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

by Ananthaswamy, Anil

  When these molecules leave the source, they have a temperature of about 220 Celsius—which would kill a cat.

  Cats or molecules, the task is to put the wavefunction of the macroscopic object into a superposition of states. In this case, to first get each molecule’s wavefunction on the same page, the beam has to be collimated in both the horizontal and vertical directions, which simply involves letting the molecules pass through narrow openings and selecting only about the one in ten million that make it through. Now, the molecules are moving in a narrow beam, but they still might have very different velocities, and hence different wavefunctions. So the molecules are further filtered—they have to go through three narrow slits that are placed at different distances and heights, such that a trajectory that passes through these three slits traces a parabola. Imagine throwing a ball. It’ll travel in a parabolic arc, the shape of which will depend on the speed at which you throw the ball. Or inversely, for any given parabolic arc, all balls with that trajectory have the same speed. Arndt and colleagues took advantage of this simple fact. They arranged the three slits so that all the molecules that get through them would follow the same parabolic path, and so have a definite velocity when they exit. Now they had a collimated beam of molecules with similar velocities (within about 10 to 15 percent of one another)—and hence similar wavefunctions.

  There was another big hurdle to cross to get these molecules to interfere. For a particle to be in a superposition of going through both paths, its wavefunction has to spread out enough to span two slits. For the kinds of distances traveled on laboratory benches, this is not an issue for particles such as photons and electrons. But not so for a molecule: it’d have to travel a long distance for its wavefunction to spread out enough, making for an impossible experiment. So Arndt’s team deployed a trick. They made the molecules first confront an array of extremely narrow single slits. This causes diffraction at each of these slits, and the wavefunction starts spreading rapidly on the other side of each slit. Now when the wave front reaches a grating with multiple slits not too far away, it’s wide enough to encounter at least two slits at the same time and enter into a superposition. To get a sense for just how small the dimensions involved are, the two slits are only 266 nanometers across (about a hundred thousand times smaller than the width of a human hair). To ensure that the molecules have a chance of hitting the slits (there’s no way to steer them precisely to any one location), the team illuminates a multi-slit grating with a molecular beam just one millimeter across that spans about 4,000 slits. Any one molecule’s wavefunction will hit only two adjacent slits out of these 4,000—so effectively, each molecule sees only a double slit.

  One final challenge remained: detecting where the molecules land after crossing the double slit. With a photon, this is relatively easy. A photographic plate can register a hit. Molecules are lumbering beasts compared to photons. “If they [land] onto a surface, they start rolling around, and if they do that, they smear the interference pattern,” said Arndt. “So you have to make sure that the molecules are bound, wherever they hit the surface.”

  This meant designing special surfaces to capture molecules and make them stick the landing. One solution the team came up with was something called reconstructed silicon, which is essentially ultra-pure silicon with naked chemical bonds on the surface, like so many arms waiting to entrap molecules. The giant molecules land on the silicon surface and bond. Over time, these molecules pile up at various locations along the silicon screen.

  But unlike a photographic plate, the pattern made by the molecules is not visible to the naked eye. Arndt’s team had to study the surface using a scanning electron microscope—and what they saw was an interference pattern. Molecules amassed in areas that made up bright fringes, with fewer in locations that made up the dark fringes.

  It’s worth reiterating that the molecules are not interfering with each other. This is single molecule interference: in the language of standard quantum mechanics, each molecule ends up in a superposition of going through two slits at the same time, and these two states interfere, causing the molecule to go to locations that end up as bright fringes and avoid places that become dark fringes.

  “This is the most pictorial representation of the weirdness of quantum physics, that you can see things [behaving] as if they were in various places at the same time,” said Arndt. “Of course, it gets more and more counterintuitive, at least psychologically, if things become bigger and bigger and more complex internally. It relates to the question: why can I not be in two places at the same time?”

  The ambiguous language that’s needed to talk about what’s happening is not surprising. The molecules are particles, individual “things,” and yet the experiment has to acknowledge not only their de Broglie wavelengths but also each molecule’s wavefunction, and the spreading out of the wavefunction. Treating molecules as real particles, with real trajectories, while a wavefunction is going through both slits, has Bohmian overtones.

  “To be honest, if you are looking at [these] matter waves, occasionally you think as a Bohmian. It’s very hard to avoid,” Arndt said. “When we describe our interferometers, we are always thinking of the entirety of the particle, its mass, electrical properties, and internal dynamics, etc. Whenever it interacts with a grating, it’s always there as an entire particle and yet it must have had information about several slits, somehow. In this context, it’s more intuitive to think there’s a pilot wave driving the particle around. That fits most nicely with Bohm’s theory.”

  But thinking in Bohmian terms is not the Viennese way. “Vienna does not have a tradition of appreciating the role of the de Broglie-Bohm mechanics,” Arndt told me. No wonder, given that the patriarch of the Viennese school of quantum mechanics, Anton Zeilinger, is a strong non-realist in the tradition of Niels Bohr and the Copenhagen school of thought.

