A Zeeman slower or Zeeman decelerator is a scientific apparatus that is commonly used in quantum optics to cool a beam of atoms from room temperature or above to a few kelvins. At the entrance of the Zeeman slower the average speed of atoms is on the order of a few hundred m/s. The spread of velocity is also in the order of a few hundred m/s. Final speed at the exit of the slower is few 10 m/s with an even smaller spread. A Zeeman slower or Zeeman decelerator is a scientific apparatus that is commonly used in quantum optics to cool a beam of atoms from room temperature or above to a few kelvins. At the entrance of the Zeeman slower the average speed of atoms is on the order of a few hundred m/s. The spread of velocity is also in the order of a few hundred m/s. Final speed at the exit of the slower is few 10 m/s with an even smaller spread. A Zeeman slower consists of a cylinder, through which the beam travels, a pump laser that is shone on the beam in the direction opposite to the beam's motion, and a magnetic field (commonly produced by a solenoid-like coil) that points along the symmetry axis of the cylinder and varies spatially along the axis of the cylinder. The pump laser, which is required to be near-resonant to an atomic or molecular transition, Doppler slows a certain velocity class within the velocity distribution of the beam. The spatially varying Zeeman shift of the resonant frequency enables lower and lower velocity classes to be resonant with the laser, as the atomic or molecular beam propagates along the slower, hence slowing the beam. It was first developed by William D. Phillips (who was awarded the Nobel Prize in Physics for this discovery in 1997 together with Steven Chu and Claude Cohen-Tannoudji 'for development of methods to cool and trap atoms with laser light') and Harold J. Metcalf. The achievement of these low temperatures led the way for the experimental realisation of Bose–Einstein condensation, and a Zeeman slower can be part of such an apparatus. According to the principles of Doppler cooling, an atom modelled as a two-level atom can be cooled using a laser. If it moves in a specific direction and encounters a counter-propagating laser beam resonant with its transition, it is very likely to absorb a photon. The absorption of this photon gives the atom a 'kick' in the direction that is consistent with momentum conservation and brings the atom to its excited state. However, this state is unstable and some time later the atom decays back to its ground state via spontaneous emission (after a time on the order of nanoseconds, for example in Rubidium 87 the excited state of the D2 transition has a lifetime of 26.2 ns). The photon will be reemitted (and the atom will again increase its speed), but its direction will be random. When averaging over a large number of these processes applied to one atom, one sees that the absorption process decreases the speed always in the same direction (as the absorbed photon comes from a monodirectional source), whereas the emission process does not lead to any change in the speed of the atom because the emission direction is random. Thus the atom is being effectively slowed down by the laser beam. There is nevertheless a problem in this basic scheme because of the Doppler effect. The resonance of the atom is rather narrow (on the order of a few megaHertz), and after having decreased its momentum by a few recoil momenta, it is no longer in resonance with the pump beam because in its frame, the frequency of the laser has shifted. The Zeeman slower uses the fact that a magnetic field can change the resonance frequency of an atom using the Zeeman effect to tackle this problem. The average acceleration (due to many photon absorption events over time) of an atom with mass, M {displaystyle M} , a cycling transition with frequency, ω = c k + δ {displaystyle omega =ck+delta } , and linewidth, γ {displaystyle gamma } , that is in the presence of a laser beam that has wavenumber, k {displaystyle k} , and intensity I = s 0 I s {displaystyle I=s_{0}I_{s}} (where I s = ℏ c γ k 3 / 12 π {displaystyle I_{s}=hbar cgamma k^{3}/12pi } is the saturation intensity of the laser) is In the rest frame of the atoms with velocity, v {displaystyle v} , in the atomic beam, the frequency of the laser beam is shifted by k L v {displaystyle k_{L}v} . In the presence of a magnetic field B {displaystyle B} , the atomic transition is Zeeman shifted by an amount μ ′ B / ℏ {displaystyle mu 'B/hbar } (where μ ′ {displaystyle mu '} is the magnetic moment of the transition). Thus, the effective detuning of the laser from the zero-field resonant frequency of the atoms is The atoms for which δ ′ = 0 {displaystyle delta '=0} will experience the largest acceleration, namely where η = s 0 / ( 1 + s 0 ) {displaystyle eta =s_{0}/(1+s_{0})} and a m a x = ℏ k γ 2 M {displaystyle a_{max}={frac {hbar kgamma }{2M}}} .