The idea sounds like magic, pure and simple. You create a light beam that can make substances vanish, give them properties they shouldn’t possess, or turn them into a perfect mimic of another substance entirely. It’s 21st-century alchemy, in principle capable not just of making lead resemble gold, but of turning ordinary materials into superconductors.
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The general approach, developed over the course of decades, is to use tailored optical pulses to reshape the electron clouds of atoms and molecules. Earlier this summer, a team of researchers at Tulane University in New Orleans and their collaborators extended the idea. They figured out how to apply the pulse strategy to solids and bulk materials, rewriting the usual laws governing how their properties are dictated by their chemical composition and structure. Using quantum control, said Gerard McCaul at Tulane, “you can almost make anything look like anything.”
Meanwhile, other researchers have already used light pulses to conjure up superconductivity—the ability to conduct electricity without resistance—in materials that would not otherwise behave this way.
But perhaps the real potential of the technique doesn’t lie in enabling marvels of mimicry but in inducing other kinds of transformation. Light beams might be used to create optical computers powerful enough to solve difficult problems such as factorization. Chemical substances could become temporarily and selectively invisible, which would assist the analysis of complex mixtures. The theoretical possibilities seem limited only by our imagination. In practice, the limitations may stem from how well we can understand and control the interactions of light and matter.
A Plan for a Pulse
After the invention of the laser in the early 1960s, many researchers quickly realized that these devices could be used to manipulate molecules, since the molecules’ electron clouds feel and respond to the laser light’s electromagnetic fields, in which all the waves oscillate in step (that is, coherently). But to truly control something, you need to be able to prod or guide it on the timescale on which its trajectory changes—which is very fast for molecules and even faster for electrons. At first, laser pulses simply couldn’t be made short enough to deliver a sufficiently rapid sequence of nudges.
During the late 1980s and early 1990s, however, the pulse durations were brought down to as little as a few femtoseconds (a femtosecond is equal to 10–15 second), approaching the time frame of atomic motions. This enabled lasers to stimulate and probe those motions selectively. However, to actually control such movements, in the early 1990s Herschel Rabitz, a chemist at Princeton University, and his co-workers pointed out that one would need shaped pulses: complex waveforms that might guide molecular behavior along particular paths. That technology for pulse-shaping was, by good fortune, being developed at the time for optical telecommunications.
But the challenge is immense. To control the path taken by a macroscopic object—a glider, say—you need to know the trajectory that you’re seeking to modify. For a quantum mechanical system, the equivalent is to know how its quantum wave function evolves in time, which is determined by a mathematical function called the Hamiltonian. And there’s the rub—in all but the simplest systems, such as a hydrogen atom, the Hamiltonian becomes too complicated for researchers to calculate the dynamics of the wave function exactly.
In the absence of that knowledge—needed to calculate in advance what control pulse you need—the only alternative seemed to be trial and error: trying out some initial control pulse and then iterating it by running the same experiment again and again. It’s like a glider pilot learning to land by trying out random motions of the control stick and then gradually refining those movements after seeing what works.
That’s a lot more complicated (if less hazardous) for quantum systems than gliders. Shaping the pulse means adding more frequencies. The challenge is to figure out which combination of frequencies is needed. “It’s like a piano, but worse, because it had about 128 keys,” said Rabitz. (Today, pulse-shaping might involve a thousand or so frequency components.)
Now McCaul, working with Denys Bondar at Tulane and his colleagues, has described a theoretical scheme for calculating the required pulse in advance.
In quantum mechanics, a particular property of a substance—electrical conductivity, say, or optical transparency or reflectivity—corresponds to the average or “expectation value” of an observable quantity. If you have the wave function of a substance and you know what kind of light pulse you’re using, you can predict the result—the expectation value—you’re going to get.
Bondar’s team inverts the problem: You start with the outcome you want to achieve (the expectation value) and calculate the light pulse that will produce it. To do that, you also need to know the system’s wave function, or equivalently its Hamiltonian—which in general you don’t. But that’s OK, so long as you can identify a good enough approximation: a kind of “toy” wave function that comes close enough to capturing the important features of the real one.
