Preparing entangled states, how is this possible in the simpest cases?

[James MC]

I'm having trouble finding comprehensible explanations of how experimenters can ever know that two particles are entangled.

I understand that the first experimental confirmation of entanglement used Calcium or Mercury vapor which when excited gave off pairs of entangled photons. But how did the experimenters know that exciting calcium vapour generates entangled photons?

I understand that later experiments used crystals that can split a photon into two photons, each of which can be directed by mirrors to travel in opposite directions to distant corners of the lab where experiments can be carried out separately on each member of the pair. But how did the experimenters know that crystal-splitting would yield entanglement among the split photons? Why couldn't they just split yet retain maximal seperability among all their physical properties?

What is the simplest-to-understand method for entangled state preparation?

Interested to hear your suggestions!

 

[DrChinese]

What is the simplest-to-understand method for entangled state preparation?

Interested to hear your suggestions!

Any interaction in which an unknown initial state produces 2 detectable particles will be a candidate for producing entangled pairs. If you look at helium in the ground state, its pair of electrons are spin entangled. Quarks in protons and neutrons are entangled. In other words, almost everything in your body is currently entangled in some form or another.

In experiments, the most common form of creating entangled photons is down conversion. A single photon is split into 2 while passing through a non-linear crystal. These start out entangled in one or mores bases.

The underlying rule is: there is a conserved total quantity such as spin. Typically, for spin entanglement, total spin is zero. Thus one particle is plus and the other is minus. However, there are many other spin permutations, and the particle count is not limited to two. It can actually be any number which is a multiple of the particle's spin. In fact, different types of particles could be spin entangled.

Spin is not the only basis for entanglement. Conceptually, any observable can demonstrate entanglement.

 

[James MC]

Thanks for your response.

I understand that entanglement pretty much follows from any interaction provided one particle is in some superposition. What I don't understand is how any experimenter can create or maintain an entangled state so that it can be manipulated in the lab. For example, you say:

In experiments, the most common form of creating entangled photons is down conversion. A single photon is split into 2 while passing through a non-linear crystal. These start out entangled in one or mores bases.

I take it that by "split" you mean that a high energy photon is converted into two low energy photons? (I thought photons were massless point particles.) Anyway, How do you know they start out entangled? Why doesn't the crystal just split them? Why should this splitting yield entanglement?

You then offer a general rule:

The underlying rule is: there is a conserved total quantity such as spin. Typically, for spin entanglement, total spin is zero. Thus one particle is plus and the other is minus. However, there are many other spin permutations, and the particle count is not limited to two. It can actually be any number which is a multiple of the particle's spin. In fact, different types of particles could be spin entangled.

But conservation principles seem insufficient to yield entanglement. Take a particle that is spin zero and let it decay into two particles, one with plus spin, one with minus (to preserve conservation). Where is the entanglement? I don't see why you need entanglement to account for conservation (plus and minus that cancel is sufficient) so why postulate entanglement?

 

[meBigGuy]

But conservation principles seem insufficient to yield entanglement. Take a particle that is spin zero and let it decay into two particles, one with plus spin, one with minus (to preserve conservation). Where is the entanglement? I don't see why you need entanglement to account for conservation (plus and minus that cancel is sufficient) so why postulate entanglement?

The entanglement is that you don't know which particle is which spin until you measure one, and there is a 50/50 chance of it being + or of being - regardless of measurement alignment. In fact, they both exist in a superposition of both spins.

If one of the resultant particles is +, then the other must be -. Once one is measured, both their states are fully defined and they are no longer entangled.

If you bring two electrons close enough for their magnetic moments to interact, then they become entangled (and may emit photons in the process). The photon splitting example creates two lower energy photons that have interacted so their states are limited.

Two unentangled particles can have spin states uu. dd, ud, du. If they are entangled, only ud and du are possible.

 

[James MC]

The entanglement is that you don't know which particle is which spin until you measure one, and there is a 50/50 chance of it being + or of being - regardless of measurement alignment. In fact, they both exist in a superposition of both spins.

If one of the resultant particles is +, then the other must be -. Once one is measured, both their states are fully defined and they are no longer entangled.

I understand what entanglement is and I understand its implications for the statistical outcomes of measurements. I also understand how it originates: when an interaction of two particles depends on the superposed state of at least one of the particles. What I don't understand is how experimenters prepare entangled states in the lab. For example, I don't see why splitting a spin-zero particle in two would yield entangled components. Why does it not yield two unentangled particles with definite opposite spins?

 

[meBigGuy]

I don't prepare them so I can only hazard a guess. A single electron has spin. Bring it near another electron and the pair entangle have a zero expectation value. A photon may be emited in the process of entanglement.

An unobserved photon has spin, and when split into lower energy photons the resulting entangled pair have spin. I don't think a real single photon can be spinless.

Are we getting closer?

 

[James MC]

I wasn't necessarily talking about photons in that example. The examples I've read about in which experimenters prepare entangled states (so that e.g. they can test Bell's theorem) is (1) a photon gets split by a crystal into two photons and (2) a spin-zero particle decays into two particles with opposite spins. I've never seen any physical principle or explanation for why the resulting particles should be entangled. That's what I'm trying to find out. Or is it just that we *infer* indirectly that they must have been entangled given the results of our measurements on the pairs, but we don't know why they were entangled?

