LAB 3-4, PHY434. Single Photon Source: Confocal Microscope Imaging of Single-Emitter Fluorescence and Hanbury Brown

and Twiss setup for Photon Antibunching Measurements

Joshua S. Geller

Department of Physics and Astronomy, University of Rochester, Rochester NY, 14627

ABSTRACT We present results indicating antibunching of two CdSe quantum dot single photon sources that fluoresce at 800nm and 705nm. We obtained antibunching histograms in TimeHarp using the Hanbury Brown and Twiss setup for photon antibunching. To do this, we prepared QD samples with concentrations of 10 nanoMol, 1 nanoMol, and 100 picoMol and placed the QD samples in a cholesteric liquid crystal host, which we exposed to 632.8nm HeNe laser light in a raster scanning confocal microscope setup. Observations of the quantum dot fluorescence were made with Avalanche Photo-Diodes through LabVIEW, and an EM-CDD camera through Andor-Solis. Keywords: single photon source, single emitter, Hanbury Brown and Twiss, antibunching, cholesteric liquid crystal, photonic bandgap material, fluorescence lifetime 1 INTRODUCTION AND BACKGROUND 1.1 Single Photon Sources Quantum information, communication, and security are growing fields of research whose practical implementation in computation, communication, banking, and security require the use of single photon sources to provide provably secure keys [1]. Single-emitters are a completely quantum prediction, as they are equivalent to a zero-valued second order correlation function at t=0,

!

g(2)(0) = 0 . This is not possible for

a classical light source like a laser. Hence, even a greatly attenuated laser beam is not a source of antibunched light. There are currently several options to create room temperature single photon sources. These include single molecules, di-molecules, semiconducting colloidal quantum dots (e.g. in nanocrystals), and color centers in nanodiamonds. In this lab, we used colloidal quantum dots. To achieve a single photon source, we can distribute a certain concentration of QD solution with a host bandgap material such as cholesteric liquid crystals. By focusing a laser beam on the sample, if single-emitter are isolated in the CLC-host, we can achieve single excitations of the electrons in an emitter and the relaxation of that CdSe emitter will give off fluorescent single-photon light. A schematic of this process is shown in Figure 1.

Fig. 1 CdSe QD energy level diagram of excitation and fluorescent emission

Bulk Dot

Conduction band

Valence band

Bulk Dot

Conduction band

Valence band

2 1.2 Photon Antibunching Figure 2 shows a schematic of the Hanbury Brown and Twiss photon antibunching setup; they were the first researchers to observe correlations between pairs of photons in 1956 [2]. The first experiment that demonstrated the existence of photon antibunching was conducted by Kimble, Dagenais, and Mandel in 1977 [3]. This was evidence of the quantization of the electromagnetic field. In contrast, the classical EM field is simply one that behaves according to Maxwell’s equations. For classical fields, the correlations between the intensities of the transmitted IT and reflected IR beams at a beam splitter are given by the degree of second-

order (temporal) coherence, or

!

g(2)

T ,R (" ) =IT (t + " )IR (t)

IT (t + ") IR (t), which is a function of the delay time τ

between the intensity measurements. We have a stationary light source so we can interpret the averages as ensemble averages and not time averages. Thus, for our 50/50 beam splitter we can assume the form:

!

g(2)

T ,R (0) = g(2)

I ,I (0) =II (0)

2

II (0)2

= g(2)(0).

for our the second order coherence at zero time delay. But the Cauchy-Swartz inequality allows one to show that the above implies:

!

g(2)(0) "1, classically. The quantum mechanical equivalent form of the preceding

shows that for a single-emission of a photon, we should have

!

g(2)(0) = 0 , but anything that violates the

classical inequality above is considered a quantum effect known as antibunching. The antibunching derivation follows:

!

g(2)

T ,R (0) =ˆ n T ˆ n R

ˆ n T ˆ n R=

a*

T a*

R aT aR

a*

T aT a*

R aR

=ˆ n I ( ˆ n I "1)

ˆ n I2

= g(2)

I ,I (0) = g(2)(0)

which, for a single incident photon, nI =1# g(2)(0) = 0

where the above comes from assuming the EM field is quantized and the rewriting the creation and annihilation operators so that the number operator of the incident field determines the second order correlation. Thus, we see that for a single incident photon, we expect a minimum at

!

g(2)(" = 0) . The 1977

experiment from [6] achieved

!

g(2)(0) = 0.4 .

