Raman Cooling
Encyclopedia
In atomic physics
, Raman cooling is a sub-recoil cooling technique that allows the cooling of atoms using optical methods below the limitations of Doppler cooling
, limited by the recoil energy of a photon given to an atom. This scheme can be performed in simple optical molasses
or in molasses where an optical lattice
has been superimposed, which are called respectively free space Raman cooling and Raman side-band cooling. Both techniques make use of Raman scattering
of laser light between by the atoms.
of the atom can be triggered by two laser
beams: the first beam excites the atom to a virtual excited state (for example because its frequency is lower than the real transition frequency), and the second beam deexcites the atom to the other hyperfine level. The frequency difference of the two beams is exactly equal to the transition frequency between the two hyperfine levels.
The illustration of this process is shown in the schematic illustration of a two-photon Raman process. It enables the transition between the two levels
and 
. The intermediate, virtual level is represented by the dashed line, and is red-detuned with respect to the real excited level, 
. The frequency difference 
here matches exactly the energy difference between 
and 
.
is now slightly red-detuned
(detuning
) with respect to its normal value. Thus, atoms moving towards the source of the laser 2 with a sufficient velocity will be resonant with the Raman pulses, thanks to the Doppler effect
. They will be excited to the
state, and get a momentum kick decreasing the modulus of their velocity.
If the propagation directions of the two lasers are interchanged, then the atoms moving in the opposite direction will be excited and get the momentum kick that will decrease the modulus of their velocities. By regularly exchanging the lasers propagating directions and varying the detuning
, one can manage to have all atoms for which the initial velocity satified 
in the state 
, while the atoms such that 
are still in the 
state. A new beam is then switched on, whose frequency is exactly the transition frequency between 
and 
. This will optically pump
the atoms from the
state to the 
state, and the velocities will be randomized by this process, such that a fraction of the atoms in 
will acquire a velocity 
.
By repeating this process several times (eight in the original paper, see references), the temperature of the cloud can be lowered to less than a microkelvin.
. An optical lattice is then ramped up, such that an important fraction of the atoms are trapped. If the lasers of the lattice are powerful enough, each site can be modelled as a harmonic trap. Since the atoms are not in their ground state, they will be trapped in one of the excited levels of the harmonic oscillator. The aim of Raman side-band cooling is to put the atoms into the ground state of the harmonic potential in the lattice site.
We consider a two level atom, the ground state of which has a quantum number of F=1, such that it is three-fold degenerate with m=-1, 0 or 1. A magnetic field is added, which lifts the degeneracy in m due to the Zeeman effect
. Its value is exactly tuned such that the Zeeman splitting between m=-1 and m=0 and between m=0 and m=1 is equal to the spacing of two levels in the harmonic potential created by the lattice.
By means of Raman processes, an atom can be transferred to a state where the magnetic moment has decreased by one and the vibrational state has also decreased by one (red arrows on the picture). After that the atoms which are in the lowest vibrational state of the lattice potential (but with
) are optically pumped
to the m=1 state (role of the
and 
light beams). Since the temperature of the atoms is low enough with respect to the pumping beam frequencies, the atom is very likely not to change its vibrational state during the pumping process. Thus it ends up in a lower vibrational state, which is how it is cooled.
This scheme allows to obtain a rather high density of atoms at a low temperature, using only optical techniques. It is still not sufficient to attain for example Bose-Einstein condensation, but it can be a starting point for such experiments. For instance, the Bose-Einstein condensation of Cesium has been achieved for the first time in an experiment that used Raman side-band cooling as its first step.
Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...
, Raman cooling is a sub-recoil cooling technique that allows the cooling of atoms using optical methods below the limitations of Doppler cooling
Doppler cooling
Doppler cooling is a mechanism that can be used to trap and cool atoms. The term is sometimes used synonymously with laser cooling, though laser cooling includes other techniques.-History:...
, limited by the recoil energy of a photon given to an atom. This scheme can be performed in simple optical molasses
Optical molasses
Optical molasses is a laser cooling technique that can cool down neutral atoms to temperatures colder than a magneto-optical trap . An optical molasses consists of 3 pairs of counter-propagating circularly polarized laser beams intersecting in the region where the atoms are present. The main...
or in molasses where an optical lattice
Optical lattice
An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate in the locations of potential minima...
has been superimposed, which are called respectively free space Raman cooling and Raman side-band cooling. Both techniques make use of Raman scattering
Raman scattering
Raman scattering or the Raman effect is the inelastic scattering of a photon. It was discovered by Sir Chandrasekhara Venkata Raman and Kariamanickam Srinivasa Krishnan in liquids, and by Grigory Landsberg and Leonid Mandelstam in crystals....
of laser light between by the atoms.
