Single Emitters and the Experimental Demonstration of Photon Antibunching 

 Kyle Guzek and Andrew Howard 

OPT 253 - University of Rochester, 2018  

In this lab, photon counting techniques were employed in order to characterize the photon emission                             statistics of various known examples of single emitters including colloidal nanocrystal quantum dots, nitrogen                           vacancy nanodiamonds, and DiI dye molecules. A confocal fluorescence microscope was employed in order to                             excite each of these sources and a Hanbury-Brown and Twiss interferometer was used to analyze the intensity                                 correlation and time interval between photons. Techniques involving embedding single emitters within gold                         nanoantenna arrays and immersing them into cholesteric liquid crystal hosts are explored. Ultimately, photon                           antibunching was unable to be unambiguously demonstrated. However, each of the five experiments                         conducted in this lab offered valuable insight into the complexity of the task, and occasionally yielded possible                                 solutions.  

I. Theory  

Single Photon Sources A traditional coherent source, such as a laser beam, can be selectively attenuated to the 

“single-photon level” such that it emits, on average, a single photon over any desired time interval, e.g. one second. However, a heavily attenuated laser beam cannot be considered a single photon source (SPS) as it still obeys Poissonian statistics [1]. Poissonian distribution dictates that, although a source can emit photons at a regular interval on average, photons will still occasionally be produced in “bunches”, where multiple photons are emitted within one time interval, or coherence time. A true single photon source is necessarily “anti-bunched” in order to ensure all photons are emitted one-at-a-time over a given coherence time [1]. This distinction is detailed in Fig. 1.1 below. 

   a)   

   b)   

   c) 

   Figure 1.1: A schematic representation of photon emission (as represented by colored circles) plotted as a                               function of time for (a) antibunched light, drawn in green, (b) random (coherent) light, drawn in red, and (c)                                     bunched light, drawn in blue. is the coherence time of all three states, used as the time scale over which the        τ c                                bunching occurs.  1

1 Figure taken from https://en.wikipedia.org/wiki/Photon_statistics  

 Antibunched sources are difficult to produce as they necessarily involve what are known as 

single emitters, sources that, due to their quantum mechanical properties, can physically only absorb and emit photons one-at-a-time. The archetypical single emitter is an atom that is restricted to two states, an excited state and a ground state. When excited, for example, by a laser field, the atom jumps to its excited state, exists for some lifetime, before finally returning to its ground state by the re-emission of a photon. While excited, the atom physically cannot absorb another photon, and must first release a photon before again absorbing and re-emitting another. This behavior ensures photon antibunching. The model of the single atom can be applied to a number of real-world single emitters, such as a single molecule, a single color center in diamond, or a quantum dot [1].  

In order to measure the behavior of an SPS, special techniques must be employed to ensure the excitation of only one single emitter at a time. For this purpose, confocal microscopy (see below) can be employed. Then, to detect the emission of a single photon over such a short time interval, an intensity correlation interferometer can be used. The most popular example of such an interferometer is the Hanbury-Brown and Twiss Interferometer (see below). 

 Confocal Microscopy 

Conventional microscopy involves illuminating a sample with light, collecting a small portion of that light with an objective lens, and imaging that light through to either an eyepiece or a detector. Confocal microscopy is so-called because the illumination source is focused onto the sample using the sample objective that is used for collection such that the illumination light cone and the collection light cone share a common focus [3]. When used to image the fluorescence of a sample, this is known is Confocal Fluorescence Microscopy. Here, a laser is used as an illumination source in order to excite a fluorescent sample, and the fluorescence is then imaged back through the same objective after which the laser light is filtered out by use of a dichroic mirror, and only the fluorescence is collected. This is represented schematically below in Fig. 1.2. 