Fig. 2: Hanbury Brown and Twiss setup for photon antibunching 1.3 Cholesteric Liquid Crystal, used as a 1D Photonic Bandgap Material Cholesteric liquid crystals (CLCs) have rod-like molecules having a short chiral tail that, for circularly polarized light with counter-handedness to the rotation of the CLC, induces a globally periodic and helical structure in the CLC which makes the CLC behave like a 1D photonic bandgap material after it is given a unilinear planar-aligned shearing force. The pitch, P0, is the distance over which a 360° rotation in the CLC structure is made, which is displayed in Fig. 3A.

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Fig. 3A Schematic CLC periodic structure, and transmission/reflection within CLC wavelength bandgap Cholesteric liquid crystals are perfect reflectors under the Bragg condition within

!

"# = #0"n navg in a

wavelength band centered on

!

"0

= navgP0 , where navg is the average of the ordinary and extraordinary refractive indices of the CLC. Thus, if emitting wavelengths are within the CLC bandgap there is suppressed emission. But at the band-edge, emission is enhanced. This is analogous to a laser cavity, since at the bottom of the stop-band the periodic structure acts like completely reflecting mirrors. At the band-edge, however, it acts like partially transmitting mirrors. Figure 3B, taken from the lab manual, shows the plot of a CLC spectral transmittance with a bandgap; one also sees the fluorescence spectrum of CdSe quantum dot (579nm peak wavelength) in the CLC-host, which has a maximum at the bang-edge. 2 EXPERIMENTAL SETUP AND PROCEDURE 2.1 Experiment Setup Fig. 4 shows our experimental setup. Both a red 632.8nm Helium-Neon (HeNe) laser with 5 mW average power, and a diode-pumped solid-state 532nm laser with 6 ps pulse duration and 76 MHz pulse repetition rate at 40 mW average power were used. We took histographic data for demonstration of fluorescence antibunching from our CdSe quantum dots using the HeNe laser, and took data for the CdSe QDs fluorescence lifetimes using the pulse laser.

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Fig. 4: Experimental Setup

Our setup sent the laser light through a spatial filter that changed the elliptic beam cross-section into a round Gaussian cross-section, and broadened the beam diameter. The beam then passed through a series of removable neutral density filters used to control the incident intensity on the quantum dot sample in the objective of our confocal fluorescence microscope. We used a confocal microscope in order to selectively detect only emitted light from single molecule CdSe fluorescence originating at the focal point of the microscope. Confocal microscopes decrease side-lobe noise in detection signals so that weak signals may be detected among stronger signals. This microscope thus allowed us to scan a sample of quantum dots and focus on a single-emitter to obtain images in three dimensions with high resolution (using special LabVIEW software). This is achieved within the confocal microscope by using a focusing lens (can also use two lenses) and a pinhole, as shown in Fig. 5. In our setup, the single photon counting Avalanche Photo-Diode (APD) diameter is small enough, at 150µm, that we used the APD detector surface area as the pinhole. We used a special high numerical aperture oil-immersion objective to achieve high resolution and intensity on the sample. A dichroic mirror was implemented to reflect the laser light but transmit the fluorescent light. The output fluorescent light is finally passed through a filter to block the laser mode and sent to the APDs in the Hanbury Brown and Twiss setup component of our experiment.

Fig. 5: Confocal Microscope Imaging System and our experimental setup schematic We note that our setup also included a temperature controlled electron-multiplying (EM)-CCD camera to which we could direct the output fluorescent beam by changing the output channel on the confocal microscope. We used the EM-CCD to align the incident laser light, to take real time images of several single-emitters using wide-field microscopy by changing the focus position, and to take spectrographic measurements of the output light. For histogram data collection to show photon antibunching, we sent the output light to a 50/50 NP beam splitter, which directed half the light to either of two APDs (labeled APD1 and APD2): this our Hanbury Brown and Twiss setup for antibunching, as shown in Fig. 2. Upon detection of a photon incident through

