We are performing polarisation quantum state tomography of photon pairs generated through spontaneous parametric down-conversion by following the approach described in this paper: https://www.researchgate.net/publication/235531853_Measurement_of_qubits
Although we expect the quantum state to be pure, we are getting fairly low purity values defined as purity=trace(rho^2)), where rho is the density matrix. What are the typical causes of spontaneous parametric down-converted photon-pair quantum state impurity when performing polarisation tomography? How can we check whether something is wrong with the photon pair generation or with our implementation of the tomography procedure?
Article Measurement of qubits
Hi ALexander! Hoppe everything is ok with you
Common sources of measured incoherence:
1. Generation of double pairs (with a probability of p^2 where p is the probability of generating one pair). While overall the state is coherent, the inability of most detectors to measure number states will appear as decoherence in the correlations.
2. Imperfect wave plates, polarizers. If wave plates are not aligned, you may be preparing something that it is not what you expect.
3. Dark counts of the detectors. They will make your measured counts incoherent if dark counts are not correlated with measured polarization.
4. Depending on the scheme: compensation of the polarization group velocities. If your system is pulsed, and depending if you are using two Type I crossed crystals or one Type II crystal, you will have problems in compensating for the GVM or the GVD.
5. The coherence length of the pump can also cause trouble if it is too short.
There may be others...
Take care!
Gabriel
Hi,
First of all, what is the exact polarization entangled photon generation method you use? Do you follow Kwiat's 1995 PRL? Do you use a pulsed or CW source?
First verify that the detectors work fine and that the measured dark counts (that arise from the detector finite temperature and stray light) does not contribute to the coincidence counts significantly. If so, you've got a problem somewhere in the electronics or you collect light that does not originate from PDC. If you use a pulsed Ti:sapphire laser that emits in the IR and then frequency doubled to the UV before the PDC you have pulsed IR radiation that can pass through your filters and be counted as signal, though its source is not at the generating crystal.
Then check and see if the single photon collection efficiency is similar to other experiments in the field (depending on the nonlinear crystal type and length, pump power, coupling efficiency, detector quantum efficiency etc.).
If the figures seem reasonable, verify that your wave plates rotate the polarization according to your plan. I assume you use 4 detectors altogether so you can block one of the PDC arms and rotate the polarization between the H and V detectors and see if you get the right results (these results also depend on each channel coupling and detector efficiency).
If you use the typical Kwiat method you need also to verify that the compensating crystals are mounted with the right orientation with respect to the generating crystal and are of half length. Have you checked that?
Let me know if that helped,
Assaf
Thank you Jian and Assaf,
We are using somewhat novel biphoton generation method, so we had to modify the tomography setup. Thanks to your detailed replies, I think I now know that the problem may be with improper compensation. We'll investigate it further. Thank you once again!
Hi ALexander! Hoppe everything is ok with you
Common sources of measured incoherence:
1. Generation of double pairs (with a probability of p^2 where p is the probability of generating one pair). While overall the state is coherent, the inability of most detectors to measure number states will appear as decoherence in the correlations.
2. Imperfect wave plates, polarizers. If wave plates are not aligned, you may be preparing something that it is not what you expect.
3. Dark counts of the detectors. They will make your measured counts incoherent if dark counts are not correlated with measured polarization.
4. Depending on the scheme: compensation of the polarization group velocities. If your system is pulsed, and depending if you are using two Type I crossed crystals or one Type II crystal, you will have problems in compensating for the GVM or the GVD.
5. The coherence length of the pump can also cause trouble if it is too short.
There may be others...
Take care!
Gabriel
Thanks a lot for the list Gabriel!
I hope we'll solve it soon.
Best regards,
Alex
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