In this way, the researchers figured out how to extend the methods from small collections of molecules, where there are just a handful of electrons to control, to large, bulky solids with a whole sea of electrons. “We look at the system as a cloud of electrons, and we start deforming the cloud,” said Bondar. The control pulse creates a kind of track that the electrons must follow, so the approach is called tracking control.
Christian Arenz, a theoretical chemist in Rabitz’s group at Princeton who is collaborating with Bondar’s team, explained that this approach makes it much easier to find the right control field for manipulating a substance’s properties. Previously, designing the control field was a matter of gradual, iterative improvement, but the tracking approach establishes “a new avenue for controlling many-body systems,” Arenz said. “I believe that this work will greatly inspire future control methods.”
To Reshape a Solid
Much of the early work on quantum coherent control focused (literally) on inducing well-defined changes in individual molecules—for example, selectively pumping energy into a given chemical bond to make it vibrate to breaking point, and perhaps thereby controlling the course of a chemical reaction. But manipulating many electrons coherently all at once in a material is a tougher challenge.
When atoms come together in solids, the outermost electron shells of neighbors overlap and form “bands” that extend throughout the material. The electronic and optical properties depend on the features of these bands. In metals, for example, the electrons with the highest energies occupy a band that is not filled to capacity, so the electrons can move throughout the atomic lattice, allowing the material to conduct electricity. In an insulating material, meanwhile, the highest-energy band occupied by electrons is entirely filled, so there are no “spaces” for these electrons to move into. They remain localized on their atoms, and the material won’t conduct.
More exotic types of electronic behavior can arise from quantum mechanical effects that make the electrons’ movements interdependent (that is, correlated), like the movement of groups of people in a crowd. In conventional superconductors, for example, the highest-energy electrons form correlated pairs (called Cooper pairs) that move in synchrony even though the two electrons might be some distance apart—like a person chasing another through a crowd. These Cooper pairs all behave identically, giving them an unstoppable momentum that enables a superconductor to conduct electricity without any resistance. It’s as if the electrons no longer notice the underlying lattice of atomic nuclei.
But what kinds of materials give rise to such properties? Usually in order to find them you need to go fishing in the sea of permutations of different elements. That’s very slow and labor-intensive—witness the huge amount of time and effort spent on developing new superconducting materials.
Imagine, though, that it’s possible to invoke a desired property in more or less any material by using light pulses to reshape the way the electrons are distributed. In this view, electron band structure is not something fixed by the material itself: The bands instead become a kind of putty that can be molded into whatever form you desire. Find the right control pulse and you might be able to join an array of mobile electrons into Cooper pairs, say, and thereby make a superconductor, perhaps from some humble substance such as iron or copper, under conditions in which it would otherwise be impossible.
This notion of using shaped laser pulses to specify and control the properties of materials has already borne fruit. For example, researchers have used it to switch materials between insulating and metallic behavior, to control magnetic properties, and to trigger superconductivity. The general idea is that the light pulses redistribute electrons among the energy bands in a way that tips the balance between one phase of the system and another—between a metal and an insulator, say. In this way, researchers have produced superconductivity at temperatures tens of degrees above the frigid extremes usually needed.
Yet despite its early promise, researchers caution that the experimental work is just getting underway. “Moving this research into the domain of extended solids, especially in the presence of strong [electron] correlation effects, is very much in its infancy,” said George Booth, a theoretical physicist at King’s College London who is collaborating with Bondar’s team. It remains to be seen, cautioned Arenz, to what extent their calculations for simple models of materials “can be generalized to other phenomena and systems.”
And no matter how successful the strategy is, these altered properties will persist only as long as you apply the control pulse. The remolded electronic structure won’t stay in place of its own accord, just as a piece of elastic won’t stay stretched if you don’t keep pulling. But for some applications—in electronic devices, say—that may not matter: You might be able to “write” the desired properties into the material only at the moment they are needed.
All That Can Be
You might object that the approach creates only superficial mimicry—the way some alchemists claimed to have “made gold” by applying some surface treatment to another metal that induced chemical reactions to gave the metal a golden sheen. That wasn’t gold in any real sense.
