The atom may not be a planetary system, but under specific circumstances it can behave like one. That is the curious finding of physicists in Austria and the US, who have confirmed a 1994 prediction that, in the presence of an applied electromagnetic field, electrons in very highly energized atomic states should behave like the Trojan asteroids of Jupiter.
Atoms with at least one electron excited to an extremely high energy level are called Rydberg atoms – after the 19th century physicist Johannes Rydberg, who pioneered the study of hydrogen energy levels. Today, researchers can access energy levels with principal quantum numbers in the hundreds and the electron is relatively far from the nucleus where the attraction is much weaker. Rydberg atoms are therefore highly prone to ionization by stray electromagnetic fields and must be very well shielded.
Although such atoms conjure up images of a planet orbiting the Sun, quantum mechanics dictates that the electron is likely to be found in variety of different places in a large and diffuse orbital. As a result, a Rydberg atom shares little in common with a planetary system.
However, it is mathematically possible to produce a superposition of atomic states that is localized in space. An electron in such a superposition will behave much like a classical particle – or a planet. The problem, however, is that the states that make up the superposition evolve in time at different rates, and so the state very quickly falls apart. But in 1994, Joseph Eberly of the University of Rochester in New York and two colleagues realized the heavens provided them with a clue about how to stabilize this fragile superposition.
The trio’s inspiration came from the planet Jupiter and its 4000 or so Trojan asteroids. These sit at the two so-called Lagrange points in Jupiter’s orbit – one 60° ahead of the planet and the other 60° behind it – and rotate in lockstep with the planet.
Similarly, Eberly and colleagues showed that the role of Jupiter could be played by a rotating external electromagnetic filed. As a result, it should be possible to create Lagrange points in a Rydberg atom, creating stable, localized electronic orbitals and bridging the divide between quantum mechanics and classical mechanics.
Until now, however, producing such a system in a laboratory has proven to be extremely difficult. In the new research – a collaboration between experimentalists at Rice University in Houston, Texas and theorists at Vienna University of Technology and Oak Ridge National Laboratory – a laser is used to excite the lone outermost electrons of potassium atoms to principal quantum numbers above 300. The researchers then apply a circularly rotating electromagnetic field, which combines several nearby orbitals to create “Trojan wave-packets”.
Finally, having achieved stable states with the electron wave-functions localized at the Lagrange points, they very slowly reduce the frequency of their applied field. The orbital period of an electron increases with distance from the nucleus just as the orbital period of a planet increases with distance from the Sun – therefore turning down the applied frequency forces the localized electron to move even further from the nucleus. As a result, the principal quantum number of the electron is boosted to around 600, making the atom about the size of the dot above the letter “i”.
Barry Dunning of Rice University explains “The electron is locked to the drive field and if you very slowly change that drive field the electron stays locked to it. We can use that to move it out to very much larger orbits – in principle arbitrarily large, but of course at some point all the stray fields begin to take over.”
Despite the similarities between a Trojan asteroid and the Trojan wave-packet, quantum mechanics dictates that the Trojan wave-packet describes only the probability of finding the electron at a given location – whereas classical mechanics tells us exactly where an asteroid will be. What the researchers were measuring was the probability of finding that single electron in a particular place – the Rice team had to make thousands of measurements on thousands of atoms and compare their findings with a mathematical model from the theorists in Vienna to work out the shape of the orbiting packet.
“The transition zone between quantum mechanics and classical physics is, I would say, the most fascinating and the least understood frontier in physics,” says Eberly. “That area is so full of fascinating puzzles and this is such a nice way to explore one aspect of that frontier zone.”
The research is described in Physical Review Letters.