  (a) (b) 

Figure 1.1: A schematic representation of a confocal fluorescence microscope, displaying (a) the excitation of                             the fluorescent sample by laser light, drawn in blue, followed by (b) the collection of the emitted fluorescence,                                   drawn in green, through the same objective.  2

 This method for imaging fluorescence offers the advantage of higher-contrast images, as no 

stray light is allowed to reach the detector, only light that is emitted by the fluorescent sample at the focus of the objective. This effect can be further supplemented by immersing the objective in oil (or any refractive substance) in order to increase the numerical aperture of the collection system. As applied to SPSs, this scheme can effectively excite single emitters at a time and recollect their emitted photons, provided that the objective forms a tight focus that is larger than the spacing between adjacent emitters.  Hanbury-Brown and Twiss Interferometer 

Originally used to determine the angular size of distant stars, the Hanbury-Brown and Twiss interferometer is a type of intensity interferometer that, through the simultaneous observation of two halves of an intensity profile can yield correlation information about the incident source [2]. Typically, the correlation measurement is achieved by use of a computer chip that can synchronize the signals between two detectors, each receiving a signal from one half of the incident intensity profile. The case for the correlation measurement of an incident light source is shown schematically in Fig. 1.3 below.  

2 Figure taken from https://ibidi.com/content/216-confocal-microscopy 

 Figure 1.3: A simplified schematic of a Hanbury-Brown and Twiss-type light interferometer. The intensity of                             an arbitrary light source is randomly split by a 50/50 beam splitter, and each component is sent to a separate                                       detector. These detectors then send electrical signals to a correlator (drawn as a computer chip here) and the                                   correlator is calibrated to receive both inputs and determine the intensity correlation between the two                             components.  

For the case of an antibunched source, each emission of a photon is a separate event in time, and so if the input intensity is that of a single photon, an intensity profile will appear only on one detector at a time, yielding a measurement of maximal anti-correlation between the two detectors. Thus, the Hanbury-Brown and Twiss interferometer provides an experimental method of deducing the degree to which a source is antibunched. In this case, each detector would necessarily represent a single-photon detector, such as an avalanche photodiode (APD), and the correlation would be measured as by the coincidence count rate between the two APDs. 

Mathematically, the coincidence count rate between one detector, reading intensity , and(t)I  the other, reading a delayed intensity , can be represented by the second order correlation(t ) I + τ  function 

=(t)g(2)⟨I(τ )⟩2

⟨I(t)I(t+τ)⟩   (Eq. 1.1) 

 

where t is the time interval between photons, known as the interphoton time, and is the time delay τ  between the two intensity readings [5]. In this formulation, at t=0, antibunched light would yield a value of = 0, as no two photons should be emitted simultaneously. For comparison, coherent(0)g(2)  light yields a value of = 1 and thermal light yields = 2. Therefore, by use of a(0)g(2) (0)g(2)  Hanbury-Brown and Twiss Interferometer, the degree to which a source is antibunched can be quantified by the value of .(0)g(2)   

 Figure 1.4: A schematic plot of the second-order correlation function, for the case of (1) bunched                    (t)g(2)              or thermal sources, drawn in green, (2) coherent sources, drawn in yellow, and (3) antibunched                             sources, drawn in red.  3

 Cholesteric Liquid Crystals 

A cholesteric liquid crystal is a type of liquid crystal (a material that behaves conventionally like a liquid but possesses the chemical structure of a crystal) comprised of a series of layers, wherein each layer has an incrementally rotated angular orientation of its component molecules. 

  (a) (b) 

 

Figure 1.4: A simplified diagram displaying (a) the organization of molecules within adjacent layers of a                               cholesteric liquid crystal, effectively creating (b) a helical structure of dipoles with a period, or “pitch”, p.  4

 

3 Image taken from: OPT 253, Lab 3-4, Lecture 1 4 Image taken from: https://www.intechopen.com/books/cellulose-fundamental-aspects-and-current-trends/crystalline-nanocellulose-preparation-modification-and-properties

The effect of this helical organization of dipoles, when exposed to light, is to reflect all incident polarizations that align with the molecules in the helix. However, this reflectance only occurs for polarizations of a certain handedness and of wavelengths that match the periodicity of the structure. Thus, cholesteric liquid crystals are a type of transmissive photonic bandgap material, meaning that there is a gap in the spectral transmittance at the wavelength that corresponds to the pitch of the crystal. 

