per se non-Gaussian and hence does not require such addi- tional procedures. This opens a wide field of possible appli- cations whose study is beyond the scope of this Letter. 3 Let us consider now the situation for a regularly arranged sample of N atoms, whose resonance fluorescence is known to show squeezing [6], contrary to the situation for randomly distributed atoms. Under optimal conditions all the phase dif- ferences, ϕ ( n ) i − ϕ ( m ) j , vanish. This requires that all atoms lie on the central plane between the two detector positions, and the (not necessarily equal) distances between the atoms are integer multiples of the pump laser wavelength. In such an optimal configuration, the condition (8) reduces to In Fig. 1 we show the minor µ normalized by ν − $^{4}$N$^{2}$σ2 $_{22}$, cf. Eq. (9) together with (3), for a linear chain of atoms. All atoms are exactly aligned along the z -axis, with an inter- atomic distance of ten wavelengths of the driving laser. The direction of the laser is chosen to be almost parallel to the z - axis, so that the Rabi frequencies are kept nearly constant for a sufficiently large number of atoms. The two detectors are positioned in the far field region (at distance r from the coor- dinate center), detector 1 in the y -direction and detector 2 can be moved in the x - y -plane. Hence, the position of the latter only depends on the azimuth angle φ$_{2}$ . The system parameters are chosen such that the incoherent part of the atomic fluores- cence plays a significant role, σ$_{22}$/ | σ$_{21}$ | $^{2}$=3 . 5 . We remind the reader that under these conditions squeezing in resonance flu- orescence would not occur. According to the condition (11), entangled light is irradiated by three or more atoms. We con- sider the situation for the numbers of atoms being N =2 , 3 , 4 . It is clearly seen from Fig. 1, that entanglement occurs for N ≥ 3 . Even for the chosen relatively poor coherence prop- erties, entanglement of the radiation fields in two directions is found in almost every direction. Note that for opposite direc- tions of the detectors relative to the atomic sample ( r$_{1}$ = − r$_{2}$ , i.e. sin ϑ =0 ) the entanglement vanishes in general. It is straightforward to reduce the condition (10) for the gen- eration of entangled spatial light modes by N atoms, by using the general property σ$_{22}$ ≥| σ$_{21}$ | $^{2}$≥ 0 , to Inserting the stationary values of σ$_{ij}$ from [19], we rewrite the entanglement condition in terms of the atomic and driving- field parameters and obtain for the Rabi frequency Ω$_{R}$ where Γ$_{1}$ and Γ$_{2}$ are the energy and phase relaxation rates, respectively. Together with the deviation Δ of the laser fre- quency from the atomic transition, these rates determine the maximal driving field for which entanglement is obtained. The Rabi frequency is chosen real, so that the right hand side of the inequality (12) has to be positive. For N =1 , this condition is equal to the requirement for the possibility to ob- serve squeezing in single atom resonance fluorescence [5]. For N> 1 the driving field can be increased by a factor of about √ N compared with a single atom. More importantly, with an increasing number of atoms the ratio Γ$_{2}$ / Γ$_{1}$ of the individual atoms can exceed the value of one, being the ulti- mate limit beyond which squeezing in resonance fluorescence of a regular N -atom system disappears [6]. Thus, for such a system entanglement is more robust against dephasing than squeezing. We would like to emphasize at this point that the reso- nance fluorescence not only provides a continuously radiat- ing entangled source with high stability against dephasing, but it is also non-Gaussian. This is easily verified, since cor- relations containing operator products ˆ E ( ± ) n 1 ˆ E ( ± ) m 2 are zero when n + m exceeds the number N of atoms. It is important that non-Gaussianity is ”at times necessary to successfully perform quantum information tasks“, cf. [23] and Refs. [4-17] therein. This includes applications for entanglement distilla- tion and swapping, quantum teleportation, universal quantum computing, and others. That is, for some important quantum tasks the non-Gaussian property is a desired resource. For this reason, protocols have been established for the aim to de-Gaussify intially Gaussian entangled radiation fields, see e.g. [24]. The resonance fluorescence source under study is The linear chain cannot be experimentally realized to arbi- trary precision. For more and more atoms the negativity of the minor increases together with the robustness of the corre- sponding entanglement against dephasing allowing less accu- racy without destroying the entanglement. For the purpose of describing a realistic system, let us consider a linear Paul trap for a chain of ions. Note that present technologies, such as the multizone trap-array architectures designed for quantum com- putation [25], may offer alternative possibilities to realize an entangled radiation source of the type under study. The posi- tions of the ions are rather well fixed in the linear trap. How- ever, they are not perfectly equidistant for more than three FIG. 1: The normalized minor µ is shown, as a function of the angle φ$_{2}$ , for a linear chain of atoms with N = 2 (solid), 3 (dashed), and 4 (dotted). The pumping strength yields σ$_{22}$/ | σ$_{21}$ | $^{2}$=3 . 5 . Ω 2 R < $^{(}$N + 1 2 Γ 2 1 Γ 2 − Γ$_{1}$ Γ$_{2}$$^{)}$$^{(}$ Γ 2 2 + Δ 2 $^{)}$, (12) σ$_{22}$ | σ$_{21}$ | 2 < N + 1 . (11) g 2 $_{1}$g 2 2 sin $^{2}$( ϑ ) [ $^{(}$σ$_{22}$ − | σ$_{21}$ | 2 ) 2 − N $^{2}$| σ$_{21}$ | 4 ] < 0 . (10) 0 p 2 p 3 p 2 2 p 0 0.05 - 0.05 - 0.1 - 0.15 - 0.2 f 2 m v 4 N - 2 s 22 - 2