5 one of the channels to an APD, a TTL pulse was generated and sent to a TimeHarp 200 time-correlated single photon counting PCI card in one of the three experiment computers. In our setup, the signal from APD1 was a “start” command to the time card, and the delayed signal from APD2 was the “stop” directive. Two APDs are used to avoid missed coincident counts on a single detector due to individual detector dead-time. A measure of the delay time between “start” and “stop” signals allows construction of a histogram indicating the time delay between two incident photons. The coincidence count, a count of the number of second photon pulses that arrives at the TimeHarp computer card at a fixed delay after a first photon pulse, gives a histogram indicating the spread of pairs of photons in time relative to the detection of the first photon. Antibunching is demonstrated when there is a dip toward zero coincident photons at a fixed delay time: that delay time should be the selected delay of the delay-control for the “stop” TTL pulse, i.e. it should be the fixed time for two photons that are coincident to the APDs in real time at 0 seconds delay. The computer components of our setup for imaging single-emitter fluorescence included a counter and timer card, and controller board. We ran LabVIEW software as well as a computer-operated nanodrive that controlled a piezo-translation stage that our sample sits on. This allowed for raster scanning the QD sample, enabling us to identify quantum dots and target them for antibunching measurement. 2.2 Experiment Procedure 2.2.1 QD Sample Preparation We used CdSe colloidal quantum dots in a cholesteric liquid crystal host (1D photonic bandgap material: CB15 + E7 liquid crystal), which were prepared with single-emitter concentrations of 10 nanomole, 1 nanomole, and 100 picomole. To prepare the sample, a capillary pipette drop of CdSe quantum dots is applied to a base of CLC-host solution on a Corning No.1 microscope cover glass slip. One must mix the solution well, for ~10min, being sure to keep the solution in a small spot on the center of the glass slip. Applying a light repeated unilinear shearing force on the cover slip aligns the chiral structure of CLC-host and makes it self-assemble to its 1D photonic bandgap structure. This process may be judged successful if the transparent color of the sample changes to a blue or red (depending on viewing angle) after shearing. Another preparation process we used yielded a single sample for taking data, and is as follows. We prepared 5 samples with single emitters by placing the samples on a thin piece of glass and created a thin film coating on the glass using a spin coating machine that spun at 3000 rpm for 40 seconds. The samples used were again CdSe. The first two samples fluoresced at 579 nm, and were from an old sample prepared in June 2006 of unknown concentration. The third and fourth samples fluoresced at 800 nm and were of 10 nanomole concentration. We took data only with sample number 4.

(a) (b)

Fig. 6 Images of CdSe quantum dots from EM-CCD, prepared by (a) shearing method in CLC-host on 11/23/2010 (b) spin-coat method on 11/9/2010 [5 micron square scan area, laser power is 65µW]

2.2.2 Setup & Alignment of Single Emitters

(1) Mount the QD/CLC-host sample to confocal microscope by, first, cleaning the sample holder with methanol before placing sample. Place a drop of oil on objective aperture, and then position glass slip so that center of objective is aligned with sample spot on glass slip. Use two small magnets to hold slip with sample in place.

6 (2) Turn confocal microscope output knob to EM-CCD port and focus the laser light on the sample. As shown in Fig. 6, when the CCD is well focused, one observes quantum dots emitting light. Some QDs blink, which gives us a method of identifying single-emitters in our sample; bunches of blinking QDs tend to average out and we do not see blinking. Thus, blinking helps locate individual QDs.

(3) To search for quantum dots in our sample we take a raster scan of the sample with the nanodrive. To do this we turn off the laser, attenuate the input and output beams with filters, in holders, turn on the APDs in a dark room (single photon APDs can be permanently damaged by too much light), and change the output port of the microscope to the Hanbury Brown and Twiss component of our setup. LabVIEW controls and records the raster scan of the sample. Fig. 7 shows the LabVIEW display. The top right image is APD1 output; the bottom right is APD2 output. The axes are measured in pixels (we used 100 or 200 pixels per scan line). The bottom left image counts photons in the point being scanned. Top left is panel display selects scan area, and controls the nanodrive. The scan area was set to 5µm x 5µm, as shown in Fig. 7.

Fig. 7 LabVIEW scan display

(a) (b) Fig. 8 Raster Scan using Confocal Fluorescence Microscopy of 1 nanoMol dilute Colloidal Quantum Dots in CB15-E7-CLC-host with pump power 150 µW. (a) 25µm x 25µm scan, showing out of focus quantum dots

(b) Photon count of “focus point” at upper-left corner in raster scanned area, indicated by crosshair and arrow. Taken 11/23/2010.

