It is common to generate quasi-disorder by a two-color optical lattice where the ratio of the two constituting wavelengths is an irrational number. I was just wondering whether one could also assign quasi-disorder to a two-color optical lattice if this ratio is rational. I mean, it is really not quite possible to obtain an irrational number in real experiments, or am I wrong?
The answer to your question is yes. In practice, frequencies cannot be measured to the accuracy required to say whether they are incommensurate or not, but as long as the size of your experimental lattice is smaller than the periodicity of the combination of the two optical fields, you obtain a pseudo disordered lattice. It is simple to do the calculation for any two given frequencies to find your limiting lattice size.
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