A new regime of strongly correlated quantum behaviour has been reached with the creation of a one-dimensional Tonks–Girardeau gas from ultracold atoms trapped within thin tubes of light.
Some materials reveal their underlying quantum nature at ultracold temperatures. Spectacular examples are superconductors and superfluids, in which frictionless currents flow at temperatures near absolute zero. It is quantum mechanics that brings about these effects, through particles condensing into a ‘superfluid’ quantum state. The resulting properties are strongly dependent on the dimensions in which the superfluid can move: in three dimensions, the motion is unrestricted; in two dimensions, the flow is confined to sheets or surfaces; and in one dimension, to lines or strings. On page 277 of this issue, Paredes et al.1 report a remarkable experiment in which they created a one-dimensional quantum gas, trapped within thin tubes of light. The interactions between the trapped ultracold rubidium atoms were enhanced by the confinement and could be modified, bringing about a continuous passage from a weakly interacting regime to strongly correlated behaviour in what is known as a Tonks–Girardeau gas2,3.
In quantum mechanics, particles are classified into two types — bosons and fermions. The classification is based on what happens to the ‘wave function’, the quantum mechanical description, of two identical particles when the particles are exchanged, one for the other. For exchanged bosons — two rubidium atoms, for example — the wave function is unchanged, but for fermions the wave function gains an overall minus sign. One consequence is that identical fermions can never be at the same point in space: swapping the particles would have no effect, but would still introduce a minus sign into the wave function; assuming the wave function is non-zero, there is then an inconsistency, as the same state would have two different wave functions.
Could bosons be made to behave in this fermionic way? The most extreme situation would be a row of impenetrable bosons on a one-dimensional string; they cannot occupy the same location and are therefore unable to pass each other and exchange places. The resulting traffic jam would involve strong correlations — the motion of each boson would be correlated with that of the next one in the line. Yet even in this case, their behaviour would not be exactly like that of fermions. The fermionic exchange rule implies more than the exclusion of two particles from the same point, as seen from the fact that the momentum of two identical fermions can never be the same, regardless of where they are located. However, in practice, so many properties of this one-dimensional string of bosons would be fermion-like that the situation is often referred to as the ‘fermionization’ of bosons.
That statement can even be made mathematically precise. More than forty years ago, it was realized that there is an exact one-to-one mapping of impenetrable bosons in a one-dimensional system onto a system of fermions that do not interact at all3. In fact, this problem connects with a general area of theoretical physics. Calculations showed that the lowest energy excitations of the system were similar to those of sound waves4. This in turn provided a powerful link to a universal class of ‘Luttinger liquids’5, describing many one-dimensional models in which the excitations have this character.
So how could such an interesting system be realized? Until recently, the discussion has been largely academic because of the lack of appropriate physical systems. But developments in the field of quantum gases have provided a natural starting point. The production of ultracold superfluid gases is now routine, and low-dimensional systems can be created using optical lattices. An optical lattice is a web of intersecting laser beams, generating a three-dimensional interference pattern. Atoms inside this web are exposed to a frictionless field of electromagnetic potential, whose spatial structure follows the intensity of the light. Many lattice structures are possible, but the relevant one here is a matrix of extremely thin, parallel tubes, which confine the atoms to one-dimensional motion.
Constricted in this way, the interactions between the atoms are then determined by only a few parameters, including their collision properties in free space6, their atomic mass and the thickness of the light tubes. Perhaps surprisingly, the effective mass of each atom can be easily changed by introducing a standing-wave light field along the length of the tubes, giving rise to a periodic one-dimensional potential. The resulting motion, in which an atom continuously absorbs and emits light as it surfs the standing wave, modifies the effective atomic mass in a way that can be controlled. Using this technique, Paredes et al.1 observed the crossover7 from the weakly interacting regime, in which the particles can freely pass one another, to a ‘fermionized’ strongly correlated gas. As proof of the creation of the Tonks–Girardeau gas, Paredes et al. measured the momentum distribution of the atoms in the tubes and found that it matched their theoretical prediction for such a state.
It should be emphasized that the Tonks–Girardeau gas only emerges if the gas is sufficiently dilute. At high density, another strongly correlated state with quite different properties may be produced. This is the Mott insulator, which was recently studied in a similar but complementary experiment8.
One of the most important aspects of Paredes and colleagues' experiment is the striking illustration of quantum control and quantum-state engineering. How this will affect the ongoing pursuit of quantum information and computation, and the investigation of a variety of quantum coherent and strongly correlated phenomena, is not yet clear. But an exciting path has been laid out before us.
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Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Phys. Rev. Lett. 92, 130403 (2004).
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Physical Review A (2006)
Physics Reports (2006)
Effective interactions, Fermi?Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides
Optics Communications (2004)
Physical Review A (2004)