# Conservation of energy during generation of entanglement

Understanding conservation of energy during generation of entanglement.

In the experiment for generation of entangled pair of photons via SPDC

Single photons are struck on a BBO crystal.

In about 1 in a trillion of such collisions, two photons emerge.

Questions:

1. Is the combined energy of the two photons exactly equal to the "pump/original" photon?

2. If a photon is the smallest quanta of energy, then how do we explain the fact that its energy has been split among two photons?

or

3. Are there two parts to the energy of a photon? i.e.

a) energy of the photon. i.e. photon as a moving ball of energy.

taking the example of a ball --> the ball can be converted to energy

b) energy on the photon. i.e. momentum of the photon

taking the example of a ball --> the ball is moving at a certain velocity it caries some force/energy/momentum

Last edited:

1. Each photon is half the frequency and therefore half the energy of the down converted photon.

2. A photon is not the smallest quanta of energy. Energy is proportional to frequency.

tom.stoer
2. there is no smallest energy quantum and no energy quantization in general; for frequency f → 0 you have for energy E = hf → 0; so a photon is the smallest quantum of energy for a fixed frequency

3. no, you can't split energy in that way; it makes no sense

2. there is no smallest energy quantum and no energy quantization in general; for frequency f → 0 you have for energy E = hf → 0; so a photon is the smallest quantum of energy for a fixed frequency

3. no, you can't split energy in that way; it makes no sense

2. there is no smallest energy quantum and no energy quantization in general; for frequency f → 0 you have for energy E = hf → 0; so a photon is the smallest quantum of energy for a fixed frequency

is frequency "quantized"?

if it is, then would you have the smallest frequency and corresponding to that the lowest energy photon in the universe?

thus would we have the smallest unit of energy?

In general, quantization occurs due to boundry conditions. Think for example on an electron whos motion normally can be anything, but if it's bound to an atom it becomes quantized into its shells (periodic boundry condition). So while a free photon does not have an limits on its frequency, if you place that photon into a system with boundry conditions, such as a cavity, then a quantization effect occurs, and only special fequencies are allowed, which also gives you a minimum possible frequency. Though note that the minimum can still be changed by changing the system and thus the boundry conditions.