Why is coherence and entanglement complementary?

[San K]

Why is coherence and entanglement complementary?

Lets take the case of a pair of entangled photon.

there is very little coherence between the entangled photons.

when we try to improve the coherence; the (degree of) entanglement starts to reduce.

why does that happen?

Does it have anything to do with Pauli's exclusion principle?

 

[bhobba]

Entaglement and decoherence are intimately rrealted - basically in decoherence phase leaks out to the enironment when it becomes entangled with it. Nothing to do with the Exclusion principle that I can see. Decoherence is generally not a reversible process.

Thanks
Bill

 

[San K]

Entaglement and decoherence are intimately rrealted - basically in decoherence phase leaks out to the enironment when it becomes entangled with it. Nothing to do with the Exclusion principle that I can see. Decoherence is generally not a reversible process.

Thanks
Bill

thanks Bill. agree with you. however the question is:

why can we not increase the coherence between entangled photons? (without reducing degree of entanglement)

I just realized that entanglement is not related with the exclusion principle in any way
because
both photons (bosons) as well as electrons (fermions) can be entangled.

 

[bhobba]

why can we not increase the coherence between entangled photons? (without reducing degree of entanglement)

I am not sure its impossible - just very difficult once they have become entangled and lost coherence. I will leave it to experimental types to see if they can actually devise a way to do it.

Thanks
Bill

 

[San K]

I am not sure its impossible - just very difficult once they have become entangled and lost coherence. I will leave it to experimental types to see if they can actually devise a way to do it.

Thanks
Bill

or the question can, alternatively, be framed as:

why can coherent particles not be entangled?

why do they necessarily have to lose their coherence? ...upon entanglement

 

[Maui]

Why is coherence and entanglement complementary?

Because decoherence works by entanglement between the system and its immediate environment.

See if this helps(a non-physicist can sometimes provide a more intuitive explanation):Let's say we shoot 2 electrons towards each other and they bounce off and scatter. Before they collide, they have a certain degree of inherent uncertainty to their position and momentum. After the collision, their uncertainty becomes JOINT, it belongs jointly to the new system, that we say is now entangled(this is essentially what worried Einstein in the 1930's and caused him to start his famous EPR debate about qm mechanics).

What decoherence does(you'll have to leave your classical pre-conceptions at this point) is point the "way" for a system in a coherent state towards its classical manifestion. As an example consider a sea of possibilities(that's our universe nonetheless) and a pointer that has interacted with its immediate environment(e.g. by colliding) and its "information" about position/momentum uncertainty has "leaked" into the environment and has become joint(entangled) with its environment. This is all decoherence does, so it basically doesn't resolve the measurement problem at all. All it does is provide a direction by which a quantum mechanical system becomes classical(emerges or becomes real if you want). Note that, the classical uncertainties are still there so some kind of measurement/interaction is still required to reach the classical level that we appear to observe.

Lets take the case of a pair of entangled photon.

there is very little coherence between the entangled photons.

when we try to improve the coherence; the (degree of) entanglement starts to reduce.

why does that happen?

Hope the above explanation provides the intuitive picture that was missing.

Does it have anything to do with Pauli's exclusion principle?

No.

 

[Cthugha]

The complementarity between coherence and entanglement or equivalently interference visibility in first-order or second order measurements is discussed for example in Birgit Dopfers PhD thesis ("www.univie.ac.at/qfp/publications/thesis/bddiss.pdf" ), unfortunately written in German around page 45 and 46.

It does NOT have anything to decoherence in the traditional sense. Just reconsider what single photon interference measures. It is a measure of spatial coherence of the light field which directly translates to a small spread in emission angle or equivalently momenta as seen at the position of the double slit. Or in other words the more point-like the light source is, the higher the visibility of the single photon interference pattern will be.

The reason for that is simple. Just imagine an extended light source and calculate the possible path differences from each point of the light source to the slits. These will of course translate into phase differences. The interference pattern behind the slit depends on the phase difference of the fields originating from the two slits. However, if there is already some phase difference introduces at the position of the slits, this will modify the interference pattern seen. So for an extended light source you will get a weighted superposition of all these slightly different interference patterns. If the spread in possible path differences is too large this corresponds to no interference pattern at all.
Under the conditions discussed in Dopfer's thesis, the minimal distance allowing to see a single photon interference pattern of perfect visibility is 770 mm.

The conditions for seeing interference in coincidence counting are rather different. The archetypical experiment is the one where the detector behind the double slit is placed behind a lens to get far field conditions and is not moved, while the detector in the other arm without any double slit is placed in the Fourier plane (each detector position corresponds to a certain k-value) and is moved around. Now each position of that detector corresponds to some specific momentum value and every photon detected on the other side will have a corresponding momentum value. There is typically no interference pattern behind the double slit (as discussed before) because the spread in momentum values is so large. However, as one now picks a certain momentum value by choosing a certain detector position in the Fourier plane, one also gets a relative count rate corresponding to the count rate one would see if one placed the detector behind the double slit at the very same position and fired a light field with the chosen momentum value at the double slit. As one moves the detector in the Fourier plane around, one picks a different momentum value and the count rate on the other side will change accordingly. If one moves further and further, the corresponding count rate will show minima and maxima according to the count rates one would see at exactly that detector position if one used light with the chosen well defined momentum. In summary one finds an interference pattern in coincidence counts.

