It seems that if the coherence length of a laser is big enough, it is possible to observe a (moving) interference picture by combining them. Is it true? How fast should photo-detectors be for observing of the interference of beams from two of the "best available" lasers? What is the coherence length of the best-available laser? More specifically, does there exist any (optical single-wavelength) laser with coherence length exceeding 500 meters?
Answer
This paper seems relevant to your question. If I'm reading the abstract correctly, the answers to your questions are:
Q: It seems that if the coherence length of a laser is big enough, it is possible to observe a (moving) interference picture by combining them. Is it true?
A: Yes
Q: How fast should photo-detectors be for observing of the interference of beams from two of the "best available" lasers?
A: 1 millisecond or faster
Q: What is the coherence length of the best-available laser?
A: More than 300 km
Q: More specifically, does there exist any (optical single-wavelength) laser with coherence length exceeding 500 meters?
A: Yes
The abstract in the paper:
Interference fringes produced by a pair of intracavity stabilized diode laser beams, each impinging separately on one aperture of a double slit, are recorded on a linear charge-coupled device array. The peculiar result of the experiment is that the fringe system is found to persist for a time of the order of 1 ms and loses contrast for longer integration times. This implies that the individual linewidths of the two beams from the stabilized lasers are narrower than 1 kHz and that the average drift rates of the central peaks are far less than 0.1 MHz/s. The device was built within the advanced undergraduate electronics laboratory of the department of physics and represents a considerable improvement over previous demonstration apparatuses used to detect interference fringes from independent lasers.
An interesting 1986 review of interference from independent sources:
"Interference between independent photons", Rev. Mod. Phys. 58, 209–231 (1986)
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