Photon Counting20090002 Taekoo Oh

06/17/2014

06/17/2014

CONTENTS

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDO-THERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

2/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

HISTORY OF LIGHT

http://commons.wikimedia.org/wiki/File:Nihal.newton_father_of_gravity.jpg

http://en.wikipedia.org/wiki/Thomas_Young_(scientist)

ISAAC NEWTON:PARTICLE

THOMAS YOUNG:WAVE

ALBERT EINSTEIN:QUANTA

http://www.brainpickings.org/index.php/tag/albert-einstein/

THE WAVE-PARTICLE DUALITY OF LIGHT!

3/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

LIGHT AS A PARTICLE

-

PHOTOELECTRICEFFECT

-𝜆

𝜆′

COMPTONSCATTERING

4/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

PHOTON STATISTICS

SUPER-POISSONIAN(BUNCHED)

POISSONIAN(COHERENT)

SUB-POISSONIAN(ANTI-BUNCHED)

Δ𝑛 = 𝑛

Δ𝑛 < 𝑛

Δ𝑛 > 𝑛

5/18

Mark Fox, in Quantum Optics: An introduction, Chapter 6.

𝑔 2 0 > 1

𝑔 2 0 = 1

𝑔 2 0 < 1

Fluctuation of the number of photon in very short time

interval?

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

OPTICAL DEVICES

He-Ne Laser

“Light Amplified by Stimulated Emission of Radiation”

𝜆 = 632.8 𝑛𝑚

He

Ne

Excitation by Electric Discharge

Collision

Collision to wall

Spontaneous Emission

6/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

OPTICAL DEVICES

Single Photon Counting Module (SPCM)

http://en.wikipedia.org/wiki/Avalanche_photodiode#mediaviewer/File:Avalanche_photodiode.JPG

At 22𝑜𝐶,

Avalanche Photodiode

Dark Count(c/s) 1500

Dead time(ns) 20(T) / 40(M)

Single PhotonTiming Resol.(ps)

350 at 825nm

OperatingTemperature

5 to 70𝑜𝐶

7/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

COHERENT LIGHT

𝑝 𝑛 = 𝑛𝑒− 𝑛

𝑛!

In the State of temporally and spatially stationary interference!

If we consider the statistics of themonochromatic coherent light,

Poisson Distribution

POISSONIAN LIGHT!

8/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

THERMAL LIGHT

𝑝 𝑛 = 𝑛𝑛

( 𝑛 + 1)𝑛+1

At a certain temperature T, an object radiatesthermal light!

Bose-Einstein Distribution

If we consider the statistics of themonochromatic thermal light,

𝜌 𝜔, 𝑇 =2ℎ𝜔3

𝑐21

𝑒 ℎ𝜔𝑘𝑇 − 1

SUPER-POISSONIAN LIGHT!

(∆𝒏)𝟐= 𝒏 + 𝒏𝟐

𝑵𝒎

9/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

PSEUDO-THERMAL LIGHTRotating Ground Disk

Monochromatic Coherent Light

Randomly DistributedPhoton

Monochromatic Pseudo-thermal Light

Partially Bunched,But in long period,

Randomly DistributedPhoton

That is, the light behaves as thermal light in coherence time!

glass

𝝉~𝟏𝟎−𝟓 𝒕𝒐 𝟏 𝒔𝒆𝒄, 𝝉 ⋉𝟏

𝒗

10/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

EXPERIMENTAL SETUP

He-NeLaser

For Coherent Light

For Pseudo-Thermal Light

Rotating Ground Disk

Polarizers

Single Photon

Counting Module

NI ELVIS

11/18

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

RESULTS

Photon Number Distribution in coherent light at 0.1ms cutoff time

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40

Pro

bability

Photon Number

Experimental Value

Theoretical Value

12/18

Average : 3.53

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

RESULTS

0

0.02

0.04

0.06

0.08

0.1

0.12

0 10 20 30 40 50 60

Pro

bability

Photon Number

Experimental Value

Theoretical Value

Photon Number Distribution in pseudo-thermal light at 0.1ms cutoff time

13/18

Average : 8.91

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

RESULTS

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50 60

Pro

bability

Photon Number

0.1ms_Theory

0.2ms_Theory

0.3ms_Theory

0.4ms_Theory

0.1ms_Experiment

0.2ms_Experiment

0.3ms_Experiment

0.4ms_Experiment

Average : 26.22

Photon Number Distribution in pseudo-thermal light at 0.1ms cutoff time

14/18

Average : 3.53

Average : 16.67

Average : 40.10

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

RESULTS

Photon Number Distribution in pseudo-thermal light from 0.01ms to 0.05ms cutoff time

15/18

0

0.02

0.04

0.06

0.08

0.1

0.12

0 5 10 15 20 25 30 35 40

Pro

bability

Photon Number

0.01ms Cutoff Time

0.02ms Cutoff Time

0.03ms Cutoff Time

0.04ms Cutoff Time

0.05ms Cutoff Time

Average : 8.91

Average : 13.84

Average : 18.14

Average : 24.02

Average : 28.05

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

06/17/2014

RESULTS

Photon Number Distribution in pseudo-thermal light with shorter coherence timefrom 0.01ms to 0.05ms cutoff time

16/18

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25 30 35 40

Pro

bability

Photon Number

0.01ms_Experiment

0.01ms_Theory

0.02ms_Experiment

0.02ms_Theory

0.03ms_Experiment

0.03ms_Theory

0.04ms_Experiment

0.04ms_Theory

0.05ms_Experiment

0.05ms_Theory

Average : 7.19

Average : 13.33

Average : 22.02

Average : 26.27

Average : 30.69

LIGHT AS A PARTICLE

OPTICAL DEVICES

COHERENT vs. PSEUDOTHERMAL

EXPERIMENTAL SETUP

RESULTS AND DISCUSSIONS

• The fluctuation of the photon number in the short time period is due to the quantum properties of the light.

• The statistics of the photon number of coherent light is Poisson distribution, without the relevance of the cutoff time.(Poissonian light)

• The statistics of the photon number of thermal light is Bose-Einstein distribution.(Super-Poissonian light)

• Pseudo-thermal light behaves as thermal light only in the case of the cutoff time within the coherence time.

06/17/2014

RECAPITULATION

17/18

06/17/2014

REFERENCE- Mark Fox, in Quantum Optics: An introduction (Oxford

University Press, 2006), Chap. 5.- Rodney Loudon, in The Quantum Theory of Light

(Oxford University Press, 2000), Chap. 5.- Li Yuan et al., CHIN. PHYS. LETT., 26, 7 (2009).- G. J. Troup, J. Lyons, PHYS. LETT. A, 29, 11 (1969).- M. Rousseau, J. Opt. Soc. Am., 61, 10 (1971).- T. Gonsiorowski, J. C. Dainty, J. Opt. Soc. Am., 73, 2

(1983).- Jed Rembold, in Statistical Mechanics (New Mexico

Tech, 2011). - W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).- F. T. Arecchi, PHYS. REV. LETT., 15, 912 (1965).

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THANK YOU!

06/17/2014