Zeeman slower
Encyclopedia
A Zeeman slower is a scientific apparatus
that is commonly used in experimental
atomic, molecular, and optical physics
to slow a beam
of atoms or molecules from initial speeds on the order of 500 m/s-1000 m/s to final speeds on the order of 10 m/s (a few Kelvin). It consists of a cylinder
, through which the beam travels, a pump laser
that is shone on the beam in the direction opposite to the beam's motion, and a magnetic field
(commonly produced by a solenoid
-like coil
) that points along the symmetry axis of the cylinder and varies spatially along the axis of the cylinder. The pump laser, which is required to be near-resonant to an atomic or molecular transition, Doppler
slows a certain velocity class within the velocity distribution of the beam. The spatially varying Zeeman shift
of the resonant frequency enables lower and lower velocity classes to be resonant with the laser, as the atomic or molecular beam propagates along the slower, hence slowing the beam.
(who was awarded the Nobel Prize in Physics
for this discovery in 1997 together with Steven Chu
and Claude Cohen-Tannoudji
"for development of methods to cool and trap atoms with laser light") and Harold J. Metcalf. The achievement of these low temperatures lead the way for the experimental realisation of Bose-Einstein condensation, and a Zeeman slower can be part of such an apparatus.
, 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
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 and brings the atom to its excited state
. However, this state is unstable, and the atom will eventually (after a time on the order of the microsecond, for example in Rubidium 87 for the D2 transition 38 µs) decay to its ground state. 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, 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 resonnance 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
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
,
, that is in the presence of a laser beam that has wavenumber
,
, 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 
. We normally require that we have a magnetic field profile varies in the 
direction such that the atoms experience a constant acceleration 
as they fly along the axis of the slower, so
where
is the maximum velocity class that will be slowed; all the atoms in the velocity distribution that have velocities 
will be slowed, and those with velocities 
will not be slowed at all. The parameter 
(which determines the required laser intensity) is normally chosen to be around .5. If a Zeeman slower were to be operated with 
, then after absorbing a photon and moving to the excited state, the atom would then preferentially re-emit a photon in the direction of the laser beam (due to stimulated emission
) which would counteract the slowing process.
This field can be realized a few different ways. The most popular design requires wrapping a current carrying wire with many layered windings where the field is strongest (around 20-50 windings) and few windings where the field is weak. An alternative design uses a single layer coil that varies rather in the pitch of the winding of such a coil. Another proposed design uses an array of permanent magnets to create the field..
. Thus it aims at a final velocity of about 10 m/s (depending on the atom used), starting with a beam of atoms with a velocity of a few hundred meters per second. The final speed to be reached is a compromise between the technical difficulty of having a long Zeeman slower and the maximal speed allowed for an efficient loading into the trap.
A limitation of setup can is the transverse heating of the beam. It is linked to the fluctuations of the speed along the three axis around its mean values, since the final speed was said to be an average over a large number of processes. These fluctuations are linked to the atom having a Brownian motion
due to the random reemission of the absorbed photon. They may cause difficulties when loading the atoms in the next trap.
Scientific instrument
A scientific instrument can be any type of equipment, machine, apparatus or device as is specifically designed, constructed and often, through trial and error, ingeniously refined to apply utmost efficiency in the utilization of well proven physical principle, relationship or technology to...
that is commonly used in experimental
Experimental physics
Within the field of physics, experimental physics is the category of disciplines and sub-disciplines concerned with the observation of physical phenomena in order to gather data about the universe...
atomic, molecular, and optical physics
Atomic, molecular, and optical physics
Atomic, molecular, and optical physics is the study of matter-matter and light-matter interactions on the scale of single atoms or structures containing a few atoms. The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the...
to slow a beam
Molecular beam
A molecular beam is produced by allowing a gas at higher pressure to expand through a small orifice into a chamber at lower pressure to form a beam of particles moving at approximately equal velocities, with very few collisions between the particles...
of atoms or molecules from initial speeds on the order of 500 m/s-1000 m/s to final speeds on the order of 10 m/s (a few Kelvin). It consists of a cylinder
Cylinder
Cylinder most commonly refers to:* Cylinder , a three-dimensional geometric shapeCylinder may also refer to:-Science and technology:* Cylinder , the space in which a piston travels in an engine...
, through which the beam travels, a pump laser
Laser pumping
Laser pumping is the act of energy transfer from an external source into the gain medium of a laser. The energy is absorbed in the medium, producing excited states in its atoms. When the number of particles in one excited state exceeds the number of particles in the ground state or a less-excited...
that is shone on the beam in the direction opposite to the beam's motion, and a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
(commonly produced by a solenoid
Solenoid
A solenoid is a coil wound into a tightly packed helix. In physics, the term solenoid refers to a long, thin loop of wire, often wrapped around a metallic core, which produces a magnetic field when an electric current is passed through it. Solenoids are important because they can create...
