 100, Visibility around 40%

Mach Zehnder Interferometer: Laser not attenuated Alignment of setup to overlap two beam spots into one and observe proper interference pattern

Initial power of laser beam was 6 microwatt. Acquisition time was 0.1s, polarizer angle at 45º , gain is 0 for first two image and 255 for the final. Fringes became faint as attenuation order was increased.



Attenuation order: 3 5 7

Mach Zehnder Interferometer: Laser attenuated Alignment of setup to overlap two beam spots into one and observe proper interference pattern

Initial power of laser beam was 6 microwatt. 7 orders of attenuation, Acquisition time was 0.005s, Intensity spots seen with gain is 255. Fringes obtained with increasing accumulation



Intensity spots Accumulations: 20 50

Mach Zehnder Interferometer: Laser attenuated



Images of interference pattern obtained by Mach-Zehnder interferometer using an attenuation of 6 orders of magnitude of 6µW laser, exposure 0.1 s and camera gain 255 with inverted image brightness. The images were taken for different polarizer angles.”Which way” information was present in angles like 0º, 80º where interference pattern was lost

Mach Zehnder Interferometer: Fringe Visibility



Where Nmax and Nmin are the maximum and minimum of the gray value

Left Image: Cross section of the interference pattern obtained from Mach Zehnder interferometer at polarizer angle 40º. Visibility of fringes is 67%. Right Image: Cross section obtained from 0º polarizer angle showing no definite fringe pattern.

Conclusion :



Demonstrated the wave-particle duality of light by using young’s double slit interferometer.

Even with such a low photon rate, however, fringe patterns are still observed, built up by the camera in discrete photon detections over an extended exposure time.

Thus interference at high light level is sum of single photon interference pattern

Thus photons are interfering with themselves despite their large average spacing.

By polarizing the light in each arm of the Mach-Zehnder interferometer, it was possible to determine which path light came from, but this also made interference impossible.

Only by using an additional polarizer to erase the “which path" information were we able to again observe interference which leaves us with the concept of quantum eraser.

Reference :


Quantum and Nano Optics Lab:

[1] M. Fox, Quantum Optics: An Introduction, Oxford University Press, 2006. [2] A. Einstein, B. Podolsky and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?,” Physical Review 47, 777-780 (1935). [3] J. Eberly, “Bell inequalities and quantum mechanics”, Amer. J. Phys., 70 (3), 286, March (2002). [4] S. Lukishova, ‘Opt 253 Lab 1 Entanglement Manual [5] H. J. Kimble, M. Dagenais, and L. Mandel, “Photon Antibunching in Resonance Fluorescence,” Phys. Rev. Lett., vol. 39, no. 11, pp. 691–695, Sep. 1977. [6] R. Hanbury. Brown and R. Q. Twiss, "Correlation between Photons in two Coherent Beams of Light," Nature (London), 177, 27 (1956). [7] Feynman, Leighton, Sands, “Feynman’s Lectures in Physics,” Addison-Wesley, vol. 3, 1965. [8] M. B. Schneider and I. A. LaPuma, “A simple experiment for discussion of quantum interference and which-way measurement,” American Journal of Physics, vol. 70, no. 3, p. 266, 2002. [9] Figures taken from online sources

Acknowledgement :



I would like to thank Dr. S. Lukishova for designing such an interesting course on Quantum and Nano Optics and also my

labmates for making the experience so enjoyable

Thank you



Quantum Optics Laboratory · 2013. 1. 4. · NV color centre in nano diamond with 5 ns exposure....

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