Zeeman-Slower

A Zeeman Slower or rare Zeeman brakeman is a device that is used in quantum optics for slowing of atomic beams. Typically, the atoms are decelerated 500-1000 m / s to about 10 m / s the speed range. Zeeman Slower based on the principle of laser cooling, the atoms that is, by absorption of laser light and then braked following re-emission of fluorescent photons. A Zeeman Slower consists of a spatially varying magnetic field through which flies the atomic beam, and an oppositely directed laser beam. The magnetic field counteracts, via the Zeeman effect of the velocity-dependent Doppler shift, which leads with slower atoms that they fall out of resonance with the laser beam.

History and use in research

The Zeeman Slower was first used by William D. Phillips ( Physics Nobel Prize in 1997, together with Steven Chu and Claude Cohen- Tannoudji "for the development of methods for cooling and trapping of atoms with laser light " ) and Harold J. Metcalf. 1982 suggested.

It is used in many experimental setups for Bose -Einstein condensation and Fermi condensates as the first stage of cooling the atoms as 500-1000 m / s atomic beam emerging from a furnace usually faster. Typically the Zeeman Slower followed by a magneto- optical trap, which is capable of capturing up to an upper limit speed of typically some 10 m / s just atoms. In further steps, the trapped atoms are then cooled with other methods (eg, sympathetic cooling, evaporative cooling) to a few micro- Kelvin above absolute zero.

Operation and design

An atomic beam is produced by evaporation of the elemental metal in a furnace (for example, sodium, lithium, rubidium ) consisting of atoms with an average speed of (depending on the type of metal and the evaporation temperature) 500-1000 m / s In order to curb these atoms by scattering of photons from an opposite current laser beam whose frequency must be adjusted so that they are also the Doppler shift

(: Velocity of the atom and: wavelength of the laser) into account, under the " perceive " the atoms of the laser light. While this is possible (so-called " chirped slowing "), but technically complex and leads to pulsed atomic beams, so is used as an alternative to the Zeeman effect. This does not change the light, but shifts the atomic levels of the atom, such that resonance is restored. Altogether, the following detuning of the atomic transition is then obtained:

Here mB is the Bohr magneton, the magnetic quantum number of the excited state and the ground state ( the transition under consideration ), and their Landé factors. The function describes the position-dependent magnetic field in the Zeeman Slower. The shift δ0 is a slight detuning of the brake laser wavelength compared to the atomic transition ( see below).

Maximum resonance with the atomic transition is made in the ideal case. It can be with the assumption of a negative constant deceleration (acceleration) Calculate the atoms in the Slower the shape of the magnetic field. Is obtained:

Here, the length of the Zeeman - slowers and. The detuning δ0 ensures a finite terminal velocity by being chosen so that the atoms after the Slower (where the magnetic field vanishes: B = 0) fall out of resonance and will not be slowed down. Without this parameter, atoms would pushed back into this at the end of slowers and can not be extracted as a beam.

In the figure to the right you can see above, the magnetic field of a Zeeman slowers and including how to reduce the speed of atoms when flying through the slowers. Fast atom (e.g., brown) come earlier in response to the brake laser, while for slow atoms later, the resonance condition is satisfied (for example, green). For very fast atoms never resonance is given, so that they fly through the Slower unrestrained. The upper limit speed for the Slower results from the resonance condition at the maximum magnetic field may be influenced by the structure of the slowers. In general permit longer Slower a higher initial magnetic field and thus a higher speed limit. At the end of slowers the magnetic field in the simplest case is again dropped to B = 0 ( ie for the case Bb = 0) and there are only atoms with the velocity

In resonance. Traps the atoms below this speed, they are no longer slowed down and vend can be interpreted as the average end or output speed of slowers. Analogously, ( again for the case Bb = 0) and the maximum Einfanggeschwindigkeit with the response at the maximum magnetic field define:

Only atoms that fly slower than this speed will be slowed by the Zeeman Slower.

Practically Zeeman Slower are typically built with current-carrying coils. Thereby is produced either by changing the density of the wires, or by changing the number of their layers of the variable magnetic field. But it is also possible Slower permanent magnets. Within the bobbin then passes a high- vacuum tube, in which the atom beam is located.

Previously it was assumed that the brakes used to nuclear transition is closed, i.e., the atoms may not disintegrate in the absorption-emission cycle, in a dark state outside the cycle. In real atoms, this is typically not fulfilled. Therefore, any additional superimposed laser beam must be used to " pump back " atoms from a dark state in the cycle. In the sodium spectrum above a corresponding transition is drawn, can be braked with the atoms = 1 ground state decay in the F.

Brakes, cooling and heating

The Zeeman Slower brakes all atoms that fly slower than his Einfanggeschwindigkeit vmax, at a speed close to its final speed vend from. Characterized both the average velocity and the velocity difference ( variation of the speeds) is reduced by these atoms. The achieved distribution width for the braked atoms ( the atoms are the Slower unrestrained, ie, with v> vmax, fly through disregarded ), regardless of the average residual velocity are also characterized by the specification of a longitudinal beam temperature. This is thus significantly reduced by the Zeeman Slower. The measurement of the velocity distribution (and hence the jetting temperature ) can be effected on the flight time broadening of packets atom or the Doppler shift of an absorption line.

The transverse velocity spread and temperature, which can be minimized by blending before Slower, on the other hand increases in Slower by an emission in a random direction following each absorption for the purpose of braking. Thus, the atoms run perpendicular to the flight direction of a random walk in velocity space:

Is the root mean square transverse velocity ( in the x or y direction), N ( t) is the number of spreading operations and the time t and Vrec the recoil velocity, that is the amount of speed change at an absorption or emission process.

To counteract this effect of the transversal heating, can, for example, behind the Zeeman Slower means of an optical molasses, a transverse cooling can be achieved. Another approach is to lead the atomic beam by means of suitably designed light and magnetic fields in the sheet, which can be effectively successively in different directions, the cooling effect of the Zeeman slowers.

Typically, the atoms are captured by the Zeeman Slower in a magneto-optical or any other case. So they fly through the potential of this case not ungefangen, the final velocity of slowers must be optimized to the maximum Einfanggeschwindigkeit the trap. In addition, the speed spread (or lateral and longitudinal temperature) should not be too large because the atoms diffuse to the final speed, and in accordance with the trapping spread to large decreases again (more atoms are still too fast).