Detection of Single Photon Emission byHanbury-Brown Twiss InterferometryGreg Howland and Steven BlochMay 11, 2009AbstractWe prepare a solution of nano-diamond particles on a glass micro-scope slide with a target concentration of 1 × 10−9M. Using a confocalmicroscope, we observe photons emitted from the particles via excitationfrom a pulsed 532 nm solid state laser at 840 µW. A Hanbury Brownand Twiss interferometer is used to probe these photons for evidence ofantibunching. At this time, we did not observe antibunching.IntroductionThe rise of q uantum information science has prompted a need for single photonson demand. Such ‘photon pistols’ provide significant practical value for quantumcommunication and quantum computing. Furthermore, they allow in-depthexp erimental study of fundamental aspects of quantum mechanics.One potential single photon source is spontaneous emission from a singleemitter, such as an atom, molecule, or quantum dot. In this case, it is o ftendifficult to ascertain whether true single photon states have been created anddetected. Fortunately, a Hanbury-Brown Twiss interferometer can be used todistinguish classical from non-classical states of light. We us e a confocal mi-croscope to image single emitters onto such an interferometer in an attempt todetect non-classical single photon states.Figure 1: Hanbury-Brown Twiss Interferometer1TheoryThe Hanbury Brown and Twiss interferometer (HBT) consists of an input beam,I, incident on a 50/50 beamsplitter with two avalanche photodiode (APD) de-tectors situated at the two outports of the beamsplitter, as shown in Fig .1. TheHBT measures correlations of the intensities, I1and I2, of the two outports ofthe beamsplitter by the second order coherence g(2)1,2(τ):g(2)1,2(τ) =hI1(t + τ )I2(t)ihI1(t + τ )ihI2(t)i(1)where τ is the time delay between the relative intensities.A classical light field, I, will be split evenly into the outp orts of the beam-splitter, such that I1= I2= I/2. For simultaneous measure ments (τ = 0) thesecond order coherence is equal to:g(2)1,2(0) =hI(t)2ihI(t)i2(2)which is the second or der coherence of the input field. Using the Cauchy-Schwartz inequality one can show tha t for a classical field g(2)1,2≥ 1.In quantum mechanical theory, the intensities in E q. 1 are treated as oper a-tors which are proportio nal to the numb e r operator ˆn = ˆa†ˆa. The τ = 0 secondorder c oherence is given as:g(2)1,2(0) =hˆa†1ˆa1ˆa†2ˆa2ihˆa†1ˆa1ihˆa†2ˆa2i(3)The operator s for the two ports c an be rewritten in terms of the input fieldoperator ˆaIand the vacuum field operator ˆaVas:ˆa1=1√2(ˆaI− ˆaV)ˆa2=1√2(ˆaI+ ˆaV) (4)The second order coherence becomes:g(2)1,2(0) =hˆnI(ˆnI− 1)ihˆnIi2(5)which is the second order coherence of the input field. This is the same resultas when the calculation is done with a classical light field.When the second order cohere nce is calculated using a coherent state oflight, which can be described both classically a nd quantum mechanically, thesame value is found in both cases , g(2)1,2(0) = 1. A similar re lationship is foundfor a thermal state of light; g(2)1,2(0) = 2. However, if we evaluate Eq. 1 using astate that cannot be described classically, one finds that g(2)1,2(0) < 1, which isin violation of the classical inequality g(2)1,2≥ 1.For g(2)1,2≥ 1 the photons are considered to exhibit bunching. Bunchingoccurs when multiple photons “bunch” together as they travel. When these2Figure 2: Experimental Setup“bunches” are incident on a bea ms plitter some of the photons are reflectedand some are transmitted, leading to an increase in the number of positivecorrela tio ns. For a purely qua ntum mechanical state the photons are co ns ideredantibunched, which means they are separated equally from each other in time.For the case of a single photon state g(2)1,2= 0.Experimental SetupA solution of nano-diamond particles was prepared on a glass microscope slide.Approximately 1 µL of solution was deposited on the slide with a pipet. Thesolution was diluted across the slide with a spin coater rotating at 30,000 RPMfor 30 seconds. The target particle concentration was 1 × 10−9M.The sample was then placed in the confocal microscopy appa ratus presentedin Fig. 2. The nano particles are excited by a pulsed 53 2 nm solid state laser ofapproximately 1 mW. A confocal imaging system images the sample onto eithera Ha nbury-Brown Twiss interferometer or an Electron Multipliying C ooled CCDcamera. A dichroic mirror prevents contamination fro m the excitation laser.The microscope can focus on an area of the sample approximately 200 nm indiameter.The camera can be used to directly view source fluorescence. The sample canalso be raster scanned over a 50 µm × 50 µm area to provide spatial resolutionto the sig nal detected by the APDs in the interferometer. APDs provide bothsingles and coincidence measurements, and their 170 µm apertures provide thepinhole necessary for the confocal setup.3To detect single-emitter fluorescence, the output is directed to the interfer-ometer. The sample is raster scanned to produce a two-dimensional plot of thesample. A potential single emitter is selected and the sample is translated tothe appropriate location. Coincidence detection is then performed using theinterferometer for approximately 5 minutes to look for antibunching.Figure 3: Raster ScanFigure 4: Coincidence DetectionResultsResults a re presented in Fig. 3 and 4. . The raster scan (Fig. 3) was takenwith excitation laser power of 840 µW. Emitters are characterized by bright4pixel blocks on the scan. The brightest of these are likely multiple emittersclustered together. The location x = 5 9, y = 25 (cross-hairs on figure) wasprobed for antibunching by observing coincidence counts. This measurement isproportional to g(2)1,2.Figure 5: Camera ImageThere is no observable dip in the g(2)1,2(τ) measurement characteristic of anti-bunching. We were unable to detect non-classical states of light at this location.It is possible we were not obs e rving a single emitter, or a longer integration timemay be necessary. The nano-particle density may also be too large on the slide.An image of the sample taken with the EM-CCD is given in Fig. 5 . Singleemitters and clusters of single emitters can be clearly seen. It is therefore likelythat with further effort a ntibunching can be observed on this sample.References[1] H. Paul, Rev. Mod. Phys. 54, (1982).[2] R.