What are the main practical applications that a Bose-Einstein condensate can have?
I assume you mean the relatively recent phenomenon of Bose-Einstein Condensation in dilute atomic vapors (first produced in 1995 in Colorado). The overall phenomenon of Bose-Einstein Condensation is closely related to superconductivity (in a very loose sense, you can think of the superconducting transition in a metal as the formation of a BEC of pairs of electrons), and that application would trump everything else.
The primary application of atomic BEC systems is in basic research areas at the moment, and will probably remain so for the foreseeable future. You sometimes hear people talk about BEC as a tool for lithography, or things like that, but that's not likely to be a real commercial application any time soon, because the throughput is just too low. Nobody has a method for generating BEC at the sort of rate you would need to make interesting devices in a reasonable amount of time. As a result, most BEC applications will be confined to the laboratory.
One of the hottest areas in BEC at the moment is the use of Bose condensates (and the related phenomenon of degenerate Fermi gases) to simulate condensed matter systems. You can easily make an "optical lattice" from an interference pattern of multiple laser beams that looks to the atoms rather like a crystal lattic in a solid looks to electrons: a regular array of sites where the particles could be trapped, with all the sites interconnected by tunneling. The big advantage BEC/ optical lattice systems have over real condensed matter systems is that they are more easily tunable. You can easily vary the lattice spacing, the strength of the interaction between atoms, and the number density of atoms in the lattice, which allows you to explore a range of different parameters with essentially the same sample, which is very difficult to do with condensed matter systems where you need to grow all new samples for every new set of values you want to explore. As a result, there is a great deal of work in using BEC systems to explore condensed matter physics, essentially making cold atoms look like electrons. There's a good review article, a couple of years old now, by Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger (RMP paper, arxiv version) that covers a lot of this work. And people continue to expand the range of experiments-- there's a lot of work ongoing looking at the effect of adding disorder to these systems, for example, and people have begun to explore lattice structures beyond the really easy to make square lattices of the earliest work.
There is also a good deal of interest in BEC for possible applications in precision measurement. At the moment, some of the most sensitive detectors ever made for things like rotation, acceleration, and gravity gradients come from atom interferometry, using the wavelike properties of atoms to do interference experiments that measure small shifts induced by these effects. BEC systems may provide an improvement beyond what you can do with thermal beams of atoms in these sorts of systems. There are a number of issues to be worked out in this relating to interatomic interactions, but it's a promising area. Full Disclosure: My post-doc research was in this general area, though what I did was more a proof-of-principle demonstration than a real precision measurement. My old boss, Mark Kasevich, now at Stanford, does a lot of work in this area.
The other really hot area of BEC research is in looking for ways to use BEC systems for quantum information processing. If you want to build a quantum computer, you need a way to start with a bunch of qubits that are all in the same state, and a BEC could be a good way to get there, because it consists of a macroscopic number of atoms occupying the same quantum state. There are a bunch of groups working on ways to start with a BEC, and separate the atoms in some way, then manipulate them to do simple quantum computing operations.
There's a lot of overlap between these sub-sub-fields-- one of the best ways to separate the qubits for quantum information processing is to use an optical lattice, for example. But those are what I would call the biggest current applications of BEC research. None of these are likely to provide a commercial product in the immediate future, but they're all providing useful information about the behavior of matter on very small scales, which helps feed into other, more applied, lines of research.
This is not by any stretch a comprehensive list of things people are doing with BEC, just some of the more popular areas over the last couple of years.
Bose condensation is interesting, because it is a quantum mechanical effect, that often results in macroscopic objects with unusual properies.
First of all Bose condensation is believed to be responsible for such phenomena as superfluidity and superconductivity. I don't think that I should explain technological and, well, "cognitive" importance of those.
But I guess that you are mainly interested in the Bose condensate -- a cloud of atoms of ordinary (some gas) but very cold matter in come optical/magnetic trap. Physics of these is a rapidly developing area right now, so my information can be not the most up-to-date. I know that people were thinking of making:
- some time/frequency standards with it
- some unusual chemical compounds/alloys with it (ultracold chemistry)
- use those clouds as high-resolution alternative for molecular beam epitaxy
And, of course, the most bizarre application people consider is a quantum computing. I know that people managed to make those traps as small as 1cm. And that they made number of clouds in one trap, "interacting" with each other through spin entanglement: see e.g. here.
More recently, they have been proposed as an array of inexpensive gravity wave detectors.