Zeeman slower

The coil of a Zeeman slowers on optical table prior to installation in an experiment with atom traps . The source for the atom beam is mounted on the thick side of the coil. The atom trap is placed in front of the front, thinner end of the coil. The slower is about 1 m long.

Schematic representation of a Zeeman slower in the experiment (see also photo above).

A Zeeman slower or, more rarely, a Zeeman brake is a device that is used in quantum optics to slow down atomic beams . Typically, the atoms are slowed down from the speed range 500-1000 m / s to about 10 m / s. The Zeeman slower is based on the principle of laser cooling , i.e. the atoms are slowed down by the absorption of laser light and the subsequent re-emission of fluorescence photons. A Zeeman slower consists of a locally varying magnetic field through which the atomic beam flies and a laser beam directed in the opposite direction. Via the Zeeman effect, the magnetic field counteracts the speed-dependent Doppler shift , which causes slower atoms to fall out of resonance with the laser beam.

History and use in research

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

It is used in many experimental setups for Bose-Einstein condensation and Fermi condensates as the first stage for cooling the atoms, which usually emerge from a furnace as an atomic beam with a speed of 500–1000 m / s. The Zeeman slower is typically followed by a magneto-optical trap that can only catch atoms up to an upper limit speed of typically a few 10 m / s. In further steps, the trapped atoms are then cooled down to a few microkelvins above absolute zero using further processes (e.g. sympathetic cooling , evaporative cooling ).

Function and structure

Hyperfine structure spectrum of sodium with magnetic field-dependent Zeeman splitting

An atomic beam, which is created in a furnace by evaporation of elementary metal (e.g. sodium , lithium , rubidium ), consists of atoms with an average speed of 500–1000 m / s (depending on the type of metal and evaporation temperature). In order to brake these atoms by scattering photons from a laser beam running in the opposite direction, its frequency must be set in such a way that it also has the Doppler shift ${\displaystyle \nu _{\text{Laser}}}$

${\displaystyle \delta _{\text{Doppler}}(v_{\text{Atom}})=(2\pi /\lambda _{\text{Laser}})\cdot v_{\text{Atom}}}$

( : Speed ​​of the atom and : wavelength of the laser), below which the atoms "perceive" the laser light. This is possible (so-called “ chirped slowing ”), but technically complex and leads to pulsed atomic beams, so that the Zeeman effect is used as an alternative. This does not change the light, but shifts the atomic levels of the atom in such a way that resonance is restored. Overall, the following detuning of the atomic transition is obtained : ${\displaystyle v_{\text{Atom}}}$ ${\displaystyle \lambda _{\text{Laser}}}$

${\displaystyle \delta (v_{\text{Atom}},z_{\text{Atom}})=\delta _{0}+\delta _{\text{Doppler}}(v_{\text{Atom}})-\delta _{\text{Zeeman}}(z_{\text{Atom}})=\delta _{0}+{\frac {2\pi \cdot v_{\text{Atom}}}{\lambda _{\text{Laser}}}}-{\frac {\mu _{B}}{\hbar }}\cdot [m_{je}g_{je}-m_{jg}g_{jg}]\cdot B(z_{\text{Atom}})}$

Here μ _B is Bohr's magneton , the magnetic quantum number of the excited state and the ground state (at the transition under consideration), as well as their Landé factors . The function describes the location-dependent magnetic field in the Zeeman slower. The shift δ ₀ is a slight detuning of the brake laser wavelength compared to the atomic transition (see below). ${\displaystyle m_{je},m_{jg}}$ ${\displaystyle g_{je},g_{jg}}$ ${\displaystyle B(z_{Atom})}$

Maximum resonance with the atomic transition is established in the ideal case . From this, assuming a negative constant braking (acceleration) of the atoms in the slower, the shape of the magnetic field can be calculated. You get:: ${\displaystyle \delta (v_{Atom},z_{Atom})=0}$

${\displaystyle B(z)=B_{0}\cdot {\sqrt {1-{\frac {z}{L_{\text{Slower}}}}}}+B_{b},\ \ \ \ \ B_{0}={\frac {\hbar k_{\text{Laser}}}{\mu _{B}\cdot [m_{je}g_{je}-m_{jg}g_{jg}]}},\ \ \ \ \ B_{b}={\frac {\hbar \delta _{0}}{\mu _{B}\cdot [m_{je}g_{je}-m_{jg}g_{jg}]}}}$