In the context of SPSs, a photonic bandgap material such as a cholesteric liquid crystal can act as a host into which single emitters can be immersed. Immersing the single emitters into a photonic bandgap material with a band gap that coincides with the fluorescence peak of an emitter enhances the visibility of single-photon emission and, in the case of a cholesteric liquid crystal host, provides a definite polarization at which single photons will be detected.   II. Experimental Procedure 

 

Experimental Setup In order to analyze the antibunching properties of the various single emitters investigated in 

this lab, an experimental setup was devised utilizing the two key components detailed in the section above. The single emitters are excited and their emissions are captured using a confocal fluorescence microscope and their antibunching properties are analyzed by a Hanbury-Brown and Twiss interferometer. The resultant experimental setup is drawn schematically in Fig. 2.1. This setup was used for each of the individual experiments detailed below.  

 Figure 2.1: A schematic representation of the system used to excite, capture, and analyze the antibunching of                                 the single emitters investigated in all parts of the lab. The confocal fluorescence microscope is shown on the left,                                     with the laser light (532 nm) drawn in green, and the resultant fluorescence drawn in red. The Hanbury-Brown                                   and Twiss interferometer is drawn on the right, with a 50/50 beam splitter directing each incident photon to                                   

either APD 1 or APD 2, and a computer chip correlating the two events. Not shown in this diagram: various                                       spatial frequency filters and neutral density filters placed in the laser beamline in order to filter the spatial profile                                     and attenuate the beam.  Raster Scanning 

In order to locate single emitters within each sample, it was necessary to first scan a large area for fluorescence. To do this, samples were put on a moving translation stage, and raster scans were performed over square-micron areas. Each raster scan was constructed by an automated process in which the translation stage is moved incrementally over an area in which each APD collects a local photon count in order to assign a value to a pixel as determined by the input parameters of window size (in μm) and resolution (in px). This procedure yields two ideally identical images of intensity over a square area. These two intensity maps were then scrutinized for evidence of fluorescence, the translation stage moved, and the area of investigation decreased. This procedure was performed with each sample until limited by resolution.  APD Coincidence Counts 

Once a single emitter was located, the translation stage was then moved to this area, and time trace plots of APD 1 and 2 were recorded. Simultaneously, an integrated computer (PCI) card was used in conjunction with TimeHarp software to record the coincidence counts between APD 1 and 2 over time. As mentioned in the above section, the number of coincidence counts as a function of time is proportional to the second-order correlation function, . APD 2 was set to have a delay relative(t)g(2)  to APD 1 in order to compensate for the “deadtime” of each detector. This way, upon detection of a photon, APD 1 acts as a “start” signal and APD 2 acts as a “stop”, and the time between these two signals characterizes the effective interphoton time. In order to achieve this, the computer card was calibrated by sending a TTL (transistor-transistor logic) pulse from each APD simultaneously, and manually adjusting the delay such that the leading edge of the pulse on APD 2 coincided with the lagging edge on APD 1.  Experiment 1 

In this portion of the lab, nanodiamonds embedded within gold “bowtie” nanoantennas were imaged using the above method of raster scanning.  

 Experiment 2 

In this portion of the lab, colloidal quantum dots clusters were investigated, using the same raster scanning method as in Experiment 1. It was additionally attempted to isolate a single quantum dot in order to observe antibunching, however, this was not achieved.     