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Fig. 8 shows a full raster scan of the sample in a 25µm x 25µm section. We can observe both clusters of quantum dots and single emitters. Single QDs may be identified by noting where stripes in the scan occur. Stripes result when a QD being scanned blinks, i.e. stops fluorescing for a brief time. (Note that we measure the average fluorescence lifetime for this sample later in the lab, after searching for antibunching.) Since we know the nanodrive scan speed is 5 ms/pixel, we know how long it takes for a line in the raster scan to be completed: 200 pixel line takes 1 second. Thus, we can later compare the fluorescence lifetime of the QDs with the scan time for a blinking QD as a check on our calculations: we require that the fluorescence lifetime is smaller than the line scan time in order to see streaks in the scan and thereby observe blinking.

(4) Antibunching observations: in LabVIEW, we attempt to select a particular QD single-emitter using the raster scan results. We move the sample to the position of the selected emitter. Then, we may expose the sample to laser light and record the fluorescent light output as photon counts in each APD, which is sent by TTL pulses through a fixed delay to the TimeHarp 200 PCI board that compiles the histogram. From the samples in Fig. 8 we observed blinking but no antibunching. This is likely because creating quantum dot samples requires good mixing in the liquid crystal host, and a moderate amount of quantum dots in solution – there may have been too many quantum dots in this sample, and may thus have clustered.

2.3 Antibunching Data and Results for CdSe Quantum Dots Recorded data was taken for a set of quantum dots that we were able to show produced antibunched histograms. These samples were observed on 11/11/2010 and on 11/18/2010 with Luke Bissell’s CdSe QD samples. The single-emitter samples are shown in Fig. 9, indicated by circles. The photon counts form the circled quantum dot(s) incident at each APD are shown as well; red represents a signal from APD1 and yellow represents a signal from APD2. From these simple plots it is possible to see that the NPBS is not a perfect splitter, or our system is not perfectly aligned, as the intensities vary slightly between APDs. Fig.9 allows one to see blinking QDs in our sample. For example, in (a), from time 250000ms to 1400000ms the target sample appears to blink. But after that time, the intensity at both APDs drops by a factor of four; this is likely bleaching of the QD. While LabVIEW displays intensity data for a single-emitter, TimeHarp records the relative time difference between subsequently detected photons in a histogram, where zero time difference in coincident photons is located at a fixed time bin-value in TimeHarp that corresponds to the delay card setting that delays the TTL pulse from APD2. The TimeHarp generated histograms corresponding to these quantum dot emissions are shown in Fig. 10. Fig 9. [below] Three Samples yielding antibunching (a) Using one 0.1 and one 0.38 transmission filter, with Luke Bissell’s sample, CLC structure (CB15 + E7

8 liquid crystal), and CLC mirror, 800 nm QD fluorescence: antibunching observed. Intensity plot of quantum dot fluorescence at point indicated. Note the streaks indicating blinking in raster scan, and intensity shifts in plot above indicating this QD may be blinking. (11/18/2010) (b) Using Luke Bissell’s sample, CLC structure (CB15 + E7 liquid crystal), and CLC mirror, 705 nm QD fluorescence from 25µm x 25µm scan: antibunching observed. Intensity plot of quantum dot fluorescence at point indicated. (11/11/2010) (c) Using Luke Bissell’s sample, CLC structure (CB15 + E7 liquid crystal), and CLC mirror, 705 nm QD fluorescence, taken from 25µm x 25µm scan: antibunching observed. Intensity plot of quantum dot fluorescence at point indicated. Note blinking from 10000ns to 200000ns, and a possible instance of bleaching after 20000ns. (11/11/2010) Fig.10 [below] shows antibunching histograms of CdSe QDs fluorescence emissions coincidence counts. Light blue curves are moving average of data points. Zero point in time of coincidence count corresponds to ~1700 x-value in all three plots. (a), (b) and (c) delay time corresponding to this zero point can be read from the TimeHarp data and occur at ~59ns. We check this zero point by splitting a single APD TTL pulse into both the start and stop channels of the time-card after antibunching measurements.