  Arndt is quick to point out that despite his tendency to think in Bohmian terms for matter waves, he’s a non-realist when it comes to the dynamics of the internal states of molecules, in that these states don’t exist until we measure them. Besides, what he’s really after is to discern if there is a quantum-classical boundary that’s predicted either by Penrose’s gravitational collapse theory or by any of the many flavors of the GRW collapse theory. Neither prediction, unfortunately, is within easy reach. Arndt recalled the early days of the GRW theory, when it was thought that molecular interferometers would see collapse and hence find the boundary between the quantum and the classical, with molecules at about 109 , or a billion, atomic mass units. Experimentalists could dream of testing the theory. Subsequently, some theorists revised the target to about 1016 atomic mass units, making the theory extremely difficult to falsify. “Theorists have a simple life,” said Arndt. “They can change their parameters.”

  Life isn’t as simple for experimentalists. If the molecules get bigger, they have to be made to move slower; otherwise their de Broglie wavelength will get so small that it’d be impossible to make fine-enough slits to see interference. And even if they could figure out how to make molecules fly slowly, there’s yet another problem to confront. Slower molecules will take longer to get through the double-slit apparatus, and when the molecules are in flight for longer, Earth’s rotation starts becoming an issue. The molecules are flying straight through the vacuum, decoupled from everything, and if their time of flight is more than a few seconds, the vacuum chamber and the gratings would have moved enough due to Earth’s rotation that the entire experiment goes out of alignment.

  Arndt’s calculations show that they can experiment in their lab with molecules of up to 108 atomic mass units, which is about 10,000 times more than the current record. They are even experimenting with sources of biological samples, like the tobacco mosaic virus, which has a size of about 107 atomic mass units. That’s “in the range of what you could do in our lab, hypothetically,” said Arndt. But the viruses haven’t cooperated. “We had many different efforts to launch them and each time they broke apart.”<
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  One way to go to bigger masses is by using metal or silicon nanoparticles. Experiments with larger particles would need to negate the effect of Earth’s gravity and hence would have to be done either in space (a very expensive proposition) or more likely in a drop tower, a special tower from which enough air has been pumped out to let objects free-fall without any air resistance, effectively mimicking conditions in outer space for a few seconds. There’s a 146-meter-high tower in Bremen, Germany, built specially for such experiments. In principle, a fully sealed vacuum chamber that encapsulates the double-slit experiment can be dropped down the tower, and during free fall—for about 4 seconds—the molecules and the experiment won’t experience Earth’s gravity, and thus everything would remain in alignment.

  While verifying collapse theories with such experiments remains a distant dream, Arndt hasn’t ruled out seeing modifications of the established evolution of quantum systems at mass scales smaller than predicted by either Penrose’s or GRW-like theories. “The experimentalist in me says, ‘Well, who knows?’ The models are made up by clever people and nobody knows whether they are true. It may well be that something happens well before. No one knows. So one should just do the experiments, see what happens.”

  If nothing happens—meaning molecules remain in superposition and their coherence is preserved—then it’s telling us that there is no quantum-classical boundary, at least at the mass scales being probed by the experiment. On the other hand, “if [coherence] is not preserved, it’s a major discovery,” says Arndt. “In either case, you win.”

  —

  It may prove impossible to do the classical double-slit experiment with molecules large enough to find evidence for collapse, especially at the mass ranges predicted by Penrose’s theory. But what if an element of the experimental apparatus itself can be put into a superposition of states? Besides having a photon go through one arm or the other of a Mach-Zehnder interferometer, what if one of the mirrors used in the interferometer could be made small enough to be put into a superposition of being at one place or another. It’s analogous to putting one of the slits in the double-slit experiment—which we have until now considered to be a macroscopic, classical, and immovable part of the apparatus—into a superposition of two positions. This would have a very strange impact on the photon going through the interferometer. Not only is it confronting two slits at once, but it’s as if one of those slits is itself in two different positions. It turns out that this type of interferometer is ideally suited to testing Penrose’s collapse theory.

  Dirk Bouwmeester, a Dutch experimentalist, has been working on one such experiment for more than a decade, an idea first suggested to him by Penrose himself. When Bouwmeester was working on his PhD in the Netherlands, he became interested in certain solutions of Maxwell’s equations of electromagnetism, in which light goes around in knots. He realized that what he was studying was closely tied to Penrose’s work on twistor theory (one of Penrose’s signature contributions to theoretical physics). In twistor theory, the most fundamental things in nature are not particles but rays of light, or twistors. Bouwmeester was still a student when Penrose came to the Netherlands to give a talk. Bouwmeester nabbed him afterward to discuss twistors. Penrose was getting ready to leave and suggested Bouwmeester come with him to the airport and they talk on the way. As it happened, “it was terribly bad weather and the flight was delayed, and we ended up talking a bit longer. That was the first time I met him,” Bouwmeester told me.