-like coil
Coil
A coil is a series of loops. A coiled coil is a structure in which the coil itself is in turn also looping.-Electromagnetic coils:An electromagnetic coil is formed when a conductor is wound around a core or form to create an inductor or electromagnet...
) that points along the symmetry axis of the cylinder and varies spatially along the axis of the cylinder. The pump laser, which is required to be near-resonant to an atomic or molecular transition, Doppler
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:...
slows a certain velocity class within the velocity distribution of the beam. The spatially varying Zeeman shift
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...
of the resonant frequency enables lower and lower velocity classes to be resonant with the laser, as the atomic or molecular beam propagates along the slower, hence slowing the beam.
History
It was first developed by William D. PhillipsWilliam Daniel Phillips
William Daniel Phillips is an American physicist and shared the Nobel Prize in Physics for 1997 with Steven Chu and Claude Cohen-Tannoudji. He is of Italian and Welsh descent.-Biography:...
(who was awarded the Nobel Prize in Physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
for this discovery in 1997 together with Steven Chu
Steven Chu
Steven Chu is an American physicist and the 12th United States Secretary of Energy. Chu is known for his research at Bell Labs in cooling and trapping of atoms with laser light, which won him the Nobel Prize in Physics in 1997, along with his scientific colleagues Claude Cohen-Tannoudji and...
and Claude Cohen-Tannoudji
Claude Cohen-Tannoudji
Claude Cohen-Tannoudji is a French physicist and Nobel Laureate. 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...
"for development of methods to cool and trap atoms with laser light") and Harold J. Metcalf. The achievement of these low temperatures lead the way for the experimental realisation of Bose-Einstein condensation, and a Zeeman slower can be part of such an apparatus.
Principle
According to the principles of Doppler coolingDoppler 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:...
, 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
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...
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 and brings the atom to its excited state
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....
. However, this state is unstable, and the atom will eventually (after a time on the order of the microsecond, for example in Rubidium 87 for the D2 transition 38 µs) decay to its ground state. 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, 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
Doppler 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...
. The resonance of the atom is rather narrow (on the order of a few megaHertz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
), and after having decreased its momentum by a few recoil momenta
Recoil
Recoil is the backward momentum of a gun when it is discharged. In technical terms, the recoil caused by the gun exactly balances the forward momentum of the projectile and exhaust gasses, according to Newton's third law...
, it is no longer in resonnance 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
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...
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 linewidthSpectral linewidth
The spectral linewidth characterizes the width of a spectral line, such as in the electromagnetic emission spectrum of an atom, or the frequency spectrum of an acoustic or electronic system...
,
, that is in the presence of a laser beam that has wavenumberWavenumber
In the physical sciences, the wavenumber is a property of a wave, its spatial frequency, that is proportional to the reciprocal of the wavelength. It is also the magnitude of the wave vector...
,
, 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 detuningLaser 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...
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 . We normally require that we have a magnetic field profile varies in the direction such that the atoms experience a constant acceleration as they fly along the axis of the slower, so
where
is the maximum velocity class that will be slowed; all the atoms in the velocity distribution that have velocities will be slowed, and those with velocities will not be slowed at all. The parameter (which determines the required laser intensity) is normally chosen to be around .5. If a Zeeman slower were to be operated with , then after absorbing a photon and moving to the excited state, the atom would then preferentially re-emit a photon in the direction of the laser beam (due to stimulated emissionStimulated emission
In optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...
) which would counteract the slowing process.
Realization
The required form of the spatially inhomogeneous magnetic field as we showed above has the form
This field can be realized a few different ways. The most popular design requires wrapping a current carrying wire with many layered windings where the field is strongest (around 20-50 windings) and few windings where the field is weak. An alternative design uses a single layer coil that varies rather in the pitch of the winding of such a coil. Another proposed design uses an array of permanent magnets to create the field..
Outgoing atoms
The Zeeman slower is usually used as a preliminary step to cool the atoms in order to trap them 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...
. Thus it aims at a final velocity of about 10 m/s (depending on the atom used), starting with a beam of atoms with a velocity of a few hundred meters per second. The final speed to be reached is a compromise between the technical difficulty of having a long Zeeman slower and the maximal speed allowed for an efficient loading into the trap.
A limitation of setup can is the transverse heating of the beam. It is linked to the fluctuations of the speed along the three axis around its mean values, since the final speed was said to be an average over a large number of processes. These fluctuations are linked to the atom having a Brownian motion
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
due to the random reemission of the absorbed photon. They may cause difficulties when loading the atoms in the next trap.