There’s an episode of Star Trek: The Next Generation in which John de Lancie’s nearly-omnipotent alien character “Q” is stripped of his powers and banished to the Enterprise as a human because fans of the show enjoyed the character and wanted to see more of him, and at one point, he finds himself assisting the engineering team in trying to solve some problem. Asked to suggest a solution, he flippantly offers “Change the gravitational constant of the universe,” which leads to a bunch of additional techno-babble that ends up driving some more of the plot in ways that don’t really matter for this post. What stuck in my mind from that episode, when I watched it back in college, was the offhand suggestion to change fundamental properties of physics, because of course that’s nonsense.
It’s kind of fun, though, to realize that this is, in fact, a thing that physicists can do, and in fact that there’s a whole field of research devoted to changing properties of atoms in empty space. A recent paper from the Joint Quantum Institute provides a nice example of this, changing the ways that atoms in the space near a glass nanofiber emit light. Admittedly, this isn’t related to gravity, but it does offer the next best thing: a connection to some of Einstein’s most important contributions to physics.
As previously discussed here, while Einstein is mostly known for saying derisive or dismissive things about quantum mechanics, he actually played a pivotal role in launching the theory. This started with one of his “miracle year” papers in 1905, which presents a “heuristic model” of the photoelectric effect in which light takes on particle character. Just as important within the atomic, molecular, and optical physics field, though, was a 1917 paper in which he uses a statistical model to explore the interactions between light and atoms in a very clever way, and in the process introduces a new process that is critical for both laser technology and the ability to change the properties of atoms in empty space.
Einstein’s statistical model of atom-photon interactions includes three kinds of interactions, two of which were already known. One of these is photon absorption, in which an atom in a low-energy internal state absorbs a photon of light and moves up to a higher-energy state. The other is spontaneous photon emission, in which an atom in a high-energy internal state spontaneously drops down to a lower-energy state, emitting a photon in the process. Both of these were established empirical facts, known for decades: absorption was discovered thanks to dark lines in the spectrum of the Sun, and spontaneous emission was necessary to explain the bright lines seen in the spectrum of a flame when a particular element is burned.
The process that Einstein introduced is stimulated emission of photons, in which an atom in an excited state encounters a photon of the appropriate frequency, which triggers the emission of another identical photon. This isn’t something that anybody had seen at that point, but Einstein argued that logically, it must exist. In 1917, the dominant paradigm for describing atoms was in terms of planetary-like orbits of electrons about the nucleus, in which case you can understand the absorption process as a kind of “pushing” on the electrons by the light: if the frequency matches the orbital period, the pushes add energy, in the same way that correctly-timed pushing of a child on a swing will increase the energy of their swinging.
In this analogy, though, it’s not just the frequency that matters, but the phase: if you push at the right frequency but the wrong points in the oscillation, you’ll remove energy from the system. (Note: Do not try this with real children on actual swings. They don’t find it as interesting as physicists do.) Thus, Einstein argued, it must be possible for light to remove energy from atoms by triggering the emission of additional light.
Einstein’s model including stimulated emission works very nicely to explain many of the features of the interaction of light with atoms, so even though the process hadn’t been seen experimentally, it was quickly accepted as a real piece of physics. It’s now the cornerstone of one of the most important technologies developed out of quantum mechanics, the laser: the word “laser” was originally an acronym for “Light Amplification by Stimulated Emission of Radiation.” A laser works by sending light through a medium containing atoms in high-energy states, which triggers stimulated emission of photons and boosts the intensity of the light exponentially: one photon interacts with one atom to produce a second photon, the two become four, the four become eight, and so on.
In the decade or so after Einstein’s 1917 paper, physics moved beyond the picture of planetary orbits that inspired the introduction of stimulated emission, but the concept remained a key piece of the physics. And with a correct understanding of the physics of the atom, it’s surprisingly easy to explain both photon absorption and stimulated emission.
Somewhat ironically, though, the phenomenon of spontaneous emission– which was an established empirical fact well before 1917– turns out to be really difficult to explain. The simplest models of quantum atoms predict that the allowed states of electron are “stationary states,” that don’t change in time. An electron in a high-energy state should just stay there forever, and the spontaneous emission rate needs to be put in by hand, as an empirical property of particular states in particular atoms.
