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In a very interesting recent Letter,^ several statistical properties of the energy levels of a single two-level atom interacting with one quantized electromagnetic mode were investigated, and it was found that the nearest-level spacing was highly correlated and regular, in contrast to chaotic dynamical behavior found in a semiclassical version of this model (for references see Ref. 1). Similar regularities in the same system had also been found by Graham and Hohnerbach^ and Graham,^ but for sufficiently strong coupling and suitably chosen initial conditions dynamical properties, e.g., the time-dependent occupation probabilities of the two levels, were found to behave irregularly, i.e., quasiperiodically with a large number of incommensurate frequencies.^'^ In this Comment we wish to examine to what extent the disparity between the regularity of the energy spectrum (cf. Fig. 1 of Ref. 1) and the irregular dynamical behavior found in Refs. 2 and 3 is a consequence of the assumption of a single two-level atom. In the semiclassical version of the model the number of atoms is irrelevant and can be absorbed in rescaled variables and parameters.Concerning the level statistics of the quantum system we find that already for a small number of atoms (iV = 9) and a correspondingly scaled down coupling constant k/VN (X = 0.5) the distribution of relative level spacings Wis) of neighboring levels of equal parity is represented reasonably well (cf. Fig. 1) by the Wigner distribution P(s)^(TTs/2)cxp(-7rs^/4), as one would expect for a quantum system which is chaotic in the classical limit. If we increase the coupling constant X, e.g., to X = 1.5, the level distribution for A^ = 9 further approaches the Wigner distribution, while it retains its regular features for A^= 1.In Fig. 2 we present the power spectrum of the electromagnetic mode gico) for a = 1.33VA^, A = 0.3, and the two values iV = 9, N=l. gio)) is defined as the Fourier transform of the time average of (i;;ol^^(^ + 3(U)) • :'^ : ••;. 1.0-;. •". •. 1.1 Qjj FIG. 2. ^(oj) forA^ = 9 (inset: yv=l).T)a{i)\ilJo}, where |i//o) is chosen as the product of the upper atomic state and a coherent state of amplitude a. For A^= 1 the sharp lines are arranged in two groups corresponding to a broad doublet. The doublet structure corresponds to a well-known regular feature of the dynamics, the periodic "revivals."'^ The distance of the maxima of the doublet is approximately k/a and gives the inverse of the revival time"^ multiplied by 277. The revivals are effectively damped as shown by the width of the doublet. When we increase a the high-frequency component of the doublet decreases in intensity, the two parts of the doublet overlap, the revivals disappear, and a quasiperiodic but effectively irregular dynamics results even for N=l}'^ This happens despite the fact that the level statistics continues to show its regularities. For iV = 9 and much smaller coupling (e.g., X = 0.03) one finds a decaplet of groups of sharp lines. However, for the strong-coupling case corresponding to Fig. 2...

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