Quantum Erasure In quantum mechanics, there are two sides to every story, but only one can be seen at a time. Experiments show that “erasing” one allows the other to appear Stephen P. Walborn, Marcelo O. Terra Cunha, Sebastião Pádua and Carlos H. Monken n 1801, an English gentleman scholar With his “slip of card,” Young set off Recently, physicists have started to Inamed Thomas Young performed a revolution in physics whose ripples shed some light on this mystery through one of the most celebrated experiments are still being felt today. His experi- the demonstration of quantum erasers— in the history of physics. Here is how ment is now a staple of freshman in which one can actually choose to turn he described it two years later, in a lec- physics laboratories, though it is now the interference fringes on or off. Our ture for the Royal Society of London: typically performed with two slits group has constructed a quantum eraser etched into a piece of opaque micro- using a more elaborate version of I made a small hole in a window film. (Thus the name, “Young’s double- Young’s experiment and used it to shutter, and covered it with a slit experiment.”) The phenomenon he demonstrate, in principle, the idea of thick piece of paper, which I per- had observed, called interference, can be “delayed choice,” in which the experi- forated with a fine needle.… I demonstrated easily enough with menter can make the decision after the brought into the sunbeam a slip of waves in a tank of water. Thus, by particle has been detected. The delayed- card, about one thirtieth of an inch analogy, Young’s experiment seemed choice experiment almost sounds like al- in breadth, and observed its shad- to prove that light is made up of tering the past. Lest any readers get ideas ow, either on the wall, or on other waves, as Dutch physicist Christiaan of building a “wayback machine,” we cards held at different distances. Huygens had advocated. But that was will explain why quantum erasers don’t What Young saw on the opposite not the end of the story. really change history. But we do believe wall was not, as one might guess, a In the early 1900s, physicists discov- that they clarify how interference phe- single thin shadow, but instead a ered that light does behave in some nomena arise in quantum mechanics. whole row of equally spaced light and ways as if composed of particles. In dark stripes or fringes, with the central particular, there is a smallest “quan- The Quantum Coin Toss band always bright. When he blocked tum” of light, called a photon. In 1909, The appearance of interference fringes the light on one side of the card, the Cambridge physicist Geoffrey Taylor in the classical double-slit experiment fringes went away. He concluded that repeated an experiment similar to is well understood. According to the light from both sides of the card was Young’s, which showed that individ- wave theory of light, when two beams required to make the pattern. But how ual photons suffer another interference of coherent light with the same wave- could two rays of light combine to phenomenon, called diffraction. By length encounter each other, they com- make a dark fringe? And why was the dimming the light until only one pho- bine. The most extreme situations are center of the shadow always bright, ton at a time reached the screen, he constructive interference, in which the instead of dark? This was hard to fath- eliminated any possibility that the pho- waves reinforce each other, or destruc- om if light was made of particles that tons could interfere with one other. Yet tive interference, in which they cancel traveled always in straight rays, an after recording the results of many each other out completely. idea that was shared by many physi- photons, Taylor found the same pat- In Young’s experiment, the paths cists, including Isaac Newton. tern of diffraction fringes. Apparently, from each slit to a given observation then, an individual photon could “in- point are not necessarily equal in terfere with itself.” length. When they are equal—that is, The authors perform research in quantum optics at And it wasn’t just photons. Other when the observation point is centrally the Universidade Federal de Minas Gerais (UFMG) objects that seemed indisputably “par- located between the slits—the waves in Belo Horizonte, Brazil. Stephen P. Walborn is ticle-like,” such as electrons, neutrons arrive in phase and interfere construc- nearing the end of his doctoral research in quantum and even molecules of carbon-60, the tively. That explains why Young al- optics. Marcelo O. Terra Cunha is a graduate student buckyball, have subsequently demon- ways saw a light band in the center of in physics and assistant professor of mathematics. Se- strated the same wavelike behavior. his card’s “shadow.” On either side of bastião Pádua and Carlos H. Monken are adjunct professors at UFMG and head researchers in the ex- The self-interference of individual par- this central band lies a region where perimental quantum optics group. Walborn’s ad- ticles is the greatest mystery in quan- one wave has to travel exactly half a dress: Departamento de Física, UFMG, Caixa Postal tum physics; in fact, Nobel Prize laure- wavelength farther than the other. 