A Zeeman slower is a
scientific apparatus that is commonly used in
atomic physics to slow and cool a
beam of hot atoms to speeds of several meters per second and temperatures below a
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
. The Gas-phase atoms used in atomic physics are often generated in an oven by heating a solid or liquid atomic sample to temperatures where the vapor pressure is high enough that there are a substantial number of atoms in the gas phase. These atoms effuse out of a hole in the oven with average speeds on the order of hundreds of m/s and large velocity distributions (due to their high temperature). The Zeeman slower is attached close to where the hot atoms exit the oven and is used to slow them to less than 10 m/s (slowing) with a very small velocity spread (cooling).
A Zeeman slower consists of a
cylinder
A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
A cylinder may also be defined as an infin ...
, through which an atomic beam travels, a
pump laser that counterpropagates with respect to the beam's direction , and a
magnetic field (commonly produced by a
solenoid-like coil) that points along the cylinder's axis with a spatially varying magnitude. The pump laser, which is required to be near-resonant with atomic transition,
Doppler slows a certain velocity class within the velocity distribution of the beam. The spatially varying magnetic field is designed to
Zeeman shift the resonant frequency to match the decreasing Doppler shift as the atoms are slowed to lower velocities while they propagate through the Zeeman slower allowing pump laser to be continuously resonant and provide a slowing force.
History
The Zeeman slower was first developed by Harold J. Metcalf and
William D. Phillips (who was awarded 1/3 of the 1997
Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
in part work for his work on the Zeeman slower ). The achievement of these low temperatures led the way for the experimental realization of
Bose–Einstein condensation Bose–Einstein may refer to:
* Bose–Einstein condensate
** Bose–Einstein condensation (network theory)
* Bose–Einstein correlations
* Bose–Einstein statistics
In quantum statistics, Bose–Einstein statistics (B–E statistics) describe ...
, and a Zeeman slower can be part of such an apparatus.
Principle
According to the principles of
Doppler cooling
Doppler cooling is a mechanism that can be used to trap and slow the motion of atoms to cool a substance. The term is sometimes used synonymously with laser cooling, though laser cooling includes other techniques.
History
Doppler cooling was si ...
, 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
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fi ...
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
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and ...
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
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
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
The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel priz ...
to tackle this problem.
The average acceleration (due to many photon absorption events over time) of an atom with mass,
, a cycling transition with frequency,
, and
linewidth
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
,
, that is in the presence of a laser beam that has
wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the '' spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to te ...
,
, and intensity
(where
is the
saturation intensity of the laser) is
::
In the rest frame of the atoms with velocity,
, in the atomic beam, the frequency of the laser beam is shifted by
. In the presence of a magnetic field
, the atomic transition is Zeeman shifted by an amount
(where
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
will experience the largest acceleration, namely
::
where
and
.
The most common approach is to require that we have a magnetic field profile that varies in the
direction such that the atoms experience a constant acceleration
as they fly along the axis of the slower. It has been recently shown however, that a different approach yields better results.
In the constant deceleration approach we get:
::
::
where
is the maximum velocity class that will be slowed; all the atoms in the velocity distribution that have velocities