  In most studies for the quantification of the third thermodynamic law, the
minimum temperature which can be achieved with a long but finite-time process
scales as a negative power of the process duration. In this article, we use our
recent complete solution for the optimal control problem of the quantum
parametric oscillator to show that the minimum temperature which can be
obtained in this system scales exponentially with the available time. The
present work is expected to motivate further research in the active quest for
absolute zero.
