Is there a way to increase the efficiency of spdc?

Can a setup be made such that the efficiency of spontaneous parametric downconversion approaches 100%? From what I have been told, this would be possible using classical input fields matching both the pump and output frequencies, but I am unsure if one could simply use laser of both frequencies on the crystal, or if one would need to apply electric fields on the crystal with an electromagnetic coil at the proper number of Teslas. Is this true, and if so, what might the details of the setup be? Alternatively, might there be any other methods of accomplishing this?
 

jfizzix

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If all you need is to convert light from the pump to the down-conversion frequency, then you can put the crystal in a high-finesse cavity that's resonant at the pump frequency. Because of multiple internal reflections, the pump power inside the cavity can be much larger than the pump power outside the cavity. This sort of object is known as an optical parametric oscillator (OPO).

There's theoretical reasons to believe that the maximum efficiency of an OPO is less than 100 percent, since the essential conditions are identical for the reverse process (second harmonic generation) to happen as well. Some models predict a maximum efficiency of 50 percent for a coherent state pump, but I don't know enough about experimental tests to comment further.

The second thing you could do, if you don't want to use the cavity, is to used a pulsed pump laser so that while the mean pump power is small, the peak power of the pulse can be many orders of magnitude higher (e.g., using a sub-picosecond pulsed pump pulse), greatly increasing the efficiency of SPDC up to multiple percent.

If you're wanting high quality photon pairs, for photon pair counting, or entanglement experiments, then you may be out of luck for getting high efficiency. In the theory of SPDC, the photon number statistics only are described by photon pairs (i.e., biphotons) for relatively low pump powers. At very high pump powers, the likelihood of getting multi-biphoton states becomes significant, and the quality of your photon pair statistics degrades (the coincidences to accidentals goes down). It is at least possible to get pair generation rates as high as a hundred million pairs per second per milliwatt of pump power.

For some information on the fundamentals of the efficiency of SPDC, you may be interested in this paper I'm working on.
https://arxiv.org/abs/1807.10885
That said, it's subject to revision, and could have any number of mistakes, so I would look more at the references it cites.
Hope this helps:)
 
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If all you need is to convert light from the pump to the down-conversion frequency, then you can put the crystal in a high-finesse cavity that's resonant at the pump frequency. Because of multiple internal reflections, the pump power inside the cavity can be much larger than the pump power outside the cavity. This sort of object is known as an optical parametric oscillator (OPO).

There's theoretical reasons to believe that the maximum efficiency of an OPO is less than 100 percent, since the essential conditions are identical for the reverse process (second harmonic generation) to happen as well. Some models predict a maximum efficiency of 50 percent for a coherent state pump, but I don't know enough about experimental tests to comment further.

The second thing you could do, if you don't want to use the cavity, is to used a pulsed pump laser so that while the mean pump power is small, the peak power of the pulse can be many orders of magnitude higher (e.g., using a sub-picosecond pulsed pump pulse), greatly increasing the efficiency of SPDC up to multiple percent.

If you're wanting high quality photon pairs, for photon pair counting, or entanglement experiments, then you may be out of luck for getting high efficiency. In the theory of SPDC, the photon number statistics only are described by photon pairs (i.e., biphotons) for relatively low pump powers. At very high pump powers, the likelihood of getting multi-biphoton states becomes significant, and the quality of your photon pair statistics degrades (the coincidences to accidentals goes down). It is at least possible to get pair generation rates as high as a hundred million pairs per second per milliwatt of pump power.