Two photon Raman process
The transition between two hyperfine statesHyperfine structure
The term hyperfine structure refers to a collection of different effects leading to small shifts and splittings in the energy levels of atoms, molecules and ions. The name is a reference to the fine structure which results from the interaction between the magnetic moments associated with electron...
of the atom can be triggered by two laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
beams: the first beam excites the atom to a virtual excited state (for example because its frequency is lower than the real transition frequency), and the second beam deexcites the atom to the other hyperfine level. The frequency difference of the two beams is exactly equal to the transition frequency between the two hyperfine levels.
The illustration of this process is shown in the schematic illustration of a two-photon Raman process. It enables the transition between the two levels
and . The intermediate, virtual level is represented by the dashed line, and is red-detuned with respect to the real excited level, . The frequency difference here matches exactly the energy difference between and .Free space Raman cooling
In this scheme, a pre-cooled cloud of atoms (whose temperature is of a few tens of microkelvins) undergoes a series of pulses of Raman-like processes. The beams are counterpropagating, and their frequencies are just as what has been described above, except that the frequency is now slightly red-detunedLaser detuning
In optical physics, laser detuning is the tuning of a laser to a frequency that is slightly off from a quantum system's resonant frequency. Lasers can be detuned in the lab frame so that they are Doppler shifted to the resonant frequency in a moving system, which allows lasers to affect only...
(detuning
) with respect to its normal value. Thus, atoms moving towards the source of the laser 2 with a sufficient velocity will be resonant with the Raman pulses, thanks to the Doppler effectDoppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
. They will be excited to the
state, and get a momentum kick decreasing the modulus of their velocity.If the propagation directions of the two lasers are interchanged, then the atoms moving in the opposite direction will be excited and get the momentum kick that will decrease the modulus of their velocities. By regularly exchanging the lasers propagating directions and varying the detuning
, one can manage to have all atoms for which the initial velocity satified in the state , while the atoms such that are still in the state. A new beam is then switched on, whose frequency is exactly the transition frequency between and . This will optically pumpOptical pumping
Optical pumping is a process in which light is used to raise electrons from a lower energy level in an atom or molecule to a higher one. It is commonly used in laser construction, to pump the active laser medium so as to achieve population inversion...
the atoms from the
state to the state, and the velocities will be randomized by this process, such that a fraction of the atoms in will acquire a velocity .By repeating this process several times (eight in the original paper, see references), the temperature of the cloud can be lowered to less than a microkelvin.
Raman side-band cooling
This cooling scheme starts from atoms in a magneto-optical trapMagneto-optical trap
A magneto-optical trap is a device that uses both laser cooling with magneto-optical trapping in order to produce samples of cold, trapped, neutral atoms at temperatures as low as several microkelvins, two or three times the recoil limit.By combining the small momentum of a single photon with a...
. An optical lattice is then ramped up, such that an important fraction of the atoms are trapped. If the lasers of the lattice are powerful enough, each site can be modelled as a harmonic trap. Since the atoms are not in their ground state, they will be trapped in one of the excited levels of the harmonic oscillator. The aim of Raman side-band cooling is to put the atoms into the ground state of the harmonic potential in the lattice site.
We consider a two level atom, the ground state of which has a quantum number of F=1, such that it is three-fold degenerate with m=-1, 0 or 1. A magnetic field is added, which lifts the degeneracy in m due to the Zeeman effect
Zeeman effect
The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field...
. Its value is exactly tuned such that the Zeeman splitting between m=-1 and m=0 and between m=0 and m=1 is equal to the spacing of two levels in the harmonic potential created by the lattice.
By means of Raman processes, an atom can be transferred to a state where the magnetic moment has decreased by one and the vibrational state has also decreased by one (red arrows on the picture). After that the atoms which are in the lowest vibrational state of the lattice potential (but with
) are optically pumpedOptical pumping
Optical pumping is a process in which light is used to raise electrons from a lower energy level in an atom or molecule to a higher one. It is commonly used in laser construction, to pump the active laser medium so as to achieve population inversion...
to the m=1 state (role of the
and light beams). Since the temperature of the atoms is low enough with respect to the pumping beam frequencies, the atom is very likely not to change its vibrational state during the pumping process. Thus it ends up in a lower vibrational state, which is how it is cooled.This scheme allows to obtain a rather high density of atoms at a low temperature, using only optical techniques. It is still not sufficient to attain for example Bose-Einstein condensation, but it can be a starting point for such experiments. For instance, the Bose-Einstein condensation of Cesium has been achieved for the first time in an experiment that used Raman side-band cooling as its first step.