Resolved sideband cooling is a laser cooling technique allowing cooling of tightly bound atoms and ions beyond the Doppler cooling limit, potentially to their motional ground state. Aside from the curiosity of having a particle at zero point energy, such preparation of a particle in a definite state with high probability (initialization) is an essential part of state manipulation experiments in quantum optics and quantum computing. Historical notes As of the writing of this article, the scheme behind what we refer to as resolved sideband cooling today is attributed to D.J. Wineland and H. Dehmelt, in their article ‘‘Proposed laser fluorescence spectroscopy on mono-ion oscillator III (sideband cooling).’’ The clarification is important as at the time of the latter article, the term also designated what we call today Doppler cooling, which was experimentally realized with atomic ion clouds in 1978 by W. Neuhauser and independently by D.J. Wineland. An experiment that demonstrates resolved sideband cooling unequivocally in its contemporary meaning is that of Diedrich et al. Similarly unequivocal realization with non-Rydberg neutral atoms was demonstrated in 1998 by S. E. Hamann et al. via Raman cooling. Conceptual description Resolved sideband cooling is a laser cooling technique that can be used to cool strongly trapped atoms to the quantum ground state of their motion. The atoms are usually precooled using the Doppler laser cooling. Subsequently, the resolved sideband cooling is used to cool the atoms beyond the Doppler cooling limit. A cold trapped atom can be treated to a good approximation as a quantum mechanical harmonic oscillator. If the spontaneous decay rate is much smaller than the vibrational frequency of the atom in the trap, the energy levels of the system can be resolved as consisting of internal levels each corresponding to a ladder of vibrational states. Suppose a two-level atom whose ground state is shown by g and excited state by e. Efficient laser cooling occurs when the frequency of the laser beam is tuned to the red sideband i.e. , where is the internal atomic transition frequency and is the harmonic oscillation frequency of the atom. In this case the atom undergoes the transition , where represents the state of an ion whose internal atomic state is a and the motional state is m. This process is labeled '1' in the adjacent image. Subsequent spontaneous emission occurs predominantly at the carrier frequency if the recoil energy of the atom