---
title: "Zeeman slower"
chunk: 2/2
source: "https://en.wikipedia.org/wiki/Zeeman_slower"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:42:14.782166+00:00"
instance: "kb-cron"
---

  
    
      
        B
        (
        z
        )
        =
        
          
            
              ℏ
              k
            
            
              μ
              ′
            
          
        
        v
        +
        
          
            
              ℏ
              δ
            
            
              μ
              ′
            
          
        
        =
        
          
            
              ℏ
              k
              
                v
                
                  i
                
              
            
            
              μ
              ′
            
          
        
        
          
            1
            −
            
              
                
                  2
                  a
                
                
                  v
                  
                    i
                  
                  
                    2
                  
                
              
            
            z
          
        
        +
        
          
            
              ℏ
              δ
            
            
              μ
              ′
            
          
        
        ,
      
    
    {\displaystyle B(z)={\frac {\hbar k}{\mu '}}v+{\frac {\hbar \delta }{\mu '}}={\frac {\hbar kv_{i}}{\mu '}}{\sqrt {1-{\frac {2a}{v_{i}^{2}}}z}}+{\frac {\hbar \delta }{\mu '}},}
  

where 
  
    
      
        
          v
          
            i
          
        
      
    
    {\displaystyle v_{i}}
  
 is the maximal velocity class that will be slowed; all the atoms in the velocity distribution that have velocities 
  
    
      
        v
        <
        
          v
          
            i
          
        
      
    
    {\displaystyle v<v_{i}}
  
 will be slowed, and those with velocities 
  
    
      
        v
        >
        
          v
          
            i
          
        
      
    
    {\displaystyle v>v_{i}}
  
 will not be slowed at all. The parameter 
  
    
      
        η
      
    
    {\displaystyle \eta }
  
 (which determines the required laser intensity) is normally chosen to be around 0.5. If a Zeeman slower were to be operated with 
  
    
      
        η
        ≈
        1
      
    
    {\displaystyle \eta \approx 1}
  
, then after absorbing a photon and moving to the excited state, the atom would preferentially re-emit a photon in the direction of the laser beam (due to stimulated emission), which would counteract the slowing process.

== Realization ==
The required form of the spatially inhomogeneous magnetic field as we showed above has the form

  
    
      
        B
        (
        z
        )
        =
        
          B
          
            0
          
        
        +
        
          B
          
            a
          
        
        
          
            1
            −
            z
            
              /
            
            
              z
              
                0
              
            
          
        
        .
      
    
    {\displaystyle B(z)=B_{0}+B_{a}{\sqrt {1-z/z_{0}}}.}
  

This field can be realized a few different ways. The most popular design requires wrapping a current-carrying wire with many layered windings where the field is strongest (around 20–50 windings) and few windings where the field is weak. Alternative designs include a single-layer coil that varies in the pitch of the winding and an array of permanent magnets in various configurations.

== Outgoing atoms ==
The Zeeman slower is usually used as a preliminary step to cool the atoms in order to trap them in a magneto-optical trap. Thus it aims at a final velocity of about 10 m/s (depending on the atom used), starting with a beam of atoms with a velocity of a few hundred meters per second. The final speed to be reached is a compromise between the technical difficulty of having a long Zeeman slower and the maximal speed allowed for an efficient loading into the trap.
A limitation of setup can be the transverse heating of the beam. It is linked to the fluctuations of the speed along the three axes around its mean values, since the final speed was said to be an average over a large number of processes. These fluctuations are linked to the atom having a Brownian motion due to the random reemission of the absorbed photon. They may cause difficulties when loading the atoms in the next trap.

== References ==