Now why does the latter not work with spatially coherent light? This is almost trivial. As said before, spatial coherence corresponds to a small spread in momenta. As you now move the detector in the Fourier plane around, you scan exactly the whole range of momenta. One will find that the spread in momenta needed to see a single photon interference pattern is so small, that when you now scan the detector in the Fourier plane where you also scan the whole range of momenta, you will reach the end of the spread before you even reach a minimum of the coincidence count interference pattern. Under the conditions discussed in Dopfer's thesis the largest possible distance to see the interference pattern in coincidence counting is 106 mm.

The difference between 106 mm distance and 770 mm distance is huge and there is no region where you can get both. Note that this is not a consequence of the setup used. With other light sources or slits, you can change the numbers, but the upper distance bound for two-photon interference will always end up to be much smaller than the lower bound for single photon interference.

As an alternative simple handwaving argument, you can also think of the effective size of the light source becoming so small that diffraction from that point source destroys all correlations. Dopfer also gives this handwaving explanation, but in my opinion it is not a really good one as it works for sources having small size, but is not so trivial to translate into sources having small angular size (this is what you get by increasing the distance between source and slit).

 

[San K]

The complementarity between coherence and entanglement or equivalently interference visibility in first-order or second order measurements is discussed for example in Birgit Dopfers PhD thesis ("www.univie.ac.at/qfp/publications/thesis/bddiss.pdf" ), unfortunately written in German around page 45 and 46.

It does NOT have anything to decoherence in the traditional sense. Just reconsider what single photon interference measures. It is a measure of spatial coherence of the light field which directly translates to a small spread in emission angle or equivalently momenta as seen at the position of the double slit. Or in other words the more point-like the light source is, the higher the visibility of the single photon interference pattern will be.

The reason for that is simple. Just imagine an extended light source and calculate the possible path differences from each point of the light source to the slits. These will of course translate into phase differences. The interference pattern behind the slit depends on the phase difference of the fields originating from the two slits. However, if there is already some phase difference introduces at the position of the slits, this will modify the interference pattern seen. So for an extended light source you will get a weighted superposition of all these slightly different interference patterns. If the spread in possible path differences is too large this corresponds to no interference pattern at all.
Under the conditions discussed in Dopfer's thesis, the minimal distance allowing to see a single photon interference pattern of perfect visibility is 770 mm.

The conditions for seeing interference in coincidence counting are rather different. The archetypical experiment is the one where the detector behind the double slit is placed behind a lens to get far field conditions and is not moved, while the detector in the other arm without any double slit is placed in the Fourier plane (each detector position corresponds to a certain k-value) and is moved around. Now each position of that detector corresponds to some specific momentum value and every photon detected on the other side will have a corresponding momentum value. There is typically no interference pattern behind the double slit (as discussed before) because the spread in momentum values is so large. However, as one now picks a certain momentum value by choosing a certain detector position in the Fourier plane, one also gets a relative count rate corresponding to the count rate one would see if one placed the detector behind the double slit at the very same position and fired a light field with the chosen momentum value at the double slit. As one moves the detector in the Fourier plane around, one picks a different momentum value and the count rate on the other side will change accordingly. If one moves further and further, the corresponding count rate will show minima and maxima according to the count rates one would see at exactly that detector position if one used light with the chosen well defined momentum. In summary one finds an interference pattern in coincidence counts.

Now why does the latter not work with spatially coherent light? This is almost trivial. As said before, spatial coherence corresponds to a small spread in momenta. As you now move the detector in the Fourier plane around, you scan exactly the whole range of momenta. One will find that the spread in momenta needed to see a single photon interference pattern is so small, that when you now scan the detector in the Fourier plane where you also scan the whole range of momenta, you will reach the end of the spread before you even reach a minimum of the coincidence count interference pattern. Under the conditions discussed in Dopfer's thesis the largest possible distance to see the interference pattern in coincidence counting is 106 mm.

The difference between 106 mm distance and 770 mm distance is huge and there is no region where you can get both. Note that this is not a consequence of the setup used. With other light sources or slits, you can change the numbers, but the upper distance bound for two-photon interference will always end up to be much smaller than the lower bound for single photon interference.

As an alternative simple handwaving argument, you can also think of the effective size of the light source becoming so small that diffraction from that point source destroys all correlations. Dopfer also gives this handwaving explanation, but in my opinion it is not a really good one as it works for sources having small size, but is not so trivial to translate into sources having small angular size (this is what you get by increasing the distance between source and slit).

good one. thanks Cthuga. it will take some time to read and digest this...

 

[Jazzdude]

Entanglement does not destroy coherence, but it distributes the phase information over the entangled systems making each subsystem on its own incoherent. So you might want to say that you cannot get interference effects without looking at the whole system carrying the phase information.

Cheers,

Jazz