Doppler cooling
Encyclopedia
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.
and Hans Georg Dehmelt
and the second being Theodor W. Hänsch and Arthur Leonard Schawlow
. It was first demonstrated by Wineland, Drullinger, and Walls in 1978 and shortly afterwards by Neuhauser, Hohenstatt, Toschek and Dehmelt. One conceptually simple form of Doppler cooling is referred to as optical molasses
, since the dissipative optical force
resembles the viscous drag on a body moving through molasses. Steven Chu
, Claude Cohen-Tannoudji
and William D. Phillips were awarded the 1997 Nobel Prize in Physics
for their work in laser cooling and atom trapping.
. Because the light is detuned
to the "red" (i.e. at lower frequency) of the transition, the atoms will absorb more photon
s if they move towards the light source, due to the Doppler effect
. Thus if one applies light from two opposite directions, the atoms will always absorb more photons from the laser
beam pointing opposite to their direction of motion. In each absorption event, the atom loses a momentum
equal to the momentum of the photon. If the atom, which is now in the excited state, emits a photon spontaneously, it will be kicked by the same amount of momentum but in a random direction. The result of the absorption and emission process is a reduced speed of the atom, provided its initial speed is larger than the recoil velocity
from scattering a single photon. If the absorption and emission are repeated many times, the mean velocity, and therefore the kinetic energy
of the atom will be reduced. Since the temperature
of an ensemble of atoms is a measure of the random internal kinetic energy, this is equivalent to cooling the atoms.
The Doppler cooling limit
is the minimum temperature achievable with Doppler cooling.
A few photons happen to "resonate
" with the atom, in a few very narrow bands of frequencies (a single color rather than a mixture like white light
). When one of those photons comes close to the atom, the atom typically absorbs that photon (absorption spectrum) for a brief period of time, then emits an identical photon (emission spectrum
) in some random, unpredictable direction. (Other sorts of interactions between atoms and photons exist, but are not relevant to this article.)
The popular idea that lasers increase the thermal energy of matter is not the case when examining individual atoms. If a given atom is practically motionless (a "cold" atom), and the frequency of a laser focused upon it can be controlled, most frequencies do not affect the atom — it is invisible at those frequencies. There are only a few points of electromagnetic frequency that have any effect on that atom. At those frequencies, the atom can absorb a photon from the laser, while transitioning to an excited electronic state, and pick up the momentum of that photon. Since the atom now has the photon's momentum, the atom must begin to drift in the direction the photon was traveling. A short time later, the atom will spontaneously emit a photon in a random direction, as it relaxes to a lower electronic state. If that photon is emitted in the direction of the original photon, the atom will give up its momentum to the photon and will become motionless again. If the photon is emitted in the opposite direction, the atom will have to provide momentum in that opposite direction, which means the atom will pick up even more momentum in the direction of the original photon (to conserve momentum), with double its original velocity. But usually the photon speeds away in some other direction, giving the atom at least some sideways thrust.
Another way of changing frequencies is to change the positioning of the laser. For example, using a monochromatic (single-color) laser that has a frequency that is a little below one of the "resonant" frequencies of this atom (at which frequency the laser will not directly affect the atom's state). If the laser were to be positioned so that it was moving towards the observed atoms, then the doppler effect
would raise its frequency. At one specific velocity, the frequency would be precisely correct for said atoms to begin absorbing photons.
Something very similar happens in a laser cooling apparatus, except such devices start with a warm cloud of atoms moving in numerous directions at variable velocity. Starting with a laser frequency well below the resonant frequency, photons from any one laser pass right through the majority of atoms. However, atoms moving rapidly towards a particular laser catch the photons for that laser, slowing those atoms down until they become transparent again. (Atoms rapidly moving away from that laser are transparent to that laser's photons — but they are rapidly moving towards the laser directly opposite it). This utilization of a specific velocity to induce absorption is also seen in Mössbauer spectroscopy.
On a graph of atom velocities (atoms moving rapidly to the right correspond with stationary dots far to the right, atoms moving rapidly to the left correspond with stationary dots far to the left), there is a narrow band on the left edge corresponding to the speed those atoms start absorbing photons from the left laser. Atoms in that band are the only ones that interact with the left laser. When a photon from the left laser slams into one of those atoms, it suddenly slows down an amount corresponding to the momentum of that photon (the dot would be redrawn some fixed "quantum" distance further to the right). If the atom releases the photon directly to the right, then the dot is redrawn that same distance to the left, putting it back in the narrow band of interaction. But usually the atom releases the photon in some other random direction, and the dot is redrawn that quantum distance in the opposite direction.
