What laser and BBO are needed to create entangled laser streams?
In order to generate entanglement you need an interaction, by which I mean that the dynamics have a term that is a function of two different degrees of freedom that you intend to entangle$^1$. The type of nonlinearity in this case is what is known as spontaneous parametric downconversion or SPD, which is a nonlinear optical process.
1) How does this work? Does one simply purchase a laser pointer and shine it at a BBO? Does this automatically create two lasers on the other side of the crystal?
SPD can be thought of as a process in which a photon is split into two. Because of things like conservation of energy and momentum, there will be specific relations between the two output photons. The most obvious is that the output beams will not be the same color as the initial "pump" beam. So although it is almost as simple as "purchasing a laser and BBO," in reality it won't be a typical visible light laser pointer. You need higher energy photons from an ultraviolet laser, which can interact with the BBO and convert into two infrared photons. In addition, this process is very inefficient, so you generally need a very bright laser (which will typically allow you to see the beam even though it will generally be a UV source). Even with a bright laser, usually you will not be able to see the downconverted light with the naked eye (due to being so dim as well as being in the near IR). However, a decent CCD (i.e. digital camera) is enough to see this light.
2) If you (a physicist) wanted two entangled laser streams what specific laser and what specific cut BBO would you purchase? Where would you buy these items?
As said before, you'll need a UV laser. This used to mean an Argon-ion laser, but now there are much cheaper Diode lasers that work in the UV. There are dozens of companies selling optical equipment such as BBO crystals or diode lasers, any specialized optics company will do$^2$.
SPD will happen with lower energy light, but if you want to see any quantum effects you need to be able to efficiently detect single photons which we know how to do in the visible and near IR, but not any lower energy$^3$.
As for details about what cut, etc., you should look for in a BBO crystal, it depends. This is a question of engineering your setup and will depend on the exact details of what are you trying to do. For instance, it depends upon whether you want to entangle polarization, time/energy, the spatial direction/position or some combination of all of these. Some of the other experimental design considerations will be the exact color of your pump beam, the temperature of the crystal, and the efficiency of the conversion.
As an example of the trade-offs, a longer crystal will give you brighter down-converted beams, but you will have poor (or no) time/energy entanglement (which is the most common method to generate single photon non-classical states via heralding).
3) In theory, if you performed the "two slit" experiment on one laser stream (i.e. forced the non-wave pattern to appear), what would the other laser stream do?
The other laser stream would do Absolutely Nothing. Measurement on one beam does not change the other beam (it only updates what you know). In fact there is a so called no-go theorem called the No-communication theorem that states a local measurement of a quantum system cannot change another distant system in any noticeable way.
If the two systems or particles are entangled, then a measurement on either system will have some intrinsic randomness to it. The statistics of this randomness (such as a fringe pattern) will not change even if you do things to the other entangled particle. However, if you perform certain measurements on both systems, they will both be random, but their randomness will be correlated (in a way that depends on the exact nature of the entanglement).
This is like flipping 2 correlated (magic) coins that always give the same result; you still get each side randomly 50% of the time, but it's only when you compare results that you find anything surprising.
Experimentally this means you need two detectors (one for each beam) and you look at situations when both detectors register an event. This is known as coincidence counting.
Footnotes
- e.g. your setup is described by a Hamiltonian with a nonlinear or interaction term.
- I'll refrain from naming companies to avoid promoting (or possibly misrepresenting) any specific company. They are easy to find via Google.
- There are methods of single photon detection at low energies, but this involves things like superconducting detectors which involve low temperatures and thus need cryogenics etc. to work with.