Bondar disagrees: The optically induced transformation, he said, “is really fundamental, actually.” To induce one type of alkali metal atom (like sodium) to optically mimic another (like rubidium), you have to use the control beam to manipulate the dipole moment of the atoms—the nonuniform way each atom’s electrical charge is distributed in space, which determines its interactions with the electric fields of light. “The dipole moment affects other things—including some chemical properties,” Bondar said. The transformation goes deeper than mere appearance.
This does not mean that would-be laser alchemists will have the ability to turn any substance into anything else, though. Michael Först, a physicist at the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg, Germany, thinks that it’s only feasible to induce behaviors that potentially exist already in the material under certain conditions. “We can’t mimic a response of a material if it doesn’t exist at all,” he said. “There has to be something in the equilibrium properties—maybe at a different temperature or pressure or in a magnetic field, say—where the material already holds the property you’re looking for.”
So rather than turning lead into gold, researchers are awakening a particular gold-like response from something that is and always remains lead. Light-induced superconductivity, then—which Först has studied experimentally—isn’t a matter of creating superconductivity from scratch, but of enabling it at higher temperatures than would otherwise be possible. “Our coherent control pulse just wakes it up,” he said. Först’s collaborator Michele Buzzi at the Max Planck Institute agrees. “You can access very fancy states using driving, but I wouldn’t go so far as saying you can take a material and make it something totally different.”
If that’s so, how far does the light-induced transformation actually go? Are you really making Cooper pairs in such a superconductor? That’s not yet entirely clear. Buzzi thinks that in their experiments “we are synchronizing Cooper pairs rather than creating them to begin with”—that is, allowing them to act in a concerted way to produce the superconducting state. “But we’re not completely sure about this,” he said.
Christiane Koch of the Free University of Berlin, who works on quantum control methods for many-particle systems, thinks that to truly change the material at a fundamental level, rather than getting it to superficially mimic a specific response, researchers will need to dig very deep into the electron clouds. That will require very intense control beams, so that the strengths of the electromagnetic fields involved rival the internal forces that shape the intrinsic electronic structure. Maybe it can be done, she said—but not easily.
Making Light of Hard Problems
Some potential uses of quantum coherent control don’t hinge on mimicry, but trade instead on the way it couples light and matter in a “designed” fashion. One such use is optical computing. Light beams are in principle great carriers of information for computing, said Bondar, not least because you can cram a lot of information into them by using many wavelengths at once. But the fundamental problem is that it’s hard to get two or more beams to talk to one another. Unlike electrons, Bondar said, “light hates to interact with light.”
Bondar’s tracking control scheme shows how that coupling could be achieved: with a piece of matter, in principle as small as a single atom, that is manipulated by a control beam. A second beam that contains incoming data then interacts with the matter. The interaction transforms the data to enact a computation. “This opens the way to single-atom computing,” said Bondar.
More strikingly, it might be possible to use this optical approach to solve difficult problems such as factorization much more quickly than classical electronic computers can. Bondar and McCaul believe it should be possible to implement a quantum factorization algorithm called Shor’s algorithm, one of the first to be proposed for quantum computers, using what amounts to just classical optics. “It’s too early to put classical computing in the dustbin of history,” Bondar said.
McCaul also hopes to use tracking control to analyze complex chemical mixtures—a problem often faced, for example, in drug discovery. Say you have a large mixture of different chemicals, he said. If you know each component’s spectrum—how it absorbs light of different frequencies to create a characteristic signature—then you can work out which compounds are in the mixture. “But the spectra can often be similar to each other, and so it becomes very hard if there are many components,” said McCaul. Tracking control could allow researchers to “turn off the optical response of each species one at a time,” he said, making them selectively invisible. McCaul has shown that in principle this could boost the discrimination between different chemicals by orders of magnitude.
Add invisibility, then, to the feats of optical alchemy that may be made possible by tracking control. In theory at least, it shows us that, seen in the right light, nothing may be quite what it seems.
Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.