Where is the length of the Zeeman slower and . The detuning ensures a finite final speed by being chosen so that the atoms after the slower (there the magnetic field disappears :) fall out of resonance and are not slowed down any further. Without this parameter, atoms would be pushed back into the slower at the end of the slower and can no longer be extracted as a beam. ${\displaystyle L_{s}}$ ${\displaystyle k_{\text{Laser}}=2\pi /\lambda _{\text{Laser}}}$ ${\displaystyle \delta _{0}}$ ${\displaystyle B=0}$

Numerical solution of the equation of motion of the atoms in a Zeeman slower

In the figure on the right you can see the magnetic field of a Zeeman slower at the top and below how the speed of atoms is reduced when they fly through the slower. Fast atoms (e.g. brown) come into resonance with the brake laser earlier, while for slow atoms (e.g. green) the resonance condition is fulfilled later. There is never any resonance for very fast atoms, so that they can fly through the slower unchecked. The upper limit speed for the slower results from the resonance condition at maximum magnetic field and can be influenced by the structure of the slower. In general, longer slowers allow a higher initial magnetic field and thus a higher limit speed. At the end of the slower, in the simplest case, the magnetic field has dropped again ( i.e. just in case ) and there are only atoms with the speed ${\displaystyle B=0}$ ${\displaystyle B_{b}=0}$

${\displaystyle v_{\text{end}}={\frac {\lambda _{\text{Laser}}\cdot \delta _{0}}{2\pi }}}$

in response. If the atoms fall below this speed, they are no longer decelerated and can be interpreted as the mean final or initial speed of the slower. Similarly, (again for the case ) the maximum trapping speed can also be defined via the resonance at the maximum magnetic field: ${\displaystyle v_{end}}$ ${\displaystyle B_{b}=0}$

${\displaystyle v_{\text{max}}=\left({\frac {\mu _{B}}{\hbar }}\cdot [m_{je}g_{je}-m_{jg}g_{jg}]\cdot B_{0}-\delta _{0}\right)\cdot {\frac {\lambda _{\text{Laser}}}{2\pi }}}$

Only atoms that fly slower than this speed are slowed down by the Zeeman slower.

In practice, Zeeman slowers are typically built with current-carrying magnetic coils. The variable magnetic field is generated either by changing the density of the wires or by changing the number of their layers. However, slowers made from permanent magnets are also possible. A high vacuum tube, in which the atomic beam is located, then runs inside the coil former.

So far it has been assumed that the atomic transition used for braking is closed, i.e. that is, the atoms cannot decay from the absorption-emission cycle to an out -of-cycle dark state . In real atoms this is typically not the case. Therefore, an additional superimposed laser beam may have to be used to “pump back” atoms from a dark state into the cycle. A corresponding transition is drawn in the sodium spectrum above, with which atoms that have decayed into the F = 1 ground state can be decelerated further.

Braking, cooling and heating

The Zeeman slower decelerates all atoms that are traveling slower than its capture speed to a speed close to its terminal speed . This reduces both the average speed and the speed differences (dispersion of the speeds) of these atoms. The achieved distribution width for the braked atoms (the atoms that fly through the slower without brakes, i.e. with v> v _max , are disregarded) can also be characterized independently of the mean residual speed by specifying a longitudinal jet temperature . This is therefore significantly reduced by the Zeeman slower. The measurement of the velocity distribution (and thus the beam temperature) can take place via the time-of-flight broadening of atomic packets or via the Doppler shift of an absorption line. ${\displaystyle v_{max}}$ ${\displaystyle v_{end}}$

The transversal speed spread or temperature, which can be kept low in front of the slower by blending, increases in the slower in that every absorption for the purpose of braking is followed by an emission in a random direction. As a result, the atoms perform a random walk perpendicular to the direction of flight in the speed space:

${\displaystyle (v_{x,y}^{\text{rms}})^{2}(t)\propto {\frac {v_{\text{rec}}^{2}}{3}}\cdot N(t)}$

This is the square mean transverse speed (in - or - direction), the number of scattering processes up to the time and the recoil speed , i.e. the amount of speed change in an absorption or emission process. ${\displaystyle v_{x,y}^{\text{rms}}}$ ${\displaystyle x}$ ${\displaystyle y}$ ${\displaystyle N(t)}$ ${\displaystyle t}$ ${\displaystyle v_{rec}}$

To counteract this effect of transversal heating , z. B. transversal cooling can be achieved behind the Zeeman slower by means of optical molasses . Another approach is to guide the atomic beam through suitably designed light and magnetic fields in an arc, which allows the cooling effect of the Zeeman slower to work in different directions one after the other.