702, Belo Horizonte, MG 30123-970, Brazil. Inter- ate Richard Feynman pronounced it There the waves interfere destructively net: [email protected] “the only mystery” in quantum theory. and a dark band appears. Next comes © 2003 Sigma Xi, The Scientific Research Society. Reproduction 336 American Scientist, Volume 91 with permission only. Contact [email protected]. Figure 1. In a modern version of Thomas Young’s double-slit experiment, a helium-neon laser illuminates a piece of microfilm, into which two slits are etched 0.1 millimeter apart. Next, the laser beam passes through a divergent lens (center), which spreads it out so that the interference fringes produced by the double slits can be seen more readily on the screen at the back. Young’s 1801 experiment used much more humble equipment: sunlight, a pinhole to make the light coherent, a card to split the beam and no divergent lens. Even so, he was able to discern at least five bright bands on the far wall. (Photograph courtesy of the authors.) a region where one wave travels exact- 2, and we find, say, that 5 percent of the root of –1), not a positive real number. ly one wavelength farther than the oth- photons pass through slit 1 and trigger Thus two nonzero probability ampli- er. Here there is once again construc- the detector. So Prob (slit 1) = 5 percent. tudes (say, 0.1 + 0.2i and –0.1 – 0.2i) can tive interference and a band of light. Next we block slit 1 and find that 5 per- add to zero, which is never true of clas- To understand why quantum inter- cent of the photons pass through slit 2 sical probabilities. ference is unexpected, it may help to and trigger the detector: Prob (slit 2) = 5 Philosophically, the meaning of draw an analogy to a coin toss. If it is a percent. Now when we uncover both probability amplitudes is still a great fair coin, the probability of getting slits, creating two possible routes, we mystery. Clearly, though, a “quantum heads is 50 percent and the probability would expect to detect 10 percent of the coin” does not work the same way as a of getting tails is also 50 percent. The photons. But no! Because we placed the classical coin. Thanks to the superposi- probability of getting heads or tails is detector in a dark fringe, we can run tion principle, a photon, our “quantum the sum of the individual probabilities: the experiment for hours and not see a coin,” can give a combination of both single photon. That is, heads and tails. Prob (heads or tails) = Prob (heads) + Prob (tails) = 100 percent Prob (1 or 2) = 0 percent ≠ Matter Waves Matter Prob (1) + Prob (2) Now consider a quantum “coin toss” If all of this sounds pretty unbelievable based on Young’s experiment. We send The mind-bending explanation that to you, then you are in good company. a beam of light at the double-slit appa- quantum physicists have found for this Even the originators of quantum ratus, and put a photodetector a certain behavior is the principle of superposi- physics struggled with its concepts, distance away on the other side. To tion, which says that wavelike events and some of them never accepted the dramatize the paradox, we place it in combine according to a probability am- theories they were forced into. The the middle of a dark interference fringe. plitude rather than a probability. Math- German physicist Max Planck, who, in Now, we turn down the light so that ematically, a probability amplitude is a 1900, was the first to propose that light only one photon at a time passes complex number (that is, a number like behaved as if it were made up of quan- through the slits. First we cover up slit 0.1 + 0.2i, where i denotes the square ta, envisioned this only as some sort of © 2003 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2003 July–August 337 a constructive interference b constructive destructive + destructive interference + slits screen c 200 photons 6,000 photons Figure 2. Physicists normally explain Young’s interference fringes with the wave theory of light (a).