Ok, so, what’s an atom laser?
Well, what’s a laser?
There are two types of particles according to the Standard Model of particle physics. They are fermions and bosons. The defining difference between them is that... well, this is quantum mechanics so everything comes in discrete “quanta”--nothing is continuous. There is a minimum amount of (non-zero) angular momentum something can have, and then how much angular momentum it actually has will always be a multiple of that. If you look at the spin of a particle, a fermion will always have an odd-number multiple of that minimum angular momentum, and a boson will always have an even-number multiple (including the possibility of zero angular momentum).
Ok, so what? Well, there’s a theorem--a mathematical proof from the late 1930s--that states that a particle with odd-number multiples of the minimum spin can never be identical to another particle, while a particle with even-number multiples of the minimum spin can.
And by identical--and this is crucial--I mean truly identical. Let’s say you have two pennies. They’re both the same year, they’re both in mint condition with no identifying scratches or fingerprints, how do you know which is which? You put them on the desk in front of you. One has heads up and the other has tails up. Not identical! You can tell them apart!
Ok, let’s say they’re solid color marbles instead. No heads, no tails. One is rolling off the side of your desk, oops! Not identical! One is moving and the other isn’t, you can tell them apart!
Ok. They’re perfectly generic cubes. No rolling. Sitting still on the desk. Oh wait, one is to the left and one is to the right! Not identical, you can tell them apart! But we’re getting closer, maybe these cubes hypothetically could be identical, if you could just get them to overlap with each other so that neither was on the left or the right. (Is that a thing you can even do??)
In the macroscopic world we’re used to, no two things are ever identical, because it’s just not a coherent (as it were) concept. Even if we’ve got a bunch of nearly identical objects we’re dealing with--a sack of pennies that we’re flipping to be either heads or tails; a bag of bouncy balls that we’ve sent sailing around a room and now have to calculate the probable location of--the idea that something can be truly all the way identical is ludicrous in context... In the microscopic world, though, it is possible for bosons to be fully identical. And when you have fully identical particles, the statistics you need to apply to figure out how a group of them will behave is different. It turns out that if objects can be identical, they are statistically likely to be identical.
Of course, most of the time any given set of objects have way too many variables to become identical. Let's say you have a cloud of bosonic gas. Even if they're all the same element, they're not going to be identical. The particles bounce around to fill their container, because it's a gas, so they're (literally) all over the place spatially. And they move with a whole range of velocities, because they're at non-zero temperature (and the definition of temperature is standard deviation of speed, squared, times some factors). But let's say you could overcome these practical limitations and make them identical. Then you have:
All your bosons have the exact same energy. This means that they're all the same type of particle--you aren't mixing helium-4 with silicon or something, since those have different masses. And furthermore, all internal states (spin; color if we're talking about photons; electron energy level if we're talking about atoms or molecules; vibration and rotation modes if we're talking about molecules) are also identical.
All of your bosons are in the exact same place and moving in the exact same direction with the exact same velocity (and/or they're stationary).
Their wavefunctions are in lock-step. If one of the particles is at the peak of its wave (for ANY wave-like parameter that can be used to describe it), all the particles are at the peak of their waves; and when one reaches its trough, all the particles do simultaneously. In other words, you have a tidal wave, rather than a regular choppy sea.
This isn't quite as hard as it sounds. There's actually a mathematical theorem that says that any one of (a) monochromaticity (same energy; it's called that because for photons, same energy implies same color), (b) same location and direction of movement, and (c) coherence (wavefunction in lock-step) implies the other two of those conditions. So if you can manage to get one of them you can get all of them.
Ok. That's a lot of setup, but we're basically there. What's it called when you meet all these conditions and have basically created a tidal wave out of your bosons? Well, traditionally it's called a Bose-Einstein condensate (BEC for short). But the BECs that we encounter the most often in our daily lives, and that we have the most uses and applications for, are lasers--BECs where the choice of bosons is, specifically, photons. So, rather than calling a laser a "photonic BEC" it's more common to call a BEC made out of an atomic gas an "atom laser." (Just plain "BEC" is probably even more common, unless you're specifically playing up the ways in which your atomic BEC is like a laser.)
There's a hell of a lot of technology built around lasers. There are two main ways in which having a tidal wave of light, rather than a choppy sea, really helps you.
The first is that when a tidal wave crashes, it crashes hard. It's the same amount of ocean you always have, but because it's all in lock step, all hitting at once, all in one spot, it does a lot more damage. Same with a laser, which is why it's much easier to start a fire by focusing a laser beam than by focusing the light from a light bulb. (In fact, because all your photons are in the same place and moving in the same direction, focusing optics just work a lot better with laser beams than with incoherent light.) Laser etching, cutting, and burning are used for so many things--ranging from data transfer onto CDs and DVDs to welding in car manufacturing. This property is also used... er... non-destructively, just as a bright controlled light source for tons of other applications, including things like barcode scanners.