  That interaction led Bouwmeester to apply for a postdoc at Oxford University. After a year studying twistor theory at Oxford, Bouwmeester moved to Innsbruck, Austria, to work with Zeilinger on quantum teleportation and entanglement. With that experience in hand, Bouwmeester came back to Oxford to set up his own quantum optics laboratory. It was during this second stint at Oxford that Penrose walked into his lab one day and said: “I have this experiment that we need to do.”

  It was the strangest thing. Penrose had plans for doing an interferometry experiment in space, which involved three satellites. It goes something like this. On one satellite, “A,” you first send an X-ray photon through a beam splitter. The photon ends up in a superposition of being reflected and transmitted. The reflected photon is sent on its way to another satellite, “B,” about ten thousand miles away. The transmitted photon, which is still on satellite A, goes toward a tiny mirror. The mirror is attached to a cantilever, so that it can move if something hits it. The mirror is so small, and the X-ray photon has so much energy, that even as the photon impacts the mirror and is reflected at right angles, it displaces the mirror a smidgen. This photon too is now sent off toward another satellite, “C,” which is a similar distance away from A as is B (note that technically it’d be quite easy to have satellites B and C combined into one satellite; it’d make the experiment cheaper too).

  Quantum mechanics says that the photon is in a superposition of taking two paths. Not just that, the tiny mirror is also in a superposition—of being displaced or not-displaced, of being in two locations, barely about 10-13 meters apart, about halfway between the size of an atomic nucleus and the atom itself (the precise displacement depends on the type of mirror and cantilever).

  The photon paths reach the two satellites, each of which has a rigid mirror that bounces the photon right back to the first satellite. The photon bounced off satellite B comes back to the beam splitter. The photon bounced off satellite C, before it can reach the beam splitter, has to again encounter the mirror that it had previously displaced. The distance between the satellites and the stiffness of the cantilever is set such that the moving mirror is back to its original position at exactly the same time the returning photon encounters it. The momentum from the mirror is transferred back to the photon, reflecting it at right angles toward the beam splitter. The mirror goes back to being at rest.

  The two photon paths are designed such that the reflections from satellites B and C both reach the beam splitter at the exact same instant. So if the photon is still in a superposition of having taken both paths, then the two paths will constructively interfere, and the photon will exit the beam splitter toward detector D1. Crucially, the photon will never exit toward detector D2, because that direction represents destructive interference.

  If this is awfully reminiscent of interference in a Mach-Zehnder interferometer, that intuition is not off the mark. This is yet another way to make two paths that light can take interfere: this particular arrangement is called a Michelson interferometer (with a tiny Penrose variation thrown in—the movable mirror).

  Okay, so why go to all this trouble? Why all the fuss about using satellites in space? For one, the vacuum of space ensures that there is very little chance of the photon or the mirror hitting stray particles, an interaction that will lead to decoherence and loss of superposition. Also, the vast distances between the satellites ensure that the photon remains in superposition for a long enough time. This long so-called coherence time is necessary to test Penrose’s ideas.

  According to Penrose, the size of the tiny, movable mirror makes all the difference as to whether or not the photon ever goes to detector D2. When the photon is in a superposition of heading toward satellites B and C, the mirror is in a superposition of being displaced and not-displaced. Penrose’s gravitational collapse theory says that the higher the mass of the mirror, the faster it’ll collapse into one position or the other.

  Let’s say that the collapse never happens in the time it takes for the photon to return to the beam splitter and hit one of the detectors. In that case, the photon will come back in a coherent superposition of having taken two paths and hit detector D1.

  But if the mirror’s quantum state were to collapse before the photon reaches the detectors, then the photon will also collapse into having taken one path or the other. That’s because the wavefunctions of the mirror and the photon are entangled, and their fates are tied up with each other. If such a collapse happens when the photon is still en route, then the photon will ar
rive at the beam splitter having taken one or the other path, not in a superposition of having taken both paths. It acts like a particle. There is no interference. So the photon has an equal chance of going to D1 or D2.

  For a given mass of the mirror, if you did this experiment a million times, and the photon always went to D1, then you can say that the mirror never collapsed. But if half the time the photon ended up at D2, the mirror has collapsed in each run of the experiment. This becomes a way to verify Penrose’s ideas of the collapse of macroscopic objects due to gravity—and find the mass scale at which collapse happens.

  When Penrose walked into Bouwmeester’s lab, he was keen on actually doing this experiment in space. He knew people at NASA; he thought they could pull it off. Bouwmeester had to bring the discussion back down to Earth. “My initial reaction was—it’s a very interesting problem to work on, but my expertise is in optics,” Bouwmeester told me. “Let’s see if we can design something that fits on an optical table.”

  And they came up with a solution, with help from a talented postdoc named Christoph Simon and a gifted PhD student, William Marshall. Sitting in his office at the University of California, Santa Barbara, in 2017, Bouwmeester showed me a picture taken in 2001 of the four of them standing in front of an optical bench. “That’s me,” said Bouwmeester, pointing to a youthful version of himself. And pointing to Penrose, he said, “Roger doesn’t change, but I do.” Indeed, Penrose looked no different from when I met him more than fifteen years after the picture was taken.