What wavelengths are used practically in optical trapping? I am currently working on my Master thesis in a cold atom research group, and have irritatingly found -- or rather not found -- that no book or paper seems to explicitly mention what wavelengths are typically used for optical trapping. Our group uses 1064 nm light typically from what I gathered around the labs and offices, but no one was able to give me a direct answer on whether you could also use e.g. 532 nm light. Is it heavily dependant on atomic species which wavelengths you'd use? I know that you typically want to be far detuned from any transition frequencies, as heating processes are stronger there.
 A: 
Is it heavily dependant on atomic species which wavelengths you'd use?

Yes.
Light has two effects on atoms, a scattering effect $\Gamma$ that goes as $I/\Delta^2$, and an optical potential effect $U$ (used for traps and optical lattices) that goes as $I/\Delta$. In the above, $I$ is the intensity and $\Delta$ the detuning $\omega_l - \omega_0$, where $\omega_l$ and $\omega_0$ are the angular frequencies of the laser and of the atomic transition respectively.
You can already see, as you've pointed out yourself, that going away from resonance gives you a strong reduction of scattering $\Gamma \propto I/\Delta^2$ and hence reduced heating effects.
Optical traps and optical lattices are usually operating in a regime where $\Delta \gg 1$ ( in some units) so that $\Gamma \propto I/\Delta^2$ is negligible, and you only have to care about $U \propto I/\Delta$. Usually you have to use a high $I$ to compensate for the large $\Delta$.
Now, if you want an attractive force (a trap), then you want $U < 0$ and hence $\Delta < 0$. This implies using a laser frequency $\omega_l < \omega_0$. Let's say your species is $^{87}$Rb with $\omega_0 = 2\pi \cdot 384$ THz, your $1064$ nm light has $\omega_l = 2\pi\cdot 282$ THz, hence it satisfies $\omega_l < \omega_0$ and gives rise to an attractive potential.
If you want a repulsive force, you want $U > 0$ and hence $\Delta > 0$. Do the maths, $532$ nm light gives you a repulsive trap.
For optical lattices in particular, the use of blue/red detuned light results in atoms pinning to the minima/maxima of the potential. Both situations have pros and cons.

As someone with a PhD in ultracold atoms in optical lattices, your best resources about this stuff are the PhD theses of previous students in your group. They will usually have all the required theory and experimental knowledge there.
A: Adding on to the answer from @SuperCiocia.
For the Alkali's the dominant transition (the $D_1$ and $D_2$ transitions from $S\rightarrow P$ transitions) typically fall in a range of about 600 - 900 nm. This means that 1064 nm light is red detuned from all of these transitions and this will from an attractive optical potential.
The reason 1064 nm specifically is used is due to the commercial availability of low cost high power Nd:YAG lasers which were developed for commercial purposes such as, for example, laser cutting.
1560 nm laser sources based on Er doped fibers have also been commercially developed such that again, low cost high power sources are widely available. These lasers were developed for telecom applications to ensure minimally lossy transmission of signal over long fiber optic lines. Note that since 1560 nm is further detuned from 1064 you need more power to get the same trapping potential. This could cause technical issues such as, for example, thermal lensing of optical elements in the beam path causing a reduction in beam quality.
It is also common to use red detuned diode lasers at say $800-900$ nm, for example.
I work with ${}^{87}Rb$ which has its $D_2$ transition at $780$ nm. It is also possible to create very near detuned optical potentials which are just detuned by $10s$ of GHz from the atomic transition itself using, for example, a diode laser.
Other laser technologies are possible. This is just slightly more detail on some of the technologies with which I am most familiar. Again, the reason for the ubiquity of 1064 nm lasers for trapping is that they are commercially available at low cost and high power and they're also tuned a nice distance away from atomic resonance.
All of that said, it is also possible to use blue detuned lasers to create optical traps as well, sometimes in conjunction with red detuned lasers. See for example https://arxiv.org/pdf/1212.4453.pdf. In this paper the authors project a 3D optical box onto the atoms such that there is no light in the center of the projection but it is like a shell around the atoms. The advantage of this is that the atoms inside the box feel no optical forces (so they behave as if they were truly free). It is only if they come near the boundary of the box where the light is that the feel a repulsive force. There are other ways to use blue detuned light to aid in forming optical potentials.
Above I have spoken mainly about Alkali's. Due to the abundance of lasers in the visible most of the atoms which are able to laser cool have their dominant transitions in the visible to near-IR range which means that a 1064 or 1560 nm laser will typically be red detuned of whatever transition you care about giving you an attractive potential. However, as the atoms get more complicated so do the cooling and trapping schemes.