The second is that when everything is in lock-step like that, any interference effect you're trying to get is more or less multiplied by the number of photons you have. It's basically how the tidal wave is so much more visible than any single wave in a choppy sea. And if you have two tidal waves going in opposite directions and they pass through each other, for a moment they're twice as tall, and in another moment they completely cancel each other out, before moving on as if none of it ever happened. Whereas if you have little waves from the wake of a boat passing through each other like that, the exact same thing happens but it just looks like a slight change of your ripple pattern--you can barely tell, just because there's too many different waves with too much going on all at once.
There's also a ton of technology built around this enhanced interference effect, like holograms and laser interferometers. In fact, most laser technologies are interferometric. CD/DVD readers, navigational laser gyroscopes, some of the backend of FIOS fiber communications networks, as well as tons of manufacturing quality-test instruments, and scientific instruments.
Lasers can be divided into two types: pulsed and continuous-wave (cw). In a pulsed laser, light is allowed to build up for a short period of time, and then it’s all released at once as a single large blast of energy, and then built up again. In a cw laser, light is constantly released at a small dribble. Pulsed lasers have reduced coherence, so they aren't as good for coherence-type applications. But they're much easier to build than cw lasers, especially at higher energies because you can build up energy and then release it all at once, so they're good for any time you want to burn something.
Back to atom lasers, then. Well, same thing here, it's much easier to build a pulsed atom laser; the first (pulsed) atomic BEC was made in 1995, but the first cw atom laser was achieved just a few months ago, so, 27 years later. That is, it's much easier to take some atoms, turn them into a BEC, do a little experiment on them, release them. Or they decay out of the BEC state itself--a BEC typically only lasts for a few seconds. This is actually pretty good, often when you're looking at a quantum state you're pretty happy if it lasts for 1/1000 of a second before decaying into some other state, or before having something collide with it and knock it into some other state. However you end up losing your BEC, whether because you did something to it or it just died on its own, you just make a new one every few seconds and start over. It's much, MUCH harder to continuously make new bits of BEC that are smoothly added to the old BEC as parts of the old BEC decay out, without any of it being ruined by your experiments, such that you continuously have some amount of BEC to work with. [I was going to write up a long-ass explanation of how a pulsed BEC is actually made, and how a continuous BEC is made, and why it's harder, but I've decided that can be its own post IF I get a request for it. The person who usually requests these posts from me has probably heard a lot of this before so it might not happen.]
There's a lot of cool physics you can study even with just a pulsed atom laser. With all the atoms identical and coherent, basically what you have is 100,000 atoms (or however many) acting as if they were one single atom. A typical BEC can be something like 100 microns across--about the size of a human hair. You can see this thing macroscopically with only moderately expensive lenses and cameras! You can essentially look at a single atom, and do things to it and see how it responds, with standard optics, because it's the size of a human hair. And because it's a quantum-coherent state, this huge macroscopic object behaves quantum mechanically rather than classically. You can split your BEC in half, separate the two halves, and bring them back together and they will interfere: you'll get stripes where there's matter and stripes where there's nothing. Let me repeat that: using (typically) metallic atoms, you get stripes with metal and stripes with nothing by overlapping two pieces, because they interfere. And this is visible on a camera. Here is a photo of it:
Yes, that is literally a photo of two overlapping metallic gas clouds interfering, so there’s places where there’s twice as much metal and places where there’s none. In addition, it's a different phase of matter, and it can be used to simulate other phases of matter, to get even more exotic things. It's a superfluid--a perfect fluid, with no viscosity--but if you tweak it just right you can make it a perfect insulator instead. You can use the fact that it's a very large quantum mechanical object to do all sorts of weird quantum mechanics things, like slowing and storing light. You can entangle large things. The possibilities are endless.
Of course, it'll be a big deal to have a continuous atom laser because you can continuously do all these same experiments--no need to wait several seconds between each data point to build yourself a new BEC. But it's really a much bigger deal than that, because (as I said above) there are fundamental physics reasons why a cw laser--whether an atom laser or a light laser--just works better for certain types of technologies. And in fact, nearly all the technological applications people have in mind for atom lasers are based around the enhanced interference effects--holography and interferometry--that are fundamentally much stronger with cw lasers than pulsed lasers. There are a lot of things that atoms are just way more sensitive to than photons are, such as magnetic fields (which photons are basically insensitive to unless they're propagating through some sort of material that is affected by magnetic fields), and gravity (which photons are barely sensitive to, but atoms, having mass, are way more sensitive to). So now that there is such thing as a cw atom laser, some cw light laser applications can be phased out in favor of cw atom lasers: finally atom lasers can become a real replacement technology that people would actually use in the real world.
Footnotes below the cut:
 The minimum angular momentum is defined as 1/2 a unit of angular momentum. So a fermion would have a spin of 1/2, or 3/2, or 5/2, or whatever, while a boson would have a spin of 0, 1, 2... This makes the math slightly easier under limited circumstances.
