Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

by Ananthaswamy, Anil

  But Aspect had some doubts. For one, he had yet to start on his PhD. Was this the right project for a doctoral thesis? Aspect went to CERN to meet Bell for advice, and Bell reassured the young Aspect that he was on the right track. But Bell also warned Aspect that the topic was considered by many as “crackpot physics.” Almost no one doubted the completeness of quantum mechanics. So why bother testing it? Bell, worried for the Frenchman’s career, asked Aspect if he had a permanent job. “I did. It was a small position, but it was permanent,” Aspect recalled telling Bell. “They could not fire me, I was sure to get a salary each month.”

  Aspect returned to France and embarked on an experiment that is now regarded as the first to all but rule out a class of so-called hidden reality theories. To accomplish his feat, Aspect developed the technology to generate single particles of light, or photons, which could be sent into his apparatus one at a time. The use of single photons caught Richard Feynman’s attention. In 1984, Aspect was invited to Caltech to speak about his tests of Bell’s theorem. Feynman was in attendance. “Everybody expected to see Feynman destroy this young French guy pretending to settle a question that didn’t exist,” said Aspect.

  During the Q&A session that followed Aspect’s talk, Feynman amiably asked if Aspect could use single photons to perform an older, more classic experiment in quantum mechanics, one that Feynman had highlighted in his own talks and lectures as one that best probed the mysteries at the heart of quantum mechanics: the double-slit experiment done with single particles. Aspect respectfully replied that a student of his, Philippe Grangier, was on the case back in Paris.

  From the time Young did his sunbeam experiment in 1801 and through the development of quantum mechanics, no one had actually done the double-slit experiment with single photons. Until Aspect came along, no one even knew how to generate single photons and be sure that there was only one photon in the apparatus at any given time. “Ordinary sources do not emit well-separated single photons. In a discharge lamp, in a bulb, or even in a laser, you have always zillions of atoms simultaneously emitting photons,” said Aspect. “As a result, what you get is an ensemble of photons, and this ensemble of photons has all the properties that can be described by classical electromagnetic waves.”

  For example, we now know that Geoffrey Ingram Taylor’s detection of interference fringes, which was done with light so faint that it was like placing a candle a mile away, was not the result of single photons hitting the photographic plate. Taylor used something called a coincidence detector, which requires at least four photons to hit the detector at the same time to create a signal big enough to be recorded.

  To appreciate how difficult it is to get photons one at a time from a source of light, consider this: you have a 100-watt lamp and you are monitoring the number of photons reaching a square opening, one centimeter to a side, placed one meter from the lamp. A rough-and-ready calculation (by Giancarlo Ghirardi in Sneaking a Look at God’s Cards ) reveals that about 24 million billion photons will pass through that one-square-centimeter opening every second. That’s 24 quadrillion photons. Getting single photons would require a technique substantially different from just turning down a lamp or dimming the light from a candle. Aspect developed such a technique. And when he carried out the double-slit experiment with single photons, classical physics had no say; only quantum mechanics could explain the results.

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  While single photons proved difficult to tame until Aspect came along, physicists weren’t biding their time, waiting for technology to catch up. There were other particles to work with. Recall that Feynman had focused on the double-slit experiment done with single electrons. He emphasized, however, that it was simply a thought experiment. In 1961–1962, Feynman gave a series of lectures to freshmen and sophomores at Caltech, which were published a year later as a three-volume set. In it, he said about single electron interference: “ This experiment has never been done in just this way. The trouble is that the apparatus would have to be made on an impossibly small scale to show the effects we are interested in.” Feynman had no way of knowing that the impossible had been accomplished in 1961—in Germany, the results being published in German.

  The 1961 experiment had its roots in work done by Gottfried Möllenstedt at the University of Tübingen. Möllenstedt invented a unique device to split a beam of electrons into two and then get them to interfere, analogous to Thomas Young using a thin card to split his sunbeam. The device is called an electron biprism. Möllenstedt came upon the idea accidentally. In the early 1950s, he was using an electron microscope, with a thin tungsten wire stretched across the objective lens of the microscope. Möllenstedt noticed that when the tungsten wire developed a charge, this caused two images to be formed, as if the microscope was seeing double. Möllenstedt realized that the charged wire was causing the microscope’s electron beam to part, creating the two images. Could such a charged wire be used to see interference fringes by splitting an electron beam and letting it recombine?

  Möllenstedt and his student Heinrich Düker took on the task. For a thin wire, they initially used gold-plated strands of spider silk (apparently, Möllenstedt “ kept a collection of spiders around the laboratory for this purpose”). Eventually, the duo figured out how to gold-plate quartz wires only about 3 microns in diameter (human hair, for comparison, is about 100 microns thick). They charged the wire by applying a voltage to it, and placed the wire in the path of a beam of electrons. The electrons, deflected by the wire’s charge, curved around the wire and eventually recombined. This was conceptually identical to a double-slit experiment: the electrons could take one of two paths, as they would if they encountered two slits.