Experiment 3 In this portion of the lab, raster scans of nanodiamonds in a cholesteric liquid crystal 

sample were performed. The coincidence count rate over time was then determined using the TimeHarp software and the procedure listed above. Additionally, the temporal profile of a TTL pulse was captured using an oscilloscope.  Experiment 4 

In this portion of the lab, we characterized the reflectance spectrum of the cholesteric liquid crystal sample used in Experiment 3. To do this, we used a simple grating spectrometer. This type of spectrometer is comprised of an entrance slit, a reflective diffraction grating, and a series of mirrors to direct the diffracted beam onto a detector. This detector was calibrated using a 532 nm laser.  Experiment 5 

In this portion of the lab, raster scans of a low concentration DiI dye solution were performed. Time traces of this data were taken as described above, as well as coincidence count rates.   III. Results and Data Analysis  

Experiment 1 - Nanodiamonds Embedded in Gold Bowtie Nanoantennas In this first experiment, we imaged nanodiamonds embedded within gold bowtie 

nanoantennas. We used a 532 nm continuous wave laser operating at a power of 2 mW for the excitation of the samples in all images. 

 

 Figure 3.1: Initial raster scans of the nanoantenna array sample (APD 1 on the left, APD 2 on the                                     right). In the top portion of both images there are unresolved numbers used as reference to distinguish                                 the nanoantenna arrays. The lower portion of the images displays the nanoantenna arrays themselves. 

 

Neutral Density filters used  0 

Pixels  100 x 100  

Size  40 x 40 μm 

 

 Figure 3.2: A raster scan of smaller window size showing only one nanoantenna array. 

 

Neutral Density filters used  0 

Pixels  100 x 100  

Size  20 x 20 μm  

 Figure 3.3: A closer raster scan of the same nanoantenna array. 

 

Neutral Density filters used  0 

Pixels  100 x 100  

Size  10 x 10 μm 

 

 Figure 3.4: A high resolution raster scan of same window as in Fig. 3.3. The semicircle feature is likely 

due to the improper alignment of the system.  

Neutral Density filters used  0 

Pixels  512 x 512  

Size  10 x 10 μm 

 By inspection of Fig. 3.4, it would seem there are no clearly visible single emitters. Both images 

seem to be comprised of a recurring semi-circle structure that may be a result of a fundamental limit in resolution, or an improper alignment of the system. The fact that the images from APD 1 and APD 2 are so markedly different suggests that improper alignment may be more likely.    

Experiment 2 - Quantum Dot Clusters For this experiment, we conducted similar raster scans for colloidal quantum dot clusters. We 

used the same laser, again at an operating power of 2 mW, making sure to align the laser to give the best possible spot size before beginning.  

 Figure 3.5: The laser spot after alignment. Note the “four leaf clover” diffraction pattern of the spot. 

 

 Figure 3.6: The initial raster scan for the quantum dot cluster sample. Peaks in intensity are clearly 

visible indicating quantum dot fluorescence.  

Neutral Density filters used  1 

Pixels  100 x 100  

Size  40 x 40 μm 

 

 Figure 3.7: A smaller window size raster scan centered around the cluster closest to the center of the 

scan in Fig. 3.6.  

Neutral Density filters used  1 

Pixels  100 x 100  

Size  20 x 20 μm 

 

 Figure 3.8: An even smaller window size scan of the central quantum dot cluster shown in Fig. 3.7. 

 

Neutral Density filters used  1 

Pixels  100 x 100  

Size  5 x 5 μm 

 

 Figure 3.9: A higher resolution image of the same quantum dot cluster as in Fig. 3.8. 

 

Neutral Density filters used  1 

Pixels  200 x 200  

Size  5 x 5 μm 

 By comparing the results of the raster scan in Fig. 3.9 to those in Fig. 3.8 we can see that we are 

fundamentally limited by the optical resolution of the system, as increasing the resolution of the raster scan failed to yield a high-resolution image of the quantum dot cluster. This effect could be mitigated by using a larger objective within the confocal microscope.  Experiment 3 - Nanodiamonds in a Cholesteric Liquid Crystal Host 

In this experiment, we measured the emission spectra of nanodiamonds in a cholesteric liquid crystal host. We took similar raster scans as above using the same laser power (2 mW), as well as a series of TimeHarp scans. We also used an oscilloscope to analyze the TTL pulses transmitted by the APDs. Figure 3.10 shows an example of such a pulse on an oscilloscope.   

