Figure 2

(a) Schematic depiction of the two dipoles embedded in the fish eye cavity, which is surrounded by mirrors on all sides. (b) Spectrum of the cavity ( ω l = l ( l + 1 ) c / ( R 0 n 0 ) , l = 1 , 2 , 3 ⋯ ) in the absence ( κ = 0 ) and the presence ( κ ≠ 0 ) of losses. The atomic resonant frequency ω 0 is tuned between two resonances of the cavity. (c) Strength of the dipole-dipole interaction δ ω ( r 1 , r 2 ) / Γ 0 between two atoms for four different lens radii: (i) R 0 = 4.93 λ , (ii) R 0 = 8.11 λ , (iii) R 0 = 11.3 λ , and (iv) R 0 = 14.48 λ , assuming lens thickness b = λ / 10 and Γ 0 = d z 2 ω 0 3 / ( 3 π ɛ 0 ℏ c 3 ) . The lens radii are chosen such that the transition frequency of the atoms ω 0 = 2 π c / λ lies halfway between the resonances of the lens ( l = 1 , 2 , 3 ⋯ ). In particular, we chose the order parameters (i) ν = 30.5 , (ii) ν = 50.5 , (iii) ν = 70.5 , and (iv) ν = 90.5 , where ν = 1 2 [ 16 π 2 ( R 0 n 0 / λ ) 2 + 1 + 1 ] and n 0 = 1 . The atom on the left is positioned exactly λ away from the mirror, whereas the position of the second atom is sweeped. The strength of the interaction peaks λ away from the opposite mirror surface with a height that is independent of the radius of the lens and the interatomic distance. (d) Enlarged view of the dipole-dipole interaction near the antipodal point, showing that the width of the peak is approximately λ / 2 .