Hi.

The problem is, that when you stabilize the second laser to the same cavity, you will not get the real frequency noise of the stabilized laser. In principle via the beat note of lasers locked to the same cavity you can only get a measure for the quality of your locking system, i.e. how big are the deviations from the cavity as a reference. The frequency noise from the cavity itself will be present on both channels and will be strongly suppressed via common mode rejection, since it is identical for the two lasers. 

To measure it correctly you should have a second (identical) cavity, which is not correlated to the first one. This means it should have a seperate vibration isolation, temperature control, .....

What you get then in the beat is the combined frequency noise of the two lasers.

I agree with the concerns of Christian regarding a linewidth measurement made using the beatnote of two lasers stabilized to the same cavity. The frequency noise will most likely have correlations which will not be obvious from the beatnote. I don't think the second cavity has to be identical, but it should of course be offering similar noise performance.

In principle I don't see a problem with stabilizing two lasers to the same cavity using PDH. The requirements would seem to be that the PDH modulation frequencies for each laser are different, such that you once you mix the photo-diode signal with the local oscillator for one laser you can filter out the frequency components from the beatnote of the other. For this reason the modulation frequencies should also differ by (safely) more than the highest frequency component of noise that is significant for you.  However I never tried this experimentally and would be interested to hear of any adverse experiences of people that have.

Christian is right. If you want to do a fair noise measurement, you shouldn´t lock the lasers to each other via a cavity. However this could be very useful if you want to have the relative noise between the lasers as small as possible.

What kind of cavity do you have? If you have a ring cavity, you could send your lasers counter propagating through the cavity (use circulators) to separate their signals from each other. If your cavity is birefrigent, you could of course use V and H polarized modes. In both cases you could use the same modulation frequency.

Hi, thanks a lot for your very instructive replies. Laser stabilization is actually new to me and I am in charge of designing a test setup and build it within next year (yet, I don't have neither NPRO nor cavity). I first have to determine free-running frequency noise, followed by stabilized laser frequency noise. My concern using only one cavity instead of two was mainly cost driven. I am going now to use your comments as a new base for my readings that were mainly directed to Danzman's group (AEI Hannover) publications (giving an idea on the required frequency noise over a very large frequency range) until now. Relatively to the cavity, I am thinking in purchasing part of the PDH/beat note setup either in REO, Menlo Systems or stablelasers. But still in this initial part, I am open to other ideas  (hansch couillaud, iodine reference, self heterodyne detection?).

For my diploma thesis (see link, in German) I locked two diode lasers with PDH to the same cavity: orthogonal polarizations, counter propagating directions, different modulation frequencies. Useful to characterize your locking system.

Thanks a lot Gregor, I will have a close look to your diploma thesis. But I may have to refresh my German first.

Hi,

we stabilized two lasers with different wavelengths to the same cavity (see supplemental material of PRL 110, 210503 (2013)): a beam at 1560 nm is used to create a cavity enhanced dipole trap (locking technique: PDH), whereas a beam at 1529 nm cancels the differential light shift induced by the first laser on the D2 rubidium transition (locking technique: serrodyne+PDH, see Opt Lett 37, 1005 (2012)).

More in general, when a laser has to be stabilized at a wavelength where there is no atomic transition available, and that cannot be obtained with frequency shifting or offset frequency lock techniques,  one can adopt the transfer cavity scheme (in English see e.g. "Setup of a stable reference cavity for laser spectroscopy", M. Meister). A resonator is referenced to a laser locked to a transition, so as to avoid long term drifts. The stability of the first laser is then transfered to a second laser at a different wavelength, by locking it to the stabilized cavity.