Many atoms have a magnetic moment, that is, their energy shifts in a magnetic field according to the formula
According to the principles of quantum mechanics, the magnetic moment of an atom will be quantized, that is, it will take on one of certain discrete values. If the atom is placed in a strong magnetic field, its magnetic moment will be aligned with the field. If a number of atoms are placed in the same field, they will be distributed over the various allowed values of magnetic quantum number for that atom.
If a magnetic field gradient is superimposed on the uniform field, those atoms whose magnetic moments are aligned with the field will have lower energies in a higher field. Like a ball rolling down a hill, these atoms will tend to occupy locations with higher field and so are called "high-field-seeking" atoms. Conversely, those atoms with magnetic moments aligned opposite to the field will have higher energies in a higher field, tend to occupy locations with lower field, and so are called "low-field-seeking" atoms.
It is impossible to produce a local maximum of the magnetic field magnitude in free space. However, a local minimum can be produced. This minimum can trap atoms which are low-field seeking if they do not have enough kinetic energy to escape the minimum. Typically, magnetic traps have relatively shallow field minima and are only able to trap atoms whose kinetic energies correspond to temperatures of a fraction of a Kelvin.
The field minima required for magnetic trapping can be produced in a variety of ways. These include permanent magnet traps, Ioffe configuration traps, QUIC traps, and others.
The minimum of magnitude of the magnetic field can be realized with the so-called "atom microchip". . One of first microchip atomic traps is shown in Fig.1. The Z-shaped conductor (actually, the golden Z-shaped strip painted on the Si surface) is placed into the uniform magnetic field (source of this field is not shown in the figure). The only atoms with positive spin-field energy were trapped. In order to prevent the mixing of spin states, the external magnetic field was inclined in the plane of the chip, providing the adiabatic rotation of the spin at the movement of the atom. In the first approximation, just magnitude (but not orientation) of the magnetic field is responsible for effective energy of the trapped atom. The chip shown has size 2cm x 2 cm; these sizes were chosen to simplify the manufacturing. In principle, the size of such microchip traps can be drastically reduced. An array of such traps can be manufactured with conventional lithographic methods; such an array is considered as a prototype of a q-bit memory cell for the quantum computer. Ways of transfer of atoms and/or q-bits between traps are under development; the adiabatic optical (with off-resonance frequencies) and/or the electrical control (with additional electrodes) is assumed.
Bose-Einstein condensation (BEC) requires conditions of very high density and very low temperature in a gas of atoms. Laser cooling in a magneto-optical trap (MOT) is typically used to cool atoms down to the micro-Kelvin regime. However, laser cooling is limited by the momentum recoils an atom receives from single photons. Achieving BEC requires cooling the atoms beyond the limits of laser cooling, which means the lasers used in the MOT must be turned off and a new method of trapping be devised. Magnetic traps have been used to hold very cold atoms while evaporative cooling has reduced the temperature of the atoms enough to reach BEC.