Collective Cooling of Coulomb-Crystal Modes in the Strong Sideband-Coupling Regime

We analyze collective laser cooling of ion Coulomb crystals based on red sideband dynamics in the strong spin–motion coupling regime. Starting from an effective many-body Dicke-type model relevant for sideband cooling, we identify distinct cooling regimes as a function of coupling strength and crystal size. In the strong-coupling limit, the red sideband interaction realizes an approximately unitary state swap between collective spin excitations and selected motional modes, allowing for direct extraction of motional entropy. We show that sequential application of such swap pulses leads to rapid cooling, even for large ion crystals. We determine effective cooling rates and minimal occupations, and derive their scaling with the number of ions, demonstrating genuine collective enhancement of the cooling dynamics. Repeated cooling cycles converge to a fundamental limit set by sideband resolution and off-resonant couplings. The mechanism applies not only to the in-phase (center-of-mass) mode but also to out-of-phase modes, provided conditions on spectral separation and pulse parameters are satisfied. Finite-size effects, blue-sideband contributions, and mode-dependent couplings determine the achievable cooling performance. Owing to the state-swap dynamics, motional phonon statistics are directly mapped onto collective spin observables, enabling intrinsic, self-certifying thermometry of the cooled modes.