For some information on the fundamentals of the efficiency of SPDC, you may be interested in this paper I'm working on.
https://arxiv.org/abs/1807.10885
That said, it's subject to revision, and could have any number of mistakes, so I would look more at the references it cites.
Hope this helps:)
To what extent would the multi-biphoton states be entangled if they were generated using an OPO?
 

jfizzix

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To what extent would the multi-biphoton states be entangled if they were generated using an OPO?
There's three degrees of freedom in which photon pairs can be entangled: polarization, position/momentum, and energy/time. Your ability to detect the entanglement will be limited by your ability to detect individual photon pairs. That said, the amount of entanglement can be measured based on how strong the correlations are in these degrees of freedom:
http://www.pas.rochester.edu/~jschneel/Schneeloch_QuantEntEPR_PRA_2018.pdf
For polarization entanglement, that's determined by experimental design, and how indistinguishable you can make the photon pairs:
For energy-time entanglement, it depends on the characteristics of the crystal, but it's limited by how narrowband you can make the pump light
For position-momentum entanglement, it also depends on the characteristics of the crystal, but depends on how wide the pump beam is as it passes through the crystal, as well as the crystal thickness.
For some specifics on the spatial correlations of photon pairs, you may be interested in:
http://www.pas.rochester.edu/~jschneel/Schneeloch_SPDC_Birthzone_Intro_JOpt_2016.pdf
 
There's three degrees of freedom in which photon pairs can be entangled: polarization, position/momentum, and energy/time. Your ability to detect the entanglement will be limited by your ability to detect individual photon pairs. That said, the amount of entanglement can be measured based on how strong the correlations are in these degrees of freedom:
http://www.pas.rochester.edu/~jschneel/Schneeloch_QuantEntEPR_PRA_2018.pdf
For polarization entanglement, that's determined by experimental design, and how indistinguishable you can make the photon pairs:
For energy-time entanglement, it depends on the characteristics of the crystal, but it's limited by how narrowband you can make the pump light
For position-momentum entanglement, it also depends on the characteristics of the crystal, but depends on how wide the pump beam is as it passes through the crystal, as well as the crystal thickness.
For some specifics on the spatial correlations of photon pairs, you may be interested in:
http://www.pas.rochester.edu/~jschneel/Schneeloch_SPDC_Birthzone_Intro_JOpt_2016.pdf
I saw that an optical parametric amplifier appears to increase SPDC efficiency using both pump and signal frequency lasers: https://en.wikipedia.org/wiki/Optical_parametric_amplifier. Would using a pair of orthogonal BBO crystals with pump and signal frequency lasers result in efficient SPDC with a decent degree of polarization entanglement?
 

jfizzix

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I saw that an optical parametric amplifier appears to increase SPDC efficiency using both pump and signal frequency lasers: https://en.wikipedia.org/wiki/Optical_parametric_amplifier. Would using a pair of orthogonal BBO crystals with pump and signal frequency lasers result in efficient SPDC with a decent degree of polarization entanglement?
If you're using a signal frequency laser, you can simulate the production of more photon pairs, but where one half of each photon pair would be a signal photon at the signal frequency, there would be no way to separate it from the quadrillions of photons (e.g., 1 milliwatt of power is about that many photons per second for common wavelengths) also at the signal frequency that came from the signal laser.
 
If you're using a signal frequency laser, you can simulate the production of more photon pairs, but where one half of each photon pair would be a signal photon at the signal frequency, there would be no way to separate it from the quadrillions of photons (e.g., 1 milliwatt of power is about that many photons per second for common wavelengths) also at the signal frequency that came from the signal laser.
That may be acceptable, although wouldn't it be possible to separate them at least in theory, since the signal and idler beams separate into cones of light?
 

jfizzix

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That may be acceptable, although wouldn't it be possible to separate them at least in theory, since the signal and idler beams separate into cones of light?
The spatial mode profile of the part of the down-converted light that is stimulated by the signal beam, would overlap with the signal beam, making it not possible to separate them. That said, you'll want to confirm that for yourself, since I'm only reasonably certain that that is the case. Good luck on your studies :)
 
The spatial mode profile of the part of the down-converted light that is stimulated by the signal beam, would overlap with the signal beam, making it not possible to separate them. That said, you'll want to confirm that for yourself, since I'm only reasonably certain that that is the case. Good luck on your studies :)
I was recently told that OPA would result in entanglement between optical fields instead of photons. Is that true, and if so, what is the difference between entanglement between fields and between photons?
 

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