When I turn up to work, I sometimes describe myself as a surface scientist. It isn't entirely true, but a large part of my work focuses on surface physics and why things stick (or not) to surfaces. But surface physics is really messy, and all sorts of different physical effects play roles at different length and time scales. This makes it difficult to create a clear picture of where and when specific aspects of physics are important.
One particularly messy corner of this de facto teenage bedroom is the Casimir effect. The Casimir effect describes how two apparently neutral metal plates will have an electromagnetic attraction to each other if they are close together. Now, a group of physicists has used a very clever experiment to measure the Casimir effect's little brother, the Casimir-Polder interaction. Even in this early iteration, their technique is quite sensitive, and it may be the first step toward a new kind of surface imaging technique.
Understanding the Casimir effect
Just to confuse you, let's consider two explanations for the Casimir effect. Both will be a little bit wrong, but they both offer some useful insight. On the classical side of physics, think of the Casimir effect as due to charge oscillations in the metal. In a metal, there is a sea of electrons that slosh about. On average, the plate is neutral, but at any instant in time, the electrons are unevenly distributed, so the plate has a net positive charge in some locations and a net negative charge in other locations.
If we place a second metal plate close by, the electrons in that plate will respond to this slight charge imbalance by mirroring. Wherever one plate has a slight negative charge, the other plate has a small positive charge. Since opposite charges attract, the resulting force tries to pull the plates together. Although this is a useful picture, it is wrong. The more accurate picture is given by quantum mechanics.
As we've mentioned before, the vacuum is not a vacuum. Instead, it teems with virtual particles that pop in and out of existence continuously. But this process is not entirely random. Imagine that you are a photon about to pop into existence between two metal plates. To come into existence, this photon must meet a specific requirement: the electric field that generated it must be zero at each plate.
This is just like plucking a guitar string. The wave motion of the string cannot include motion at the ends of the string because the ends are held fixed. This limits the sound frequencies that the string can produce. Likewise, the metal plates provide lots of free electrons that keep the electric field zero in the plate. So a photon that bounces back and forth between these two plates has to have a wavelength that also keeps the electric field zero in the plate.
On the outside of the plates, there are no such restrictions. As a result, the number of particles generated outside the plates is larger than the number generated between the plates. When two plates are close together, the number of photons generated between the plates is much smaller, meaning there is a small net force on the outside, driving the two plates together.
The force due to the Casimir effect is very small, but thanks to the ever-reducing size of mechanical devices, it has become an important consideration in design work. Likewise, the physics and chemistry of a single atom approaching a metal surface has its own version of the Casimir effect, called the Casimir-Polder force. In this case, the classical description is much more useful.
As the atom approaches the surface, the outer electrons of the atom repel the electrons in the metal. This creates a small net positive charge in the plate's surface. That, in turn, distorts the electron orbitals of the atom, creating a net negative charge on the surface side of the atom (it can also happen in the reverse manner). This sets up an attractive force between the atom and the surface.
Measuring this force is challenging. The problem is that, once the atom is really close to the surface, there is a lot of different physics at play, and separating individual effects out is nearly impossible. Instead, you want to measure the Casimir-Polder force at a distance from the surface, before the other, shorter-range forces start to dominate.
To do this, a team of researchers performed a very clever experiment. They produced a metallic grating structure on a glass surface (a grating just means that the metal surface is broken up into stripes). The researchers then dropped a Bose Einstein condensate (BEC) made of rubidium atoms onto the surface. The BEC is a very cold gas of atoms, so cold that the wave-like nature of the atoms dominates over their particle-like behavior (see sidebar).
Bosons, on the other hand, constructively interfere with each other. The interference between the wave functions makes it favorable for them to occupy the same state. As the population of bosons in a state increases, the wave function value gets higher, so new bosons quickly enter the new state in a self-reinforcing process, hence condensation and BEC.
Once a BEC has been generated, the atoms must be considered as extended, wave-like objects. But the BEC itself is still much larger than the individual bosons that make it up. So, if we divide a BEC in two and force the two halves to travel different distances before mixing them back together again, the two wave functions will mix and interfere with each other, creating locations where the probability of finding individual atoms is very high, and others where it is zero. When we image the BEC, we find bright and dark stripes that look exactly like interference from two light waves.
By itself, using a BEC and a grating structure doesn't provide any advantage. To make a clean experiment, the researchers took advantage of the fact that light can be used to repel or attract a BEC, depending on its color and intensity. The strength of this force is well understood. In this case, the researchers chose a color of light that would repel the BEC, the idea being that the Casimir-Polder force is attractive and the light force repels. If one can measure the difference in force, then the Casimir-Polder force can be obtained after accounting for the force due to the light field.
This is where all the elements come together. The laser is shone through the underlying glass substrate onto the grating. The researchers shine the light in such a way that, in the absence of the grating, the light would be reflected off the glass surface. The electric field of the light, however, still hits the metal grating. In response, the charges in the metal start to oscillate, and, if the spacing between the strips of metal are chosen right, these oscillations resonate with each other, creating a large field in the gaps between the metal strips.
This light field, close to the surface, is confined to the region between the metal strips. In these areas, the BEC atoms are slowed and then repelled, while over the metal they are accelerated to the surface by the Casimir-Polder force. After they bounce off the surface—the Casimir-Polder force is not strong enough to prevent reflection—the difference in distance travelled and the velocity profile of the BEC atoms create an interference pattern (see sidebar). By measuring this interference pattern for different laser light intensities, the acceleration due to the Casimir force can be calculated.
Commonly, researchers who need to think about the Casimir-Polder force use an approximation to estimate its value. According to these findings, though, the approximation underestimates the Casimir-Polder potential, while an exact calculation agrees with the experimental data. Notably, the uncertainties in the calculations are larger than the uncertainties in the experiment, which is quite unusual.
What's exciting, though, is that this may be the start of a new surface mapping technique. Of course, we have plenty of those already, like all the various forms of electron microscopy, atomic force microscopy, helium ion microscopy, and, well the list could continue for a long, long time. But this technique might hit a sweet spot of wide-area mapping with relatively good spatial resolution and be sensitive to things like charge mobility, polarizability, and thin layers on top of the surface. I would certainly be interested in playing with that.