{"id":4275,"date":"2024-09-22T16:23:04","date_gmt":"2024-09-22T16:23:04","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=4275"},"modified":"2024-09-22T16:23:05","modified_gmt":"2024-09-22T16:23:05","slug":"can-we-detect-individual-photons","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/09\/22\/can-we-detect-individual-photons\/","title":{"rendered":"CAN WE DETECT INDIVIDUAL PHOTONS?"},"content":{"rendered":"\n

Let\u2019s do a back-of-the-envelope calculation of just how many photons are produced by a typical 60-W lightbulb: although we know that the filament acts as a blackbody, and thus produces a wide range of wavelengths, let\u2019s take 600 nm as an average for our quick estimate. The energy of a photon is E<\/em> = hf<\/em> = hc<\/em>\/\u03bb, so the energy (in Joules) of a single photon of 600-nm light is E<\/em>\u03bb=600nm<\/sub> = 6.626 \u00d7 10\u221234<\/sup> [J \u00b7 s] \u00d7 2.998 \u00d7 108<\/sup> [m\/s]\/600 \u00d7 10\u22129<\/sup> m = 3.31 \u00d7 10\u221219<\/sup> J.<\/p>\n\n\n\n

A power of 60 W means 60 J\/s, so the number of photons produced by a 60-W lightbulb is approximately 60 [J\/s]\/3.31 \u00d7 10\u221219<\/sup> [J\/photon] = 1.81 \u00d7 1020<\/sup> photons per second. That is a huge number!<\/p>\n\n\n\n

Only a small fraction of these reach our eyes, even if we look directly at the lightbulb. This is because the photons are spread over a sphere, and only a small fraction of the photons reach our eyes at a safe distance from the filament. Imagine that you are driving around at night, and you want to see if your friend is still awake. You look at the window from a block away (let\u2019s assume 100 m) and see that the light is still on. How many photons reach your eye?<\/p>\n\n\n\n

The photons can be assumed to be flying away from the lightbulb equally in all directions. Since you stand 100 m away, let\u2019s place the lightbulb at the center of a sphere with a radius r<\/em> = 100 m. The sphere has a surface area of 4\u03c0r<\/em>2<\/sup>, so an r<\/em> = 100 m sphere has a surface area of 125,664 m2<\/sup>. The pupil of the human eye has an effective diameter of 8 mm (r<\/em> = 4 mm) in the dark, so its area r<\/em>2<\/sup> is around 50 \u00d7 10\u22126<\/sup> m2<\/sup>. We need to scale down the total number of photons emitted by the lightbulb by 50 \u00d7 10\u22126<\/sup> m2<\/sup>\/125,664 m2<\/sup> = 400 \u00d7 10\u221212<\/sup>. That means that 400 \u00d7 10\u221212<\/sup> \u00d7 1.81 \u00d7 1020<\/sup> = 72.4 \u00d7 109<\/sup> photons from a 60-W lightbulb at a distance of 100 m reach your eye every second. That\u2019s still a lot of photons from a relatively dim source!<\/p>\n\n\n\n

A typical phototube barely gives a measurable current at that level, so how could we ever expect to detect a single photon? Fortunately, some very smart engineers at Westinghouse and RCA figured out that the single electron released from a photocathode by a single photon could be accelerated toward another electrode in order to produce secondary electrons. Two or more electrons are then released when the accelerated photoelectron slams into the electrode. As shown in\u00a0Figure 28, the same process can be repeated over and over again with the secondary electrons used to successively multiply the number of electrons released in a cascade. A much larger number of electrons finally reach the anode as the result of a single photon hitting the photocathode. Commercially available\u00a0photomultiplier tubes<\/em>\u00a0(PMTs) based on this principle produce as many as 106<\/sup>\u00a0to 107<\/sup>\u00a0secondary electrons at the anode for each photon that releases a photoelectron from the photocathode.<\/p>\n\n\n\n

