In ultra-
low-temperature physics
In physics, cryogenics is the production and behaviour of materials at very low temperatures.
The 13th IIR International Congress of Refrigeration (held in Washington DC in 1971) endorsed a universal definition of “cryogenics” and “cr ...
, Sisyphus cooling, the Sisyphus effect, or polarization gradient cooling involves the use of specially selected
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 fir ...
light, hitting atoms from various angles to both cool and trap them in a potential well, effectively rolling the atom down a hill of
potential energy
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Common types of potential energy include the gravitational potentia ...
until it has lost its
kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...
. It is a type of
laser cooling
Laser cooling includes a number of techniques in which atoms, molecules, and small mechanical systems are cooled, often approaching temperatures near absolute zero. Laser cooling techniques rely on the fact that when an object (usually an atom) ...
of atoms used to reach temperatures below the
Doppler cooling limit
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 ...
. This cooling method was first proposed by
Claude Cohen-Tannoudji
Claude Cohen-Tannoudji (; born 1 April 1933) is a French physicist. He shared the 1997 Nobel Prize in Physics with Steven Chu and William Daniel Phillips for research in methods of laser cooling and trapping atoms. Currently he is still an activ ...
in 1989, motivated by earlier experiments which observed sodium atoms cooled below the Doppler limit in an
optical molasses
Optical molasses is a laser cooling technique that can cool neutral atoms to temperatures lower than a magneto-optical trap (MOT). An optical molasses consists of 3 pairs of counter-propagating circularly polarized laser beams intersecting in the ...
.
Cohen-Tannoudji received part of the
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 1997 for his work. The technique is named after
Sisyphus
In Greek mythology, Sisyphus or Sisyphos (; Ancient Greek: Σίσυφος ''Sísyphos'') was the founder and king of Ancient Corinth, Ephyra (now known as Corinth). Hades punished him for cheating death twice by forcing him to roll an immense bo ...
, a figure in the
Greek mythology
A major branch of classical mythology, Greek mythology is the body of myths originally told by the Ancient Greece, ancient Greeks, and a genre of Ancient Greek folklore. These stories concern the Cosmogony, origin and Cosmology#Metaphysical co ...
who was doomed, for all eternity, to roll a stone up a mountain only to have it roll down again whenever he got it near the summit.
Method
Sisyphus cooling can be achieved by shining two counter-propagating laser beams with orthogonal polarization onto an atom sample. Atoms moving through the potential landscape along the direction of the standing wave lose kinetic energy as they move to a potential maximum, at which point optical pumping moves them back to a lower energy state, thus lowering the total energy of the atom. This description of Sisyphus cooling is largely based on Foot's description.
Principle of sisyphus cooling
The counter-propagation of two orthogonally polarized lasers generates a standing wave in polarization with a gradient between
(left-hand circularly polarized light), linear, and
(right-hand circularly polarized light) along the standing wave. Note that this counter propagation does not make a standing wave in intensity, but only in polarization. This gradient occurs over a length scale of
, and then repeats, mirrored about the y-z plane. At positions where the counter-propagating beams have a phase difference of
, the polarization is circular, and where there is no phase difference, the polarization is linear. In the intermediate regions, there is a gradient elipticity of the superposed fields.
Consider, for example, an atom with ground state angular momentum
and excited state angular momentum
. The
sublevels for the ground state are
and the
levels for the excited state are
In the field-free case, all of these energy levels for each J value are degenerate, but in the presence of a circularly polarized light field, the
Autler-Townes effect, (AC Stark shift or light shift), lifts this degeneracy. The extent and direction of this lifted degeneracy is dependent on the polarization of the light. It is this polarization dependence that is leveraged to apply a spatially-dependent slowing force to the atom.
Typical optical pumping scheme
In order to have a cooling effect, there must be some dissipation of energy.
Selection rules for dipole transitions dictate that for this example,
and
with relative intensities given by the square of the
Clebsch-Gordan coefficients. Suppose we start with a single atom in the ground state,
, in the
state at
with velocity in the +z direction.
The atom is now pumped to the
excited state, where it spontaneously emits a photon and decays to the
ground state. The key concept is that in the presence of
light, the AC stark shift lowers the
further in energy than the
state. In going from the
to the
state, the atom has indeed lost
in energy, where
approximately equal to the AC Stark shift
where omega is the
Rabi frequency The Rabi frequency is the frequency at which the probability amplitudes of two atomic energy levels fluctuate in an oscillating electromagnetic field. It is proportional to the Transition Dipole Moment of the two levels and to the amplitude (''not ...
and delta is the detuning.
At this point, the atom is moving in the +z direction with some velocity, and eventually moves into a region with
light. The atom, still in its
state that it was pumped into, now experiences the opposite AC Stark shift as it did in
- light, and the
state is now lower in energy than the
state. The atom is pumped to the
excited state, where it spontaneously emits a photon and decays to the
state. As before, this energy level has been lowered by the AC Stark shift, and the atom loses another
of energy.
Repeated cycles of this nature convert kinetic energy to potential energy, and this potential energy is lost via the photon emitted during optical pumping.
Limits
The fundamental lower limit of Sisyphus cooling is the recoil temperature,
, set by the energy of the photon emitted in the decay from the J' to J state. This limit is
though practically the limit is a few times this value because of the extreme sensitivity to external magnetic fields in this cooling scheme. Atoms typically reach temperatures on the order of
, as compared to the doppler limit
.
References
*
*{{cite web, url=http://www.lkb.ens.fr/recherche/onl/intro_Eng.htm , title=intro_Eng , publisher=Lkb.ens.fr , date= , accessdate=2009-06-05
Nuclear physics
Cooling technology