 

[meBigGuy]

The idea of causing 2 electrons to interact (spin entangle) is pretty straightforward. Are you OK with that?

Moving On:
If a photon is split into two photons, you have to get conservation of energy and momentum, correlated polarizations, and phase matching in the frequency domain. Why do they have correlated polarizations? Think of the original photon as a wave for a bit. Crudely stated, the sum of the parts must equal the whole.

 

[James MC]

The idea of causing 2 electrons to interact (spin entangle) is pretty straightforward. Are you OK with that?

Well, I know that if the spin of particle 1 changes as a result of the spin of particle 2, and particle 2 is in a spin superposition, then they will become spin-entangled. But what I've been asking about is how experimenters prepare such states. Or at least, how do they come across such states, so that they can test the properties of entanglement. Basically, I get the abstract stuff but am trying to wrap my head around concrete examples.

Moving On:
If a photon is split into two photons, you have to get conservation of energy and momentum, correlated polarizations, and phase matching in the frequency domain. Why do they have correlated polarizations? Think of the original photon as a wave for a bit. Crudely stated, the sum of the parts must equal the whole.

I would be pretty keen to hear an elaboration of this idea. On the face of it, the propositions "original photon is a wave" and "sum of parts must = whole" do not entail that the parts must be entangled. After all, such propositions apply to classical entities too.

 

[DrChinese]

I understand that entanglement pretty much follows from any interaction provided one particle is in some superposition. What I don't understand is how any experimenter can create or maintain an entangled state so that it can be manipulated in the lab. ... I take it that by "split" you mean that a high energy photon is converted into two low energy photons? (I thought photons were massless point particles.) Anyway, How do you know they start out entangled? Why doesn't the crystal just split them? Why should this splitting yield entanglement?

You then offer a general rule:

But conservation principles seem insufficient to yield entanglement. Take a particle that is spin zero and let it decay into two particles, one with plus spin, one with minus (to preserve conservation). Where is the entanglement?

OK, during parametric down conversion (PDC) you have an input photon (which is definitely NOT a point particle in most normal situations) and 2 output photons. You have entanglement of the 2 output photons due to conservation rules IF the particles are indistinguishable. The why of this is that the conservation rule is more fundamental than the idea that the particles are separate entities. They aren't, and they are not localized as you might expect. (Even a single photon can hardly be considered localized because its wave function is not.)

The entangled state is maintained until there is decoherence, ie one of the photons interacts with its surrounding environment. You probably already know that a normal single particle likewise remains in its same state until it interacts with its environment, so this is the same principle.

Now you mention that there is conservation in the classical world. Yes, this is true. But there is no entanglement in the classical world, only in the quantum world, as the classical world does not have superpositions, Heisenberg Uncertainty Principle, etc. While this distinction may seem semantic at first glance, it should be stated that Bell's Theorem drew a clear line in the sand on this point. Entangled (quantum) particle statistics are DIFFERENT than product state (classical) statistics. So experiments demonstrate the existence of these phenomena, for which classical predictions are flat out wrong.

I can give you a specific example if that helps. A pair of PDC Type I entangled photons will be polarization matched 25% of the time when they are measured at settings 120 degrees apart. The classical prediction is greater than 33%. This measly 8% difference is enough to invalidate classical comparisons, such as the ones you are making. There are hundreds of similar differences which have been published to date.

 

[DrChinese]

I can give you a specific example if that helps. A pair of PDC Type I entangled photons will be polarization matched 25% of the time when they are measured at settings 120 degrees apart. The classical prediction is greater than 33%. This measly 8% difference is enough to invalidate classical comparisons, such as the ones you are making. There are hundreds of similar differences which have been published to date.

And to drive home the point: Bell tells us that the classical prediction must be greater than 33%. However, there actually is NO specific classical prediction, and as far as I know there never has been! The classical prediction had been 100% matching at an angle difference of 0 degrees, which is the same as the quantum prediction. No one had ever thought to consider other angles prior to Bell!

You can run through the exercise yourself if you don't accept what I am saying above. A classical setup cannot be created which matches experiment.

 

[meBigGuy]

I would be pretty keen to hear an elaboration of this idea. On the face of it, the propositions "original photon is a wave" and "sum of parts must = whole" do not entail that the parts must be entangled. After all, such propositions apply to classical entities too.

The classical parallel is that I have a dime and a penny and shake them in my hands and then separate my hands with a coin in each. The outputs are obviously highly correlated. I measure one, and I know the other. In quantum mechanics, however, it isn't that simple. In quantum space each hand has a superposition of a penny and a dime and even if you do the same thing every time the left hand will produce a penny 50% of the time, and the right hand will properly correlate.

Let's try another approach:
If I have two independent electrons A and B that have independent alignment there is always 1 polarization what will detect A up with 100% certainty and another (same or different as required) polarization that will detect B up with 100% certainty.

If the electrons are entangled, any polararization will detect A or B up with 50% probability, and the other will correlate. There is no polarization to get 100% up.

Now, that doesn't speak to how the lab technician brings two electrons together in a magnetic field, turns off the field, and let's them stabilize into the lowest possible energy state (opposite spins, entangled), possibly emitting a photon (excess energy) in the process.