Such an apparatus would be constructed with many lasers, corresponding to many boundary lines that completely surround that cloud of dots.
As the laser frequency is increased, the boundary contracts, pushing all the dots on that graph towards zero velocity, the given definition of "cold".
in momentum space with steps equal to the photon momentum due to spontaneous emission and photon absorption
. This constitutes a heating effect, which counteracts the cooling process and imposes a limit on the amount by which the atom can be cooled. Moreover, the optical transition used for cooling in reality must have a finite frequency width, which limits the velocity discrimination (i.e. the likelihood that an atom will scatter light from the "correct" beam, as described above), and therefore the temperature. This temperature is called the Doppler temperature. Lower temperatures, down to the recoil temperature, may be obtained by sub-Doppler cooling such as Raman Cooling
. Beyond that, evaporative cooling is used to further cool the ultracold atom
s.
an atom has, the more ways there are for it to emit a photon from the upper state and not return to its original state, putting it in a dark state
and removing it from the cooling process. It is possible to use other lasers to optically pump
those atoms back into the excited state and try again, but the more complex the hyperfine structure is, the more (narrow-band, frequency locked) lasers are required. Since frequency-locked lasers are both complex and expensive, atoms which need more than one extra repump laser are rarely cooled; the common rubidium
Magneto-optical trap
, for example, requires one repump laser. This is also the reason why, to date, molecules have not been laser cooled: in addition to hyperfine structure, molecules also have rovibronic coupling
s and so can also decay into excited rotational or vibrational states.
dimensions may be used to cool the three motional degrees of freedom
of the atom.
Common laser-cooling configurations include optical molasses, the magneto-optical trap
, and the Zeeman
slower
.
Atomic ions, trapped in an ion trap
, can be cooled with a single laser beam as long as that beam has a component along all three motional degrees of freedom. This is in contrast to the six beams required to trap neutral atoms. The original laser cooling experiments were performed on ions in ion traps. (In theory, neutral atoms could be cooled with a single beam if they could be trapped in a deep trap, but in practice neutral traps are much shallower than ion traps and a single recoil event can be enough to kick a neutral atom out of the trap.)
technique. This process itself forms a part of the magneto-optical trap
but it can be used independently.
Doppler cooling is also used in spectroscopy and metrology, where cooling allows narrower spectroscopic features. For example, all of the best atomic clock technologies involve Doppler cooling at some point.
Laser cooling
Laser cooling refers to the number of techniques in which atomic and molecular samples are cooled through the interaction with one or more laser light fields...
, though laser cooling includes other techniques.
History
Doppler cooling was simultaneously proposed by two groups in 1975, the first being David J. WinelandDavid J. Wineland
David J. Wineland is an American physicist at the National Institute of Standards and Technology physics laboratory in Boulder...
and Hans Georg Dehmelt
Hans Georg Dehmelt
Hans Georg Dehmelt is a German-born American physicist, who co-developed the ion trap technique with Wolfgang Paul, for which they shared one-half of the Nobel Prize in Physics in 1989...
and the second being Theodor W. Hänsch and Arthur Leonard Schawlow
Arthur Leonard Schawlow
Arthur Leonard Schawlow was an American physicist. He is best remembered for his work on lasers, for which he shared the 1981 Nobel Prize in Physics with Nicolaas Bloembergen and Kai Siegbahn.-Biography:...
. It was first demonstrated by Wineland, Drullinger, and Walls in 1978 and shortly afterwards by Neuhauser, Hohenstatt, Toschek and Dehmelt. One conceptually simple form of Doppler cooling is referred to as 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...
, since the dissipative optical force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
resembles the viscous drag on a body moving through molasses. 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...
, 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...
and William D. Phillips were awarded the 1997 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 their work in laser cooling and atom trapping.
Brief Explanation
Doppler cooling involves light whose frequency is tuned slightly below an electronic transition in an atomAtom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
. Because the light is detuned
Laser 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...
to the "red" (i.e. at lower frequency) of the transition, the atoms will absorb more photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s if they move towards the light source, due to 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...
