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Decay of a dark soliton into vortex rings in a Bose-Einstein condensate
Vortices are fundamental excitations of gases and liquids. Well-known examples include tornados, whirlpools, and smoke rings. The main characteristic of vortices is that nearby matter tends to flow in circles around the core. In quantum fluids and gases, such as superfluid helium and trapped Bose-Einstein condensates (BECs), this flow is quantized. Why? Quantum mechanics says that all the atoms in these quantum fluids can be described by the same single wavefunction. Since the motion of atoms in one location is linked with the motion of atoms everywhere else, atoms can flow in circles only in very special ways. To be technical: as the atoms circulate, the phase of the wavefunction must change only by a multiple of 2pi.
There are many ways of creating vortices in fluids. A familiar method to coffee and tea drinkers is to rotate a spoon in the cup. Another way is to rotate the cup! While this second approach sounds much more impractical, it actually turns out to be a convenient way to stir up superfluids. Arrays of vortex lines were produced this way back in the 1970's in superfluid helium. Simulations by the theory group of Charles Clark at NIST show that similar quantized vortices can be produced in BECs by rotating the traps that keep them confined. Since the vortex cores have no atoms inside, they would appear in photographs as circular holes. These predictions were recently confirmed by experiments performed in a group in Paris led by Jean Dalibard (these results were also presented on March 12 at the March American Physical Society meeting in Seattle).
Creating vortex rings in superfluids is a bit more difficult. One way is to insert a particle like an electron; this is a bit like firing a cannon and watching the resulting puff of smoke form a ring. Unfortunately, the resulting quantized vortex rings are much too small to see, even though they change the macroscopic properties of the superfluid in important and observable ways. We have devised another approach to creating these excitations. First, the BEC is prepared very carefully to have a large region inside with no atoms at all. If this region is perfectly flat, right in the middle of the BEC, and the wavefunction changes sign on either side, the state is called a `stationary dark soliton'. The emphasis is on `very carefully', because the slightest perturbation will quickly destroy it! Simulations show that the soliton will disintegrate into concentric vortex rings.
While it sounds close to impossible to prepare a real BEC in such a delicate state as a stationary dark soliton, experimentalists at JILA (a joint institute of NIST and the University of Colorado) have succeeded in doing just that. The soliton is prevented from disintegrating by filling the void with another condensate, made of the same kind of atom but in a different state. When the filler atoms are selectively removed from the trap, the soliton quickly decays, but the things it decays into are still too small to see directly. So, the experimentalists turned off the trap holding the atoms, which causes the BEC to expand rapidly. Once the BEC is large enough, the vortices show up clearly in photographs as two dark spots in the BEC cloud. Just to be sure that these were really vortex rings, pictures were taken from two different points of view; if two spots show up in both pictures, it must be a ring.