Super- and subradiance in dilute disordered cold atomic samples: observations and interpretations

Cooperative quantum-optical planar arrays of atoms

“…Ω ( jℓ) νµ + iγ ( jℓ) νµ represents the real and imaginary parts of the dipole radiation kernel [Eq. (12)], and in an infinite array, they depend on q,…”

“…While super-radiance has been extensively studied for many years [4], experiments on subradiance were, until a few years ago, limited to systems of two or a few particles [5][6][7][8][9][10]. More recent experiments have shown small long-lived fractions of disordered atom clouds [11,12] and spatially-extended subradiant mode resonances in resonator arrays [13].…”

“…θ) 3δ ν,µ − (r jℓ • ê * ν )(r jℓ • êµ ) −[δ ν,µ − 3(r jℓ • ê * ν )(r jℓ • êµ )] cos 2θ e ikr jℓ cos θ = 3γ[δ ν,µ − (r jℓ • ê * ν )(r jℓ • êµ )] sin kr jℓ kr jℓ + 3γ[δ ν,µ − 3(r jℓ • ê * ν )(r jℓ • êµ )] 2γ ( jℓ) νµ = 2ξIm G ( jℓ) νµ ,(B5)where we have used Eq (12)…”