 Figure 3.10: The oscilloscope image of a TTL pulse from an APD. 

  

 Figure 3.11: An initial raster scan of the sample, displaying several nanodiamond clusters. 

 

Neutral Density filters used  1 

Pixels  100 x 100  

Size  40 x 40 μm 

 

 Figure 3.12: The time trace (right) for both APD 1 and 2 at the location highlighted by the green 

crosshairs in the raster scan (left).  

 Figure 3.13: The TimeHarp data corresponding to the time trace shown in figure 3.12. All                               TimeHarp images represent the coincidence counts between APD 1 and APD 2 over time. 

 As quantum dots are true single emitters, they should display antibunching phenomena, and 

we would expect the above TimeHarp plot to resemble that of Fig. 1.4 for the case of antibunching. The result of Fig. 3.13 did not resemble the Fig. 1.4 whatsoever, and the coincidence counts recorded were shockingly low, so another attempt was made using one less ND filter and performing the time trace at a different location.  

 Figure 3.14: A raster scan over the same area as in Fig. 3.11, with one less ND filter. 

Neutral Density filters used  0 

Pixels  100 x 100  

Size  40 x 40 μm 

  

 Figure 3.15: Another time trace (right) for both APD 1 and 2 at the location highlighted by the 

green crosshairs in the raster scan (left).  

 Figure 3.16: The TimeHarp data corresponding to the time trace in Fig. 3.15. 

 Noting that the coincidence counts on the TimeHarp data were in disagreement with those in 

the raster scan, another attempt was made using a different point on the raster scan in Fig. 3.14.  

 Figure 3.17: A third attempt at observing the coincidence counts at yet another bright spot on the 

raster scan shown in Fig. 3.15.  

 Figure 3.18: The TimeHarp data corresponding to the time trace shown in Fig. 3.17. 

  

 Figure 3.19: The calibration taken for the TimeHarp data in Fig. 3.18. 

 Considering the disagreement between Fig. 3.18 and 3.17, in which the TimeHarp trace 

yielded coincidence counts well below 10 whereas the raster scan yielded APD 1 and 2 singles counts well in the hundreds, we finally concluded there must be a fault in the connection between the detectors and the computer card recording coincidence counts. 

Theoretically, we would expect that the TimeHarp data (representative of the second order correlation function of the intensities at each detector) would resemble that of the plot on Fig. 1.4 for the case of antibunched light, centered around the calibration peak in Fig. 3.19. However, as stated, due to a probable error in the connection between the computer card and APDs, we were unable to find this trend.    

Experiment 4 - Reflectance Spectrum of Cholesteric Liquid Crystal In this experiment, we measured the reflectance spectrum of a cholesteric liquid crystal sample 

prepared in lab. To measure the spectrum, we used a simple grating spectrometer that maps the displacement on the detector directly to wavelength. To calibrate this spectrometer, we used a 532 nm laser.  

 Figure 3.20: The spectrum of the laser at 532 nm, acting as our calibration. 

 

 

Figure 3.21: The reflectance spectrum of the cholesteric liquid crystal sample prepared in lab.  

 Figure 3.22: The corresponding line spectrum of the reflective liquid crystal sample. 

 The reflectance spectrum found in this experiment for the liquid crystal sample can be used to 

correct for the spectrum found in Experiment 3, as, in this case, the liquid crystal acts as a host for the nanodiamonds.   

Experiment 5 - DiI Dye Molecules In this experiment we performed a raster scan and time trace for a bright spot found in a 

solution of DiI dye molecules at a laser power of 2 mW. We then used TimeHarp to yield the coincidence count rate.  