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Antibunching in (a) from Fig. 9

Antibunching in (b) from Fig. 9

Antibunching in (c) from Fig. 9

From the TimeHarp histograms we can determine that at ~60ns delay, there is a reduction in number of coincident photons on the APDs compared to the number of photons at the other displayed delay times. We conclude from this data that 60ns is approximately the delay setting of the APD2 circuit, with the remaining small amount of delay attributed to the delays due to different length wires, etc. Thus, finding the zero-point delay of the APD2 delayed circuit, as we do in the Appendix, is sufficient to allow us to conclude that this reduction toward zero coincidence counts at 61.8ns is indication of a single-emitting source. As the coincidence counts at 61.8ns do not drop exactly to zero, we may attempt to explain this by

10 considering the error in our data. Of course, it is possible that these zero-points would become better defined and visible if we had let the experiment run longer. However, it is possible to compute the approximate number of emitters at each of the three locations shown above; if there are more than one emitter, we may observe less antibunching behavior, which could explain why the histograms do not drop completely to zero at the zero-point. To do this, we normalize the photon count and compare our experimental results to the theory described in the introduction.

The normalized photon count is

!

Z =1"1

ne

"#t

$ , where n is the number of single-emitters,

!

" is the

fluorescence lifetime of the QD, and

!

"t is the time interval between subsequently incident photons on the APDs in the Hanbury Brown and Twiss setup. For a true single emitter, N = 1, so we expect that Z = 0 for

!

"t = 0. To compute this fit, we first desire data on the fluorescence lifetime. The average fluorescence lifetime of our CdSe QD sample was computed using data taken on 12/2/2010. Below are the results of fitting the measured photon counts of a blinking quantum dot, two QDs that were not blinking, and a background sample to an exponential decay. We take two data sets as just described for a total of eight samples. The lifetime data is shown in Fig.11A, and the fitted data is reported in Fig. 11B using linear fits to the logarithm of the lifetime measurements. We use two fits per sample as on the log-fit plots we clearly see two linear components with different slopes. Fig. 11A . TimeHarp Data from 12/2/2010 of fluorescence lifetime of a blinking CdSe quantum dot (BQD), two non-blinking CdSe QDs (NB QD), and the background (BG) fluorescence lifetime. Note: this lifetime

!

" is much shorter than the scan interval time for a single line of the raster scanner in our confocal microscope, which explains why we may see blinking in the QDs.

(a) Background lifetimes. Left: Set 1, Right: Set 2.

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(b) Blinking Quantum Dots. Left: Set 1, Right: Set 2.

(c) Non-blinking Quantum Dots, Set 1.

(d) Non-blinking Quantum Dots, Set 2. Fig. 11B Linear fits of the form

!

A " t /# to the Log of the lifetime data. We determine two lifetimes from each plot using the two slopes identified in each data plot, and the lifetimes calculated are reported with each plot.

12 To measure the fluorescence lifetime, we connect the electrical pulse output of the laser to the variable delay card and change the delay between the laser’s electrical pulse and the TTL pulse from the fluorescence signal from the APD2. TimeHarp records a histogram of the photon counts in the APD and we fit the resultant data to the function

!

Photon Count = A exp["t

#]. Taking a fitting function of

!

Z = 1"1

ne

"t

# , where

!

" , the fluorescence lifetime,

and n, the predicted number of emitters, are parameters of the fit, we try to fit the histogram data for three samples. The fixed antibunching histogram zero-delay point is set to zero by subtracting 61.8ns (see appendix) from the recorded times. Below we attempt to approximate the antibunching histograms, and report the best-fit n values.

Emitter # & Lifetime

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Fig. 12. Fitting antibunching curves with expected number of emitters (n) and lifetime determined by fit.

The agreement between the normalized photon counting theory,

!

Z = 1"1

ne

"t

# , and the experimental data is

related to the predicted number of emitters, n, and the predicted lifetime,

!