Figure 28\u00a0Photomultiplier tubes are the workhorse detector of experimental particle physics.\u00a0(a)<\/strong>\u00a0The photoelectrons released at the photocathode of a PMT are accelerated toward an electrode (first dynode), and cause the release of two or more secondary electrons. Each of these causes the release of two or more electrons from the second dynode. The cascade continues until a very large number of electrons are available for detection at the anode.\u00a0(b)<\/strong>\u00a0Technicians on a rubber boat inspect some of the 11,242 PMTs in the Super-Kamiokande neutrino detector in Japan.\"\"<\/p>\n\n\n\n

Today, the PMT is the workhorse detector in experimental particle physics. One of the most extreme is the Super-Kamiokande detector used to hunt for elusive particles called neutrinos<\/em>. This massive detector is buried deep within an abandoned zinc mine in Japan. It uses 11,242 PMTs to look at photons produced when the neutrinos decelerate as they hit 50,000 tons of pure water.<\/p>\n\n\n\n

Let\u2019s build the PMT probe (Figure 29) that we\u2019ll use for many experiments in the following chapters. We chose the RCA 6655A PMT because it is affordable and widely available in the surplus market. This tube has ten dynodes that multiply a single photoelectron into 1.6 \u00d7 106<\/sup>\u00a0secondary electrons at the anode when operated at + 1,000 V. You can increase the voltage beyond + 1,000 V, and operate the PMT safely at +1,250 V, but be careful not to exceed its absolute maximum voltage of + 1,600 V.<\/p>\n\n\n\n

Figure 29\u00a0This versatile photomultiplier probe is useful for many experiments described in this book. It is based on the RCA 6655A PMT, and features a gain of 1.6 million when operated at +1,000 V.\"\"<\/p>\n\n\n\n

As shown in\u00a0Figure 30, we enclosed our PMT probe in a die-cast aluminum box (Bud Industries model AN-1323). The PMT and its magnetic shield fit snugly within a 10-cm-long piece of aluminum optical instrument construction rail (66-mm profile, Thorlabs model XT66-100). A matching faceplate (Thorlabs model XT66SM2) screws to the 66-mm-profile rail from outside the aluminum box. It is used as a convenient, light-tight interface to other optical components. The plate is sealed against the metallic enclosure with black RTV silicone caulking, which can be purchased at any auto supply store. All other possible light leakage paths around the PMT are sealed with black electrician\u2019s tape. There is enough room inside the box to accommodate the PMT\u2019s tube socket, resistor divider, capacitors, potentiometers, and coaxial connectors. The bottom cover for the enclosure is not shown in the picture, but we drilled a blind hole in the center and tapped it to accept a\u00a01<\/sup>\/4<\/sub>\u2033 20 TPI machine screw, so that we may mount the probe on a standard camera tripod or on an optical table post.<\/p>\n\n\n\n

Figure 30\u00a0Inside view of our PMT probe. The PMT and its magnetic shield fit snugly within a 10-cm-long piece of 66-mm aluminum optical instrument construction rail. A matching faceplate is used as an interface to other optical components. All possible light leakage paths around the PMT are sealed with black electrician\u2019s tape. The resistive voltage divider and filter capacitors are assembled directly on the PMT\u2019s tube socket.\"\"<\/p>\n\n\n\n

A word of caution: never expose the PMT\u2019s sensitive face to bright light! This will cause permanent damage to the tube, especially when the tube is powered. While not in use, our PMT is protected with a faceplate cap with an SM-2 series end-cap (Thorlabs model SM2CP2).<\/p>\n","protected":false},"excerpt":{"rendered":"

Let\u2019s do a back-of-the-envelope calculation of just how many photons are produced by a typical 60-W lightbulb: although we know that the filament acts as a blackbody, and thus produces a wide range of wavelengths, let\u2019s take 600 nm as an average for our quick estimate. The energy of a photon is E = hf = hc\/\u03bb, so the energy […]<\/p>\n","protected":false},"author":1,"featured_media":4171,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[512],"tags":[],"class_list":["post-4275","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-light-as-particles"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/bulb.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4275","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=4275"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4275\/revisions"}],"predecessor-version":[{"id":4281,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4275\/revisions\/4281"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4171"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4275"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4275"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4275"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}