 If we want to treat a macroscopic situation statistically, that is, if we have a situation where the idea of "identical" just doesn't even make sense as a concept, we use Maxwell-Boltzmann statistics. Those are the statistics we’re relatively used to. If you flip two pennies, according to Maxwell-Boltzmann statistics, you have four possible outcomes each with equal probability: a 1/4 chance of both heads, a 1/4 chance of both tails, a 1/4 chance of the penny on the left being heads and the penny on the right being tails, and a 1/4 chance of vice-versa. This adds up to a 1/2 chance of a mix of a heads and tails, and a 1/2 chance of both heads or both tails.
If you have fermions, objects for which there is such an idea of being truly identical but they can’t do it, we use Fermi-Dirac statistics. Now you can’t get both heads or both tails, so the only possibilities are heads-tails and tails-heads. These are equally likely, and the total probability of all possibilities has to add up to 1, so you have a 1/2 chance of heads-tails and a 1/2 chance of tails-heads, and 0 chance of both heads or both tails. We won’t really get into the implications of this here, the most interesting of which is that if you can manage to turn this into a paradox you get a black hole (in fact, this is how a lot of smaller black holes observed in astronomy are thought to have come about).
If you have bosons, objects which can be truly identical, tails-heads and heads-tails are the same event. So you have three possible events: heads-heads, tails-tails, and heads-tails. As in all the previous examples, each one has an equal probability: 1/3 chance of heads-heads, 1/3 chance of tails-tails, and 1/3 chance of mixed heads-tails; this gives you a total of a 2/3 chance of both objects being identical. So once you’re in a situation where objects CAN be truly identical, you have an enhanced probability that they WILL be truly identical.
 BEC is just the really general name. There are a lot of more specific names. "Laser," obviously, if it's made of photons. "Superfluid" if it's made of atoms, or, hypothetically, molecules (slightly less hypothetical if you look at reduced-dimensional crystals). "Superconductor" if it's made of electron pairs (an electron is a fermion, but two electrons stuck together is a boson because if you add two odd numbers you always get an even number).
 There are a lot of scientific applications where the monochromaticity is what really matters, because when you're doing a science experiment the purity of your sample can be important. But most technological applications are about either the coherence or the light all being bunched together (bunched in its non-technical sense).
 This is due to the Heisenberg uncertainty principle. In quantum mechanics, a particle's state is never definite, it's always spread between different possibilities. An electron is simultaneously in multiple places at once, for example. The Heisenberg uncertainty principle states that there are certain fundemental parameters a particle might have, and some of them come in pairs. While a particle's state in any given parameter can never been definite, the more definite it is in one parameter, the less definite it is in the other parameter of the pair. For the most common example, position and momentum are paired properties. So an electron might simultaneously be in multiple places at once, but the more localized it is--the less spread out over multiple places--the less can be said about how fast it's going, or in what direction. Conversely if you can get it down to a narrow range of momenta, by cooling it lets say, it's going to spread itself out over a much larger space.
Anyway. Back to lasers. Time and energy are a Heisenberg uncertainty pair. If you have a laser pulse, you have a fairly narrow amount of time over which your laser beam exists, which means you have a wider spread of the energy (color) of your photons--they're going to be less perfectly monochromatic. According to the theorem that velocity spread, energy spread, and coherence are all tied, this means a pulsed beam also spreads out faster, and your coherence is a little less perfect. So when all that matters is sheer power, a pulsed laser is great, you can get a lot of power in that thing for a very brief amount of time. But for applications where coherence matters, a pulsed laser is a bad choice.
 A macroscopic quantum state is extremely delicate--hell, any quantum state is extremely delicate--and if the vacuum you're holding it in is anything less than perfect (and there's no such thing as perfect vacuum), the occasional random background gas atom is going to come crashing through and rip your BEC to pieces. Typically BECs are made in vacuum chambers that are only a little more vacuum-y than, like, the moon. Not great, but still about the best we can do with current technology, without going to unnecessary extremes.
But even, let's say, you could make a vacuum chamber without any background gas whizzing around at all. You'd still have background radiation to contend with. Even if you could entirely block cosmic radiation coming in from the outside, the walls of the chamber would radiate blackbody radiation. True vacuum and stuff cannot coexist in the same universe, and our universe has stuff in it.
 Pretty much any paradox in physics leads to a singularity, but that's not as interesting as it sounds most of the time. Most of the time, a singularity in physics looks like the calm at the eye of a storm, or that there's no water at the center of the vortex in your bathtub drain. The way you get a paradox with Fermi-Dirac statistics is to pit relativity against Pauli exclusion (a name for the concept that two fermions can never be identical), by creating a situation where either causality or Pauli exclusion has to be violated. Because anything weird in relativity usually manifests as gravity, you end up with a gravitational singularity in this case. Or to put it way more boringly, if you add too much stuff to an already-dense neutron star (neutrons are fermions), it'll collapse into a black hole.