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Actually, Fig. 3 may also be plotted with nst versus the maximal photon number nm = η∼ 2 / κ∼ 2. By definition in Eq. 12, Zs is a function of nst and so is Zs† H2 Zs, which we denote as f (nst). To the lowest order, f (nst) is linear in nst, f (nst) =β nst. From Eq. 10, we then have nm = nst [1+ (Δ∼ c′ +4Nβ nst) 2 / κ∼ 2], which can be mapped exactly to the input-output relation in the discussion of dispersive optical bistability; see 3rd ed. (Springer-Verlag, Berlin
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