13 (A)  a =0.5 Along lattice Δ=ν,  θ =0 (B)  a =0.5 Along lattice Δ, θ  optimized (C)  a =0.744 Along lattice Δ, θ  optimized (D)  a =0.5 Across lattice Δ=ν,  θ =0 (E)  a =0.5 Across lattice Δ, θ  optimized (a) Heating rate,  cooling rate , and equilibrium phonon number, scaled to non-interacting=1 (b) Components of heating rate / 10$^{-3}$η$^{2}$Ω$^{2}$Γ -1 (c) Components of cooling rate /  η $^{2}$Ω$^{2}$Γ-1 (d) Dipole interaction coefficients ( c (p)-2iΔ)/Γ,  d$_{α}$ (p)/Γ η ,  e$_{αα}$ (p)/Γ η 2 -π/ a 0 π/ a 0 2 4 p (A a) -π/ a 0 π/ a -4 0 4 p (A b) -π/ a 0 π/ a 0 1 2 p (A c ) -π/ a 0 π/ a -2 0 2 p (A d) -π/ a 0 π/ a 0 2 4 p (Ba) -π/ a 0 π/ a -4 0 4 p (Bb) -π/ a 0 π/ a 0 1 2 p (Bc) -π/ a 0 π/ a -2 0 2 p (Bd) -π/ a 0 π/ a 0 2 4 p (Ca) -π/ a 0 π/ a -4 0 4 p (Cb) -π/ a 0 π/ a 0 1 2 p (Cc) -π/ a 0 π/ a -2 0 2 p (Cd) -π/ a 0 π/ a 0 2 4 p (Da) -π/ a 0 π/ a -4 0 4 p (Db) -π/ a 0 π/ a 0 1 2 p (Dc) -π/ a 0 π/ a -2 0 2 p (Dd) -π/ a 0 π/ a 0 2 4 p (Ea) -π/ a 0 π/ a -4 0 4 p (Eb) -π/ a 0 π/ a 0 1 2 p (Ec) -π/ a 0 π/ a -2 0 2 p (Ed) FIG. 9: (Color online) Various functions of the (one-dimensional) phonon wave vector p . Different rows are different functions, different columns are different settings, given at the top (lattice spacing a , cooling of either the along- or across-lattice motion, laser detuning and direction either standard (Δ = ν , ϑ = 0) or optimized (for minimum total phonon number)). (a) Heating rate R$_{h}$$_{α}$ ( p ) (thin red), cooling rate R$_{c}$$_{α}$ ( p ) (thick blue) and steady state phonon number (thin black), each scaled to its own non-interacting value (dotted horizontal line). (b)/(c) Rates of the individual processes contributing to heating/cooling (cf. Fig. 5): emission/absorption of a phonon either when an excitation is created by the laser (thin blue), when it hops by dipole-dipole interaction (thick orange), or when it decays (thin black), and interferences between these (dotted). (d) Fourier space dipole interaction parameters c ( p ) (thin blue), d$_{α}$ ( p ) (thick orange), e$_{αα}$ ( p ) (thin black), real parts solid, imaginary parts dotted. In all cases ν = 10 Γ and α is the direction of motion being cooled ( x for along-lattice or y for across-lattice).