Do Signal and Idler Photons from PDC Always Share Equal Energy?

[Demystifier]

Do the two photons (signal and idler) created by PDC always have equal energy?
(Of course, it depends on the Lorentz frame, but I mean in the frame in which the nonlinear crystal is at rest.)

 

[DrChinese]

Do the two photons (signal and idler) created by PDC always have equal energy?
(Of course, it depends on the Lorentz frame, but I mean in the frame in which the nonlinear crystal is at rest.)

They are close to equal, but that is not a requirement of the PDC crystal output stream. It actually follows conservation of energy (you would expect that) and there is a spread of outputs. (The sum of the output frequencies is equal to the input frequency.)

Here is a good reference that shows the spread of output wavelengths/frequencies in Figure 1:

Entangled photon apparatus for the undergraduate laboratory

 

[denian]

Parametric down conversion (PDC) is a nonlinear process in which a high-energy photon is converted into two lower-energy photons, known as the signal and idler photons. These two photons are typically entangled, meaning that their properties are correlated and cannot be described independently of each other.

In the frame where the nonlinear crystal is at rest, the two photons created by PDC may not always have equal energy. This is because the energy of the photons is determined by the conservation of energy and momentum in the process. While the total energy of the two photons will always be equal to the energy of the original photon, the distribution of energy between the signal and idler photons can vary.

This is due to the fact that the PDC process is probabilistic in nature and is affected by various factors such as the properties of the nonlinear crystal and the input photon. As a result, the energy of the signal and idler photons may not always be equal, but rather follow a distribution of possible energy values.

Furthermore, PDC can also occur in different types of crystals, such as type-I and type-II crystals, which have different energy conservation rules and can lead to different energy distributions between the signal and idler photons.

In summary, while the two photons created by PDC can have equal energy in some cases, it is not always the case in the frame where the nonlinear crystal is at rest. The specific energy distribution between the signal and idler photons is determined by various factors and can vary depending on the experimental setup.