" , where n determines the scaling of the fit, and the lifetime determines the slope. From Fig. 12, one sees that our first sample from Luke Bissell of 705nm fluorescing CdSe QD in CLC-host from 11/11/2010 is most nearly a true single-emitter (n = 1.18), as the antibunching curve indicates. Comparing this result with Fig. 9, we may determine that there appears to be a relationship between emitter intensity and whether or not one has a true single-photon source; this might be expected, as clusters of emitters would on average be brighter than a single-emitter. But, due to the limited successful antibunching samples taken, is difficult to conclude whether sample intensity is related to single-photon source intensity. We also note that the lifetimes that produce fitted curves using our model are an order of magnitude larger than the lifetimes calculated using the lifetime data presented above. The substantial disagreement indicates that these quantum dot lifetimes need to be further researched. 3 SUMMARY In this Laboratory, antibunching was demonstrated for CdSe quantum dot fluorescence in a CLC-host. This is demonstration of a true single photon source (unlike using an attenuated laser beam which must have bunching do to its lifetime statistics) using the Hanbury Brown and Twiss setup. It was found that sample preparation is crucial to successful production of antibunching. This is because the concentration of quantum dots must be low enough to be able to isolate single-emitters away from each other in the CLC-host. We measured the lifetime of several quantum dot samples and found that they vary substantially; and there is no apparent agreement between the histogram-predicted lifetimes and the lifetime data. We further observed the spectrum of our single-emitters, and present this data in the Appendix. 5 ACKNOWLEDGEMENTS I would like to thank Dr. Lukishova for her guidance and expertise in directing this research laboratory, Sophie Vo for grading and for answering questions, and PHY 434 classmates Justin Winkler, Omar Magana Loaiza, and Mongkol Moongweluwan for working together to understand these laboratories.

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5 APPENDIX 5.1 Identifying Zero-point Delay in Delay-Card in APD2 TTL Circuit To determine the zero-point delay between the two APD TTL signals, we use a T-connector split the TTL pulse from APD1 to both the start and stop channels of the time-card. So the APD1 TTL goes through the delay card; but it is the same signal that is simultaneous created when APD1 is triggered. So the only delay present should be the inherent delays in the circuit, which is dominated by the delay-card. Just as for the antibunching measurements, we use the second order correlation of the TTL pulse recorded in LabVIEW, but this time we have just APD1 TTL pulse split down each arm of the timing circuit. The self-second correlation results in a peak about the fixed delay time setting of the delay-card. This is shown in Append. Fig. 1.

Appendix Fig. 1 Zero-Point Delay Indicated by delay card setting as determined by removing APD2 and splitting APD1 TTL pulse to both start and stop channels of time-card, and histographically recorded into

TimeHarp. 5.2. Pump Beam Data for Lifetime Measurements

In the lifetime measurement experiment, our excitation pump beam was a diode-pumped solid-state 532nm laser with 6 ps pulse duration and 76 MHz pulse repetition at 40 mW average power. We connected the electrical output of laser to an oscilloscope and show the pulse shape in Appendix Fig. 2.

Appendix Fig. 2 Laser Pulses: we see negative polarity with voltage ~450mV and a pulse separation of ~13.3ns.

Zero-Point Delay: 61.8ns

15 5.3 [Appendix Fig. 3] Ex. of TimeHarp Histogram with No Antibunching 5.4 Spectroscopic Measurement of 800nm fluorescing CdSe QD sample in CLC-host with CLC mirror, taken with Andor Solis software and EM-CCD camera (Gain of 155) on 11/18/2010. Note, the peak at 700nm is an artifact of HeNe laser resonance [Left: Intensity display, Right: Count display]. (Appendix Fig. 4 below) 5.5 Attached Mathematica documentation of calculation of emitter-number per sample as well as fitting antibunching curve. FILE: LBSampleAntibunchFit1111Data.nb

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6 REFERENCES [1] M. A. Neilson, I. L. Chuang, “Quantum Computation and Quantum Information.” Cambridge University Press (2000) [2] R. Hanbury Brown and R. Q. Twiss, Nature (London), 177, 27 (1956) [3] H. J. Kimble, M. Dagenais, L. Mandel, “Photon Antibunching in Resonance Fluorescence”, Phys. Rev. Lett., 39, 691 (1977) [4] B. Lounis, H.A. Bechtel, D. Gerion, P. Alivisatos, W.E. Moerner, “Photon antibunching in single CdSe/ZnS quantum dot Fluorescence.” Chem. Phys. Lett., 329, 399 (2000) [5] P. Grangier, G. Roger, A. Aspect, Europhys. Lett., 1, 173 (1986) [6] S. Lukishova, “Confocal microscope imaging of single-emitter fluorescence and the Hanbury Brown and Twiss setup for Photon Antibunching.” University of Rochester Teaching Lab for OPT 453/PHY 434 (2008)