 Figure 3.23: A raster scan of a sample of DiI dye molecules. 

 

Neutral Density filters used  3 

Pixels  100 x 100  

Size  40 x 40 μm 

 

 Figure 3.24: The time trace (right) for the point highlighted by the green crosshairs in the raster scan 

(left).  

 Figure 3.25: The TimeHarp calibration data. The green arrow at the bottom of the peak indicates 

the center of the calibration.  

 Figure 3.26: A first attempt at demonstrating photon antibunching through coincidence count rate.                         The green arrow represents the center of the calibration, where we would expect to see evidence of                                 photon antibunching. 

In order to experimentally demonstrate photon antibunching we would expect to see a dip in                             the coincidence count rate at around the time marked by the green arrow (representing the center of                                 the calibration in Fig. 3.25). No noticeable dip could be distinguished from the noise. 

 

 Figure 3.27: A second attempt at demonstrating photon antibunching. The green arrow represents                         the center of the calibration, where an antibunching feature is expected. The dashed red rectangle                             highlights a feature in the data which appears to demonstrate photon antibunching. The red arrow                             represents the center of that feature. 

 As very clearly marked in Fig. 3.27, we found a noticeable dip in the coincidence count rate at 

a time of around 26 ns. The location of this feature, however, clearly differs from the location of the expected peak, at around 42 ns. Nonetheless, the feature appears to follow the expected trend as dictated by Eq. 1.1 to some significant degree. We conjecture that it is possibly a true feature of antibunching, and that some element introducing a delay within the system has gone un-accounted for, introducing a 16 ns disparity between the calibration data and the experimental data.    

IV. Conclusion Although we were unable to unequivocally prove the presence of photon antibunching in the 

sources that were investigated, the results of this experiment stand to offer a clear path toward experimental demonstration. In Experiment 1, through the analysis of nanodiamond emitters embedded in gold bowtie nanoantennas, the effects of improper laser alignment in a confocal microscope were demonstrated. In Experiment 2, we found, after aligning the laser properly, that a larger objective in a confocal microscope is likely required to accurately pinpoint the location of single emitters in quantum dot clusters. In Experiment 3 and 4, we found that by using a cholesteric liquid crystal host, and characterizing its spectrum, we can effectively increase the visibility of single emitters. And finally, in Experiment 5, we concluded that, in our current experimental design, it may be possible that not all sources of delay are accounted for in the propagation of information from the APDs to the computer chip. Not only have these findings demonstrated the difficulty of experimentally verifying photon antibunching, but they have each demonstrated possible avenues for improving the efficacy of an experiment that attempts to do so. Rather than experimentally demonstrate photon antibunching, as intended, the results of this lab have instead provided its authors a wide breadth of instructive lessons on how to design a careful experiment that just might.     

Contributions of Each Student  

Kyle Guzek - Results and Data Analysis Andrew Howard - Abstract, Theory, Experimental Procedure, Conclusion  References  

[1] Lukishova, Svetlana. “Lab 3-4 Lecture 1”, OPT 253, University of Rochester (2018).  

[2] Fox, Mark. Quantum Optics: An Introduction. Vol. 15. OUP Oxford (2006).  

[3] Paddock, Stephen. “Introductory Confocal Concepts”, Nikon, MicroscopyU (2018)  https://www.microscopyu.com/techniques/confocal/introductory-confocal-concepts.  

[4] Baym, Gordon. "The physics of Hanbury Brown--Twiss intensity interferometry: from stars to nuclear collisions." arXiv preprint nucl-th/9804026 (1998).  

[5] Lukishova, S. G., et al. "Room-temperature single-photon sources based on nanocrystal fluorescence in photonic/plasmonic nanostructures." Emerging Technologies in Security and Defence II; and Quantum-Physics-based Information Security III. Vol. 9254. International Society for Optics and Photonics (2014).