Atom cooling by nonadiabatic expansion

Motivated by the recent discovery that a reflecting wall moving with a square-root-in-time trajectory behaves as a universal stopper of classical particles regardless of their initial velocities, we compare linear-in-time and square-root-in-time expansions of a box to achieve efficient atom cooling. For the quantum single-atom wave functions studied the square-root-in-time expansion presents important advantages: asymptotically it leads to zero average energy whereas any linear-in-time (constant box-wall velocity) expansion leaves a nonzero residual energy, except in the limit of an infinitely slow expansion. For finite final times and box lengths we set a number of bounds and cooling principles which again confirm the superior performance of the square-root-in-time expansion, even more clearly for increasing excitation of the initial state. Breakdown of adiabaticity is generally fatal for cooling with the linear expansion but not so with the square-root-in-time expansion.