Usually the atoms are trapped in a magneto-optical or other trap after the Zeeman slower. So that you do not fly through the potential of this trap unscathed, the end speed of the slower must be optimized to the maximum capture speed of the trap. In addition, the speed spread (or lateral and longitudinal temperature) should not be too great, since the atoms scatter around the final speed and if the spread is too great, the trapping efficiency decreases accordingly (more atoms are too fast).

literature

• Harold J. Metcalf, Peter van der Straten: Laser Cooling and Trapping , Springer Verlag, 1999, ISBN 0-387-98728-2 , pp. 58-59.

Individual evidence

1. ↑ translated from: Nobel Prize in Physics press release, 1997
2. ^ ^{A b} William Phillips, Harold Metcalf: Laser Deceleration of an Atomic Beam . In: Physical Review Letters . tape 48 , no. 9 , March 1982, p. 596-599 , doi : 10.1103 / PhysRevLett.48.596 ( online PDF ).
3. ^ John V. Prodan, William D. Phillips: Chirping the light? Fantastic? Recent NBS atom cooling experiments . In: Progress in Quantum Electronics . tape 8 , no. 3-4 , January 1984, ISSN  0079-6727 , pp. 231-235 , doi : 10.1016 / 0079-6727 (84) 90019-3 .
4. ↑ Harold J. Metcalf, Peter van der Straten: Laser Cooling and Trapping , Springer Verlag, 1999, ISBN 0-387-98728-2 , pp. 58-59.
5. ↑ ^{a b} Jan Krieger (2008): Zeeman slower and experiment control for the NaLi experiment (PDF; 11.5 MB), diploma thesis, University of Heidelberg
6. ↑ Kenneth J. Günter: Design and implementation of a Zeeman slower for ⁸⁷ Rb . In: Report, Ecole Normale Supérieur, Paris . 2004 ( PDF ).
7. ^ SC Bell, M. Junker, M. Jasperse, LD Turner, Y.-J. Lin, IB Spielman, RE Scholten: A slow atom source using a collimated effusive oven and a single-layer variable pitch coil Zeeman slower . In: Review of Scientific Instruments . tape 81 , no. 1 , 2010, ISSN  0034-6748 , p. 013105 , doi : 10.1063 / 1.3276712 .
8. ↑ P. Cheiney, O. Carraz, D. Bartoszek-Bober, S. Faure, F. Vermersch, CM Fabre, GL Gattobigio, T. Lahaye, D. Gue ry-Odelin, R. Mathevet: A Zeeman slower design with permanent magnets in a Halbach configuration . In: Review of Scientific Instruments . tape 82 , no. 6 , 2011, ISSN  0034-6748 , p. 063115 , doi : 10.1063 / 1.3600897 .
9. ↑ ^{a b} Christopher Slowe, Laurent Vernac, Lene Vestergaard Hau: High flux source of cold rubidium atoms . In: Review of Scientific Instruments . Vol. 76, No. 10 , 2005, ISSN  0034-6748 , p. 103101 , doi : 10.1063 / 1.2069651 (English).
10. ↑ JGC Tempelaars, RJW Stas, PGM Sebel, HCW Beijerinck, EJD Vredenbregt: An intense, slow and cold beam of metastable Ne (3s) 3 P 2 atoms . In: The European Physical Journal D - Atomic, Molecular and Optical Physics . tape 18 , no. 1 , January 1, 2002, ISSN  1434-6060 , p. 113–121 , doi : 10.1140 / e10053-002-0013-8 .
11. ↑ Kenneth J. Günter: Design and implementation of a Zeeman slower for ⁸⁷ Rb . In: Report, Ecole Normale Supérieur, Paris . 2004 ( PDF ).
12. ↑ ^{a b} Michael A. Joffe, Wolfgang Ketterle, ALex Martin, David E. Pritchard: Transverse cooling and deflection of an atomic beam inside a Zeeman slower . In: JOSA B . tape 10 , no. 12 , 1993, pp. 2257-2262 .
13. ↑ A. Witte, Th. Kisters, F. Riehle, J. Helmcke: Laser cooling and deflection of a calcium atomic beam . In: Journal of the Optical Society of America B . tape 9 , no. 7 , 1992, ISSN  0740-3224 , pp. 1030 , doi : 10.1364 / JOSAB.9.001030 (English, abstract ).