Correctly calculating the rate of spontaneous emission for a particular atom requires the beginnings of “quantum electrodynamics,” which combines quantum physics with special relativity. This was first managed by Paul Dirac in 1930 or so, and the ability to do these calculations was one of the signature successes of his relativistic quantum equation for the electron.
How do we understand the physics of spontaneous emission on a conceptual level, without doing a whole bunch of math with the Dirac equation? Well, it turns out to be useful to think about it in terms of stimulated emission. The key realization is that empty space isn’t zero-energy space, but necessarily contains a tiny bit of “vacuum energy” in the electromagnetic field. Pick a frequency of light, any frequency you like, and a chunk of empty space will contain half a photon’s worth of energy at that frequency.
Now, for most purposes, that energy is useless– the claims of scammers aside, this energy can’t be extracted and exploited to do useful work. It is a real physical phenomenon, though, with real physical consequences. The most important of which is spontaneous emission: you don’t go too terribly wrong if you think about the spontaneous emission of photons as being “stimulated” by that half-a-photon worth of energy. The term in the equations that makes high-energy states in atoms prone to emitting light and dropping down to low-energy states involves an interaction between the atom and the vacuum energy, in much the same way that stimulated emission involved interaction between a real photon and the atom.
That vacuum energy is a fundamental part of our quantum universe, though, so it might seem indistinguishable from just asserting that atoms just have an inherent propensity to decay, and that’s all there is to it. The interesting thing, though, is that you can modify the spontaneous emission rate of an atom in empty space by changing what you put around it. Truly open and empty space can sustain any wavelength of light moving in any direction you like, but if you take a couple of mirrors and put them facing each other so light bounces back and forth between them, you change the modes of light that can happily exist between those mirrors: light directed along the axis of the mirrors whose wavelength is such that an integer number of half-wavelengths fits between the mirrors will constructively interfere with itself as it bounces back and forth. Light along that axis at a different wavelength, though– say, 5/7ths of the distance between mirrors– will get out of phase with itself over multiple bounces, and end up destructively interfering. This process changes the properties of the space inside the cavity between the mirrors, making it a space in which certain combinations of wavelength and direction are enhanced, while other combinations are simply not allowed to exist.
If you take this sort of cavity and place an atom inside it, you can change the way it interacts with empty space to emit light. If you arrange things so that the wavelength emitted by the decaying atom would closely match one of the allowed wavelengths inside the cavity, you can significantly speed up the spontaneous decay, making it far more likely to emit light into that enhanced mode. If you arrange things so that the natural wavelength of the atom is forbidden within the cavity, on the other hand, you can keep the atoms in the excited state for a much longer time, because there’s just nowhere for that light to go. The modification of spontaneous emission is known as the “Purcell effect” after E.M. Purcell who first discussed it in the 1940′s, and it’s the inspiration for the more general field of Cavity Quantum Electrodynamics, which has a rich history in physics and was the topic that won Serge Haroche a share of the 2012 Nobel Prize in Physics.
The JQI experiment that made me start thinking about this stuff is a neat twist on the idea, because it doesn’t involve enclosing the atoms in a cavity. Instead, they’re placed near an optical fiber that’s around 500nm thick. This fiber provides a kind of enhancement of certain modes of light– in this case, combinations that include not just wavelength and direction, but also the polarization of the light– that can more easily couple into the fiber and travel along it, and a corresponding suppression of other combinations of wavelength, direction, and polarization. As a result, they can either increase or decrease the lifetime of atoms near the fiber, depending on how they’re prepared.
I find this especially cool because this isn’t done by directly touching the atoms, which are never in contact with anything. In a very real sense, the presence of the fiber changes the properties of the empty space around it, and its the interaction with that empty space that changes the properties of the atoms. Admittedly, this is still a long way from waving a hand and changing the gravitational constant of the universe, but anything that changes space itself is pretty amazing in my book.
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(Disclaimer: The JQI paper includes several friends and former co-workers of mine as authors.)
