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I have been reading about entangled particles, lasers, the two slit experiment, etc. I really know nothing from physics (i.e. equations, formulas, theory); so please respond accordingly. From my understanding, one typically uses a beta barium borate crystal (BBO) to entangle particles.

  1. How does this work? Does one simple purchase a laser pointer and shine it at a BBO? Does this automatically create two lasers on the other side of the crystal?

  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?

The reason for my questions:

  1. 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?
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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

  1. e.g. your setup is described by a Hamiltonian with a nonlinear or interaction term.
  2. I'll refrain from naming companies to avoid promoting (or possibly misrepresenting) any specific company. They are easy to find via Google.
  3. 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.
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  • $\begingroup$ Thank you for your response, but there are a number of things I don't understand in your post. What is a CCD? Do all BBO's work? When I look on websites it seems BBO's are cut of different sizes and widths? Which would be purchased? Do you actually get two beams on the other side of the crystal (at what angle, 45deg?)? Is the No-communication theorem actually a "theorem"? Could it one day be shown to be false? I really don't understand the "absolutely nothing" response. $\endgroup$ – Bobby Ocean Mar 25 '15 at 2:15
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    $\begingroup$ I've updated the post to explain what a CCD is, elaborate on the "absolutely nothing" comment, and try to explain how the exact type (cut/size etc) of the BBO is a complicated engineering question that depends on a lot of details. As for your question about the no-communication theorem, this is as true as quantum mechanics (and/or the locality assumed by relativity). Disproving this theorem means you are inventing/discovering physics beyond our current best theories which would be a very big deal. $\endgroup$ – Punk_Physicist Mar 25 '15 at 15:09
  • $\begingroup$ Still a little confused? If I observe a particle go through one slot (instead of interacting with itself and going through both) then won't the entangled particle behave in the same fashion; i.e. as though it was observed? I must be misunderstanding what "entanglement" means. $\endgroup$ – Bobby Ocean Mar 26 '15 at 1:48
  • $\begingroup$ If you just put detectors in the paths of both beams measuring one arm does not change the other. However if you look at coincidences where you selectively postselect on certain states, then the outcome depends on what you do in both arms. Using the magic entangled coins, flipping the two coins still give random events (e.g. HTTHTTT where H=both coins are heads & T=tails). However if you flip the coins and ignore all times that coin 1 gets heads, then you'll see TTTT... in coin 2. $\endgroup$ – Punk_Physicist Mar 26 '15 at 6:10
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I'm not sure I can answer your questions about quantum mechanics honestly without equations, but I can tell you something about the details of generating entangled photons with BBO.

First, there are two things you need to know about laser light: it has a definite polarization (orientation of the electric field) and definite energy (or, equivalently, a definite wavelength). We'll be making pairs of photons that are entangled in their polarizations: that is, both have undefined polarization before they are measured but identical polarizations afterwards.

Here's what a BBO crystal does: it has a special axis, such that if you shine in light that is polarized along this axis (light from what we call the pump laser), it sometimes turns one of these photons into two lower-energy photons that have the same polarization*, a process called downconversion. So, for example, if you have a BBO where this axis is horizontal, if you shine in vertically polarized light it just passes through, but if you shine in horizontally polarized light it can be downconverted.

You asked about the details of the cut of the BBO: for the purposes of these experiments. This sets some of the properties of the outcoming photons, like: 1) the specific energies (which must sum up to the energy in the original photon), and 2) whether they exit the crystal in the same direction as the original photon or at different angles. So, the specific cut of BBO you want depends on details of the experimental design. For example: 1) some experiments have the pairs of photons come out at opposite angles from the central pump laser with the same energy, and 2) others might have the downconverted photons exit collinear to the pump, but with different energies so all the different kinds of light can be separated by more optics down the line.

There is also some latitude in choosing the pump beam, but the choice I've used is a particularly familiar one: it is essentially a fancy Blue Ray laser, which has a wavelength of 405 nm. This leads to downconverted photons with about half as much energy, with a wavelength of 810 nm. In principle this would look like shining a blue laser at the BBO and getting out two barely-visible red beams. But in practice, only a tiny fraction of the photons that enter the crystal are downconverted, so you only ever see your blue pump and you have to use sensitive detectors to find the red photons.

Now, with all that as setup, here is a way to make entangled photons: you need two thin pieces of BBO, and you orient them such that one has its downconversion axis horizontal and the other vertical. Then you shine your pump laser through both of them, but you set it up such that the polarization of your laser is at 45 degrees, neither horizontal nor vertical.

Why does this make entangled photons? Well, in quantum physics a photon that has diagonal polarization can just as well be said to be both vertically and horizontally polarized, in the same sense that Schrodinger's Cat is said to be both alive and dead before you look at it (that is, it is a superposition of horizontally and vertically polarized). So if a photon that is both horizontally and vertically polarized is downconverted, it becomes two photons that are either both horizontally polarized or both vertically polarized - but neither has a definite polarization until it is measured, and each is guaranteed to have the same polarization as the other. And that's precisely what it means to be entangled.

Regarding the experiment that you suggest, remember how I defined entanglement: the polarization of each photon looks individually random, and it is only when you compare photons from the same pair that you see anything interesting. Therefore, any experiment that measures each stream of photons individually won't see anything interesting. The interesting experiments have a form like this: you change something about one of the photons, and then measure its entangled partner. There are a lot of fun but similar ideas.

*Pedantic note: I'm simplifying some of the geometry slightly here. In the setup I'm familiar with, the downconverted light was perpendicular to the nonlinear optic axis, and the downconverted light was itself perpendicular to the pump photons.

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