  However, despite using “powerful optics,” the team did not see any fringes at first—they were just too small, just as Feynman had feared. But when they exposed a photographic plate to the electrons for 30 seconds and then looked at the photograph, using a powerful optical microscope, they saw “fine interference fringes.” This was in 1954. In a paper published soon after, in Naturwissenschaften , they compared their fringes to optical fringes seen earlier by the French physicist Augustin-Jean Fresnel. The journal’s editor, while praising Möllenstedt and Düker, also pointed out that “ Thomas Young had produced [such] . . . interferences ten years before Fresnel.”

  It’s easy to understate the importance of this work. Electrons—which are particles of matter—are producing interference fringes, which are a phenomenon associated with waves. This was exactly what Louis de Broglie had postulated in 1924: that matter, and not just light, exhibited wave-particle duality. Using nothing but the value of the voltage applied to the quartz wire, the geometry of the apparatus, and the observed fringes, Möllenstedt and Düker proved correct de Broglie’s formula for matter waves, which says that the wavelength of a particle, λ , equals Planck’s constant, h , divided by the particle’s momentum, p (so λ = h/p ). The equation is audacious: the left-hand side deals with the properties of waves, and the right-hand side with properties of particles. You couldn’t ask for a more succinct expression of wave-particle duality. Möllenstedt wrote to de Broglie, and de Broglie replied, “ It was . . . a great pleasure to see that you have obtained a new and particularly brilliant proof of the formula.”

  Möllenstedt’s young German student, Claus Jönsson, watched these experiments being done. By 1961, Jönsson performed a formal double-slit experiment with electrons, the same year that Feynman started talking of his thought experiments at Caltech. Jönsson wrote up his reports in German; it’d take years for the work to be translated into English, explaining why Feynman continued to regard it as an experiment in thought only.

  But these experiments thus far were done with many electrons passing through the double slit (or passing by the charged wire) at the same time. The experiment with single electrons took somewhat longer. And different teams claim the credit for pulling it off: one in 1974, and the next in 1989. Conceptually, the experiments were similar to Möllenstedt and Düker’s, e
xcept for the guarantee that only one electron was going through the apparatus at any one time (whether this actually happened is the source of dispute between the two teams).

  In 1974, Italian physicists Pier Giorgio Merli, GianFranco Missiroli, and Giulio Pozzi in Bologna, Italy, recorded on a television monitor the arrival of the electrons after they had gone past the biprism. To observe the interference pattern with the naked eye required some fancy optics that magnified the fringes a few hundred times. The Italians also had to develop technology for “storing” the electrons that arrived at the monitor for a few minutes so that one could see the fringes once all the electrons had been collected—otherwise the spot created by the first electron would have long vanished by the time the last electron arrived. The team made a 16mm movie of the fringes taking shape on the monitor; the movie even won an award at the Seventh International Scientific and Technical Movie Festival held in Brussels in 1976.

  In 1989, Akira Tonomura and colleagues at Hitachi in Japan did a similar experiment, with an extremely well controlled source of electrons. Tonomura’s team also created technology to record electrons on a screen the way one can record particles of light on a photographic plate: one by one, to build up an image over time. This way, they didn’t have to store the first electron until the last one arrived. The Hitachi team’s film of the electrons hitting the screen (the actual elapsed time was twenty minutes, but the film is sped up) is one of the most fascinating short films in the history of physics. Electrons appear as dots on the screen, seemingly at random, but soon enough the fringes build up, a magical demonstration of single-particle interference. The movie belies the challenge the experimenters faced: the entire equipment, including the electron source and the biprism, had to be held unerringly stable the entire time; had anything moved even fractions of a micron, it would have destroyed the fringes.

  A little over a decade later, Physics World published an article to celebrate the fact that the double-slit experiment done with single electrons was voted “the most beautiful experiment” in physics. It failed to mention the 1974 Italian effort, prompting a letter of protest from the Italian team. Physics World updated its article, including the Italian team’s letter and Tonomura’s reply arguing for the Japanese team’s place in history: “ We believe that we carried out the first experiment in which the build-up process of an interference pattern from single electron events could be seen in real time as in Feynman’s famous double-slit gedankenexperiment . This was under the condition, we emphasize, that there was no chance of finding two or more electrons in the apparatus.”

  There is, however, no doubt about who was the first to test the double slit with single photons.

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  The double-slit experiment that Aspect and Grangier did in Paris starts with a piece of glass that reflects half the light that falls on it, and transmits the other half. This is actually a fairly common occurrence with glass. Think of sitting in a train that’s racing through the countryside at night. If it’s completely dark outside and you are looking at the windowpane, you will see the inside of the carriage reflected in the glass. But when the train passes by some lighted buildings outside, you see the buildings while simultaneously seeing your own reflection in the glass. The windowpane is both reflecting and transmitting light. In labs, such glass is called a beam splitter or a half-silvered or semi-transparent mirror (albeit the glass does its job far more precisely than your average windowpane), and as the name suggests, it splits a beam of light into two. Half the energy of the wave is reflected and half is transmitted.

