Tunable cavity optomechanics with ultracold neutral atoms

Optomechanical systems are typically implemented in solid state, with significant environmental couplings, thermal occupation of the mechanical resonator mode, and optomechanical parameters fixed during device fabrication. Here we present a widely tunable optomechanical system, in which the mechanical resonator is the collective motion of an ensemble of ultracold neutral atoms, trapped in the ground state of a harmonic oscillator potential. The atoms can be positioned anywhere along a strongly coupled cavity optical probe field, allowing access to both linear and quadratic optomechanical couplings, with contrast in coupling as large as $80\%$. Varying the optical fields provides high-dynamic- range control of both the mechanical resonator natural frequency (over a factor of 10) and the strength of the per-photon optomechanical coupling (over a factor of more than 1000). We demonstrate highly tunable cavity shifts and optical bistability. We also discuss experiments to explore wave mixing, squeezing, and spin-opto-mechanical interactions in our system.