- #1
greypilgrim
- 522
- 36
Hi,
If we pump a beta barium borate (BBO) crystal, we get one circle of vertically polarized photons ##\left|V\right\rangle## and an intersecting circle of horizontally polarized ones ##\left|H\right\rangle##: http://quantum.ustc.edu.cn/old/img/image002.gif
At the intersection points of the circles, we get entanglement
$$\left|\psi\right\rangle= \frac{1}{\sqrt{2}}\left(\left|H\right\rangle\left|V\right\rangle+ \left|V\right\rangle\left|H\right\rangle\right)\enspace.$$
Why do we get an entangled state and not just a mixed state
$$\rho= \frac{1}{2}\left( \left|H\right\rangle \left|V\right\rangle\left\langle H\right|\left\langle V\right|+ \left|V\right\rangle\left|H \right\rangle\left\langle V\right|\left\langle H\right|\right)\enspace?$$
I know we can confirm the entanglement in many experiments, but I guess somebody first had to come up with the idea that this actually creates entanglement.
As a related question, in this case there is no relative phase shift, but I've also read papers where the BBO created
$$\left|\psi\right\rangle= \frac{1}{\sqrt{2}}\left(\left|H\right\rangle\left|V\right\rangle- \left|V\right\rangle\left|H\right\rangle\right)\enspace,$$
on what does the relative phase depend?
If we pump a beta barium borate (BBO) crystal, we get one circle of vertically polarized photons ##\left|V\right\rangle## and an intersecting circle of horizontally polarized ones ##\left|H\right\rangle##: http://quantum.ustc.edu.cn/old/img/image002.gif
At the intersection points of the circles, we get entanglement
$$\left|\psi\right\rangle= \frac{1}{\sqrt{2}}\left(\left|H\right\rangle\left|V\right\rangle+ \left|V\right\rangle\left|H\right\rangle\right)\enspace.$$
Why do we get an entangled state and not just a mixed state
$$\rho= \frac{1}{2}\left( \left|H\right\rangle \left|V\right\rangle\left\langle H\right|\left\langle V\right|+ \left|V\right\rangle\left|H \right\rangle\left\langle V\right|\left\langle H\right|\right)\enspace?$$
I know we can confirm the entanglement in many experiments, but I guess somebody first had to come up with the idea that this actually creates entanglement.
As a related question, in this case there is no relative phase shift, but I've also read papers where the BBO created
$$\left|\psi\right\rangle= \frac{1}{\sqrt{2}}\left(\left|H\right\rangle\left|V\right\rangle- \left|V\right\rangle\left|H\right\rangle\right)\enspace,$$
on what does the relative phase depend?