  Something funny happens when the incident light is made of just one photon, the smallest indivisible unit of light. It can’t be split further into two halves. So the incident photon will be either transmitted or reflected as one whole. Let’s put photon detectors D1 and D2, one at the end of each beam. Since the photon travels undivided, if the photon is reflected, then D1 clicks, and if it’s transmitted, D2 clicks. Both detectors never click at the same time: the photon does indeed behave as an indivisible unit of energy.

  Turns out that if you send lots and lots of photons, one at a time, into the beam splitter, then on average, half the time D1 will click, and half the time D2 will click. There’s an important observation here that will become more and more relevant: one can never predict with certainty what a given photon will do. For each photon, we can assign only a probability for the outcome—it’ll either go to D1 with probability of 0.5 or to D2 with a probability of 0.5.

  The immediate reaction to this from our classically attuned minds is to say, well, the fact that we can’t predict what the photon will do must have something to do with our lack of knowledge about the complete state of the photon. It was a similar argument that initially prompted Einstein to think that there must be some hidden variables.

  For example, when we flip a coin, we assign a probability of one-half to the outcome that it’ll land heads, and one-half that it’ll come up tails. But the reason we cannot predict with certainty whether a coin will come up heads or tails is because we don’t know everything there is to know about the coin’s initial conditions (the angle at which it’s flipped, the initial velocity, etc.); if we had full knowledge of the initial conditions, knowledge that could be encoded with additional variables, we could in principle predict the outcome.

  Could something similar be at work with the photons? What if there were some attributes of the photon that weren’t being captured in the mathematical formalism? And if we knew the values of these hidden variables, then could we not predict with certainty what each photon would do?

  Putting aside concerns about hidden variables for now, let’s make the experimental setup a bit more interesting. Let’s put fully reflecting mirrors in the paths of the beams so that the beams are turned at right angles, toward each other. D1 and D2 are still at the ends of these beams. What can we expect if we send tens of thousands of photons, one at a time, into the apparatus?

  Well, nothing different. All we’ve done is increase the distance traveled by the photons, but nothing else has changed. So D1 still clicks half the time, and D2 half the time.

  To complicate things further, let’s add a second beam splitter, exactly at the point where the paths of the two beams cross. Now, a photon reaching the second beam splitter will be either reflected or transmitted.

  Based on what we know, we can analyze what’s expected of each photon that enters the apparatus. A photon that’s reflected by the first beam splitter and then transmitted by the second beam splitter ends up at D1. Let’s call this photon rt . The photon that’s transmitted first and reflected next also arrives at D1. This photon is tr . So photons that take the paths rt and tr reach D1. Similarly, rr and tt end up at D2.

  What happens then, if we send 10,000 photons, one at a time, into the apparatus? We know from previous experiments that half of the photons would be sent one way by the first beam splitter and half the other way (speaking always, on average). So 5,000 photons would take path R and 5,000 would take path T (the fate of any given photon, however, is still not for us to predict with certainty). At the second beam splitter, the 5,000 that took path R should be split in half again; 2,500 should go to D1 and 2,500 should go to D2. The same analysis holds for the 5,000 photons that took path T. Total them up and our naive but perfectly logical conclusion is that 5,000 photons should reach D1 and 5,000 should reach D2.

  By now, if our minds are getting used to quantum strangeness, we shouldn’t be surprised to learn that that’s not what happens. Adding the second beam splitter has profound implications. Before the second beam splitter was in place, it was clear when D1 clicked that the photon had come through path R, and if D2 clicked, the photon came via T. Now, with the two beam splitters in place, a photon reaching D1 could have taken either path rt or tr , and a photon reaching D2 could have taken either path rr or tt . If you detect a photon at D1, there’s no way to tell which path it took. The same goes for a photon detected at D2. The two paths, for any given photo
n, have become indistinguishable. This is exactly what happens in a double slit. Once a photon lands on the far screen, there’s no way to tell which slit the photon came through. If nothing about the experimental setup makes the photon take one or the other path, the mathematical formalism says that it takes both paths, in a manner of speaking. Now that we know as much, can we figure out what happens to the 10,000 photons?

  The clue is in the name of the apparatus sketched above. It’s called a Mach-Zehnder interferometer, after Ludwig Mach (son of the physicist Ernst Mach) and Ludwig Zehnder. In 1892, Mach improved an instrument that Zehnder had designed a year earlier for optics experiments (they weren’t thinking of single-particle quantum mechanics at the time). The Mach-Zehnder interferometer is a special case of a double-slit experiment. Light can take one of two paths (analogous to going through one slit or the other) and then interfere when the paths recombine in the second beam splitter (or at the location of the screen in the case of the classic double slit). Conceptually, anything you can do with a classic double slit, you can do with a Mach-Zehnder interferometer: modern experimental physicists, when they say they are performing a double-slit experiment, are in all likelihood using this interferometer. It’s an experimentalist’s delight. “It’s just smarter,” Aspect told me.

  Why interference happens, especially when we send one particle at a time into the apparatus, is a curious phenomenon. It’s exactly what Aspect and Grangier studied when they built such an interferometer.