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Quantum physics

United through repulsion

Mutually repulsive atoms placed at periodic intervals in a ‘crystal of light’ can, counterintuitively, be forced into stable couplings. That theoretical prediction has just seen experimental confirmation.

Nature likes to save energy. Whenever independent particles can arrange themselves freely, they choose the configuration that minimizes their total energy. That's why a molecule can be formed from two or more atoms: the bound configuration is stable because the total energy of the atoms is smaller when they are close together than when they are far apart. On page 853 of this issue, Winkler et al.1 report a fundamental extension to this concept of a molecule — atom pairs bound together through repulsive, rather than attractive, forces.

It seems intuitive that, to obtain a bound system of particles, an attractive force between them is required. But it is also easy to see that attraction by itself is not sufficient: to reach an equilibrium configuration, a repulsive force must also be present, or the system would simply collapse. This phenomenon is quite general In astrophysics, for example, certain types of supernovae are the results of implosions that occur when a star's self-gravity is no longer balanced by the pressure generated by thermonuclear reactions in its core. Stable stars, on the other hand, exist when some repulsive force counterbalances the attraction of gravity. In a neutron star, this repulsion is provided by the rules of quantum mechanics, which forbid particles of half-integer spin, such as neutrons, getting too close to one another. Similar quantum-mechanical effects can be reproduced, at very low temperatures only billionths of a degree from absolute zero, on the entirely different scale of atomic physics in the matter phase known as a Bose–Einstein condensate2,3.

What is surprising is that, in the quantum world, attraction isn't even necessary to form a stable bound system: repulsion can be enough. This prediction, like so much of quantum mechanics, is counterintuitive, as one would expect two repelling particles simply to fall apart to minimize their interaction energy. But in the presence of a periodic spatial perturbation this should no longer be true. Here, the energy of a particle cannot vary continuously, but is restricted to particular ranges of values. A pair of two repelling particles can therefore be stable simply because, if it fell apart, conservation of energy would require the two isolated atoms to have energies that would fall in a forbidden range.

Although periodic structures are the natural forms in which the atoms arrange themselves into crystals — and as such are very common in physics — interactions with the environment in the solid state dissipate energy, preventing the observation of the bound, repulsive pairs predicted by the theoretical model. Winkler and colleagues1 circumvent this obstacle by using a periodic structure made of light. In such an ‘optical lattice’, ultracold atoms are ordered in a regular array of microscopic traps caused by the interference of two or more laser beams. The resulting ordered system of atoms resembles a solid-state configuration, and neutral atoms in an optical lattice do indeed share many properties with electrons in a metal. In contrast to a solid-state crystal, however, light crystals are free from defects and dissipative vibrations, and have thus proved ideal systems for the investigation of otherwise elusive quantum-physical phenomena4.

In Winkler and colleagues' experiments, the capabilities of the optical lattice are combined with a powerful tool that atomic physicists can now use to change the nature of the interactions between two atoms, transforming attractions into repulsions, and vice versa. This trick is achieved by placing cold atoms in a uniform magnetic field, and tuning the intensity of the field across a resonance — known as a Feshbach resonance5 — that occurs when the energy of a bound molecular state is exactly equal to the energy of two colliding atoms. Following on from the observation of Bose–Einstein condensation6,7 (which involves ‘bosonic’ atoms of integer spin; atoms of half-integer spin are termed ‘fermionic’), Feshbach resonances have made possible the observation of striking phenomena — including the formation of cold molecules8 and culminating in the observation of super-fluidity among ultracold fermionic atoms9.

Winkler et al. take a cold gas of bosonic rubidium (87Rb) atoms, which naturally have repulsive interactions, and first fill a three-dimensional, cubic optical lattice such that each lattice site confines either no atoms, or two identical atoms (Fig. 1). The authors then use a Feshbach resonance to control the interaction between the atoms forming the pairs. When interactions are cancelled, the pairs are not stable and the atoms quickly fall apart, diffusing within a few milliseconds across the lattice and hopping from one site to the next. When repulsive interactions are restored, however, the separation process is halted. The pairs of atoms then live much longer together — several hundred milliseconds — clearly demonstrating that their stability is induced by the mutual repulsion of the constituents. The authors obtain additional information about the nature of the pairs by measuring the velocity distribution of the atoms and the energy of the bond.

Figure 1: Repulsive pairs.

Repulsion between pairs of identical rubidium atoms in an artifical optical lattice causes them to be stable against separation, as Winkler and colleagues1 demonstrate.

This new type of bound object remains stable because, in the structured environment of the lattice, the large repulsive interaction between the atoms cannot be converted into kinetic energy. This result is general, as magnetic fields could be used to tune the strength of the interaction between other atomic species. An even broader impact could be achieved by extending the concept to mixtures of different atoms, and also by playing with quantum gases of dif-ferent nature, both bosonic and fermionic4. Once more, it seems, optical lattices are demonstrating how useful they are for investigating many-body phenomena unobservable in other systems in which the interaction with the environment is too strong. As cold atoms are themselves a type of experimental simulator of quantum-physical effects, the result is a toolbox10 that kits us out to explore fascinating new avenues in quantum information and quantum states of matter.


  1. 1

    Winkler, K. et al. Nature 441, 853–856 (2006).

    ADS  CAS  Article  Google Scholar 

  2. 2

    Donley, E. A. et al. Nature 412, 295–299 (2001).

    ADS  CAS  Article  Google Scholar 

  3. 3

    Anglin, J. R. & Ketterle, W. Nature 416, 211–218 (2002).

    ADS  CAS  Article  Google Scholar 

  4. 4

    Bloch, I. Nature Phys. 1, 23–30 (2005).

    ADS  CAS  Article  Google Scholar 

  5. 5

    Feshbach, H. Ann. Phys. 5, 357 (1958).

    ADS  CAS  Article  Google Scholar 

  6. 6

    Cornell, E. A. & Wieman, C. E. Rev. Mod. Phys. 74, 875–893 (2002).

    ADS  CAS  Article  Google Scholar 

  7. 7

    Ketterle, W. Rev. Mod. Phys. 74, 1131–1151 (2002).

    ADS  CAS  Article  Google Scholar 

  8. 8

    Donley, E. A. et al. Nature 417, 529–533 (2002).

    ADS  CAS  Article  Google Scholar 

  9. 9

    Grimm, G. Nature 435, 1035–1036 (2005).

    ADS  CAS  Article  Google Scholar 

  10. 10

    Jaksch, D. & Zoller, P. Ann. Phys. 315, 52–79 (2005).

    ADS  CAS  Article  Google Scholar 

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Fallani, L., Inguscio, M. United through repulsion. Nature 441, 820–821 (2006).

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