Optical Cooling by Photon Recoil

Although the recoil effect is very small when a single photon is absorbed, it can be used effectively for optical cooling of atoms by the cumulative effect of many absorbed photons. This can be seen as follows  

When atom A stays for the time T in a laser field that is in resonance with the transition /) - / ), the atom may absorb and emit a photon hco many times, provided the optical pumping cycle is short compared to T and the atom behaves like a true two-level system. This means that the emission of fluorescence photons hco by the excited atom in level k) brings the atom back only to the initial state /), but never to other levels. With the saturation parameter S = Bikp coik)/Aik, the fraction of excited atoms becomes 

The fluorescence rate is NkAk = Nk/rk. Since Nk can never exceed the saturated value Nk = Ni- -Nk)/2 = N/2, the minimum recycling time for the saturation parameter S oo (Sect. 3.6) is AT = 2xk. 

When an atom passes with a thermal velocity v = 500 m/s through a laser beam with 2-mm diameter, the transit time is 7 = 4 xs. For a spontaneous lifetime Zk = 10 s the atom can undergo q (r/2)/r = 400 absorption-emission cycles during its transit time. 

When a laser beam is sent through a sample of absorbing atoms, the LIF is generally isotropic, that is, the spontaneously emitted photons are randomly 

The absorbed photons, however, all come from the same direction. Therefore, the momentum transfer for q absorptions adds up to a total recoil momentum p = qhk (Fig. 9.4). This changes the velocity v of an atom which flies against the beam propagation by the amount Au = hk/M per absorption. For q absorption-emission cycles we get 

Atoms in a collimated atomic beam can therefore be slowed down by a laser beam propagating anticollinearly to the atomic beam [1120]. This can be expressed by the cooling force  

Note That the recoil energy transferred to the atom 

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Optical sideband cooling is quite analogous to the Doppler cooling by photon recoil discussed in Sect. 9.1. The only difference is that the confinement of the ion within the trap leads to discrete energy levels of the oscillating ion, whereas the translational energy of a free atom corresponds to a continuous absorption spectrum within the Doppler width. 

An interesting aspect of collision-aided radiative excitation is its potential for optical cooling of vapors. Since the change in kinetic energy of the collision partners per absorbed photon can be much larger than that transferred by photon recoil (Sect. 9.1), only a few collisions are necessary for cooling to low temperatures compared with a few thousand for recoil cooling [1093]. 

Fig. 9.13 Cooling, deflection and compression of atoms by photon recoil. The electro-optic modulators (EOM) and the acousto-optic modulator (AOM) serve for sideband generation and frequency tuning of the cooling laser sideband [1136]...

Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping theoretical analysis. Journal of the Optical Society of America B, 6, 2112-2124. 

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