. Thus if one applies light from two opposite directions, the atoms will always absorb more photons from the 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 pointing opposite to their direction of motion. In each absorption event, the atom loses a momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
equal to the momentum of the photon. If the atom, which is now in the excited state, emits a photon spontaneously, it will be kicked by the same amount of momentum but in a random direction. The result of the absorption and emission process is a reduced speed of the atom, provided its initial speed is larger than the recoil velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
from scattering a single photon. If the absorption and emission are repeated many times, the mean velocity, and therefore the kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which 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 acceleration, the body maintains this kinetic energy unless its speed changes...
of the atom will be reduced. Since the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
of an ensemble of atoms is a measure of the random internal kinetic energy, this is equivalent to cooling the atoms.
The Doppler cooling limit
Doppler cooling limit
Doppler temperature is the minimum temperature achievable with Doppler cooling, one of the methods of laser cooling.When a photon is absorbed by an atom moving in the opposite direction, its velocity is decreased according to the laws of momentum conservation. Accordingly, when a photon is emitted...
is the minimum temperature achievable with Doppler cooling.
Detailed Explanation
The vast majority of photons that come anywhere near a particular atom are almost completely unaffected by that atom. The atom is almost completely transparent to most frequencies (colors) of photons.A few photons happen to "resonate
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
" with the atom, in a few very narrow bands of frequencies (a single color rather than a mixture like white light
White
White is a color, the perception of which is evoked by light that stimulates all three types of color sensitive cone cells in the human eye in nearly equal amounts and with high brightness compared to the surroundings. A white visual stimulation will be void of hue and grayness.White light can be...
). When one of those photons comes close to the atom, the atom typically absorbs that photon (absorption spectrum) for a brief period of time, then emits an identical photon (emission spectrum
Emission spectrum
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state....
) in some random, unpredictable direction. (Other sorts of interactions between atoms and photons exist, but are not relevant to this article.)
The popular idea that lasers increase the thermal energy of matter is not the case when examining individual atoms. If a given atom is practically motionless (a "cold" atom), and the frequency of a laser focused upon it can be controlled, most frequencies do not affect the atom — it is invisible at those frequencies. There are only a few points of electromagnetic frequency that have any effect on that atom. At those frequencies, the atom can absorb a photon from the laser, while transitioning to an excited electronic state, and pick up the momentum of that photon. Since the atom now has the photon's momentum, the atom must begin to drift in the direction the photon was traveling. A short time later, the atom will spontaneously emit a photon in a random direction, as it relaxes to a lower electronic state. If that photon is emitted in the direction of the original photon, the atom will give up its momentum to the photon and will become motionless again. If the photon is emitted in the opposite direction, the atom will have to provide momentum in that opposite direction, which means the atom will pick up even more momentum in the direction of the original photon (to conserve momentum), with double its original velocity. But usually the photon speeds away in some other direction, giving the atom at least some sideways thrust.
Another way of changing frequencies is to change the positioning of the laser. For example, using a monochromatic (single-color) laser that has a frequency that is a little below one of the "resonant" frequencies of this atom (at which frequency the laser will not directly affect the atom's state). If the laser were to be positioned so that it was moving towards the observed atoms, then 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...
would raise its frequency. At one specific velocity, the frequency would be precisely correct for said atoms to begin absorbing photons.
Something very similar happens in a laser cooling apparatus, except such devices start with a warm cloud of atoms moving in numerous directions at variable velocity. Starting with a laser frequency well below the resonant frequency, photons from any one laser pass right through the majority of atoms. However, atoms moving rapidly towards a particular laser catch the photons for that laser, slowing those atoms down until they become transparent again. (Atoms rapidly moving away from that laser are transparent to that laser's photons — but they are rapidly moving towards the laser directly opposite it). This utilization of a specific velocity to induce absorption is also seen in Mössbauer spectroscopy.
On a graph of atom velocities (atoms moving rapidly to the right correspond with stationary dots far to the right, atoms moving rapidly to the left correspond with stationary dots far to the left), there is a narrow band on the left edge corresponding to the speed those atoms start absorbing photons from the left laser. Atoms in that band are the only ones that interact with the left laser. When a photon from the left laser slams into one of those atoms, it suddenly slows down an amount corresponding to the momentum of that photon (the dot would be redrawn some fixed "quantum" distance further to the right). If the atom releases the photon directly to the right, then the dot is redrawn that same distance to the left, putting it back in the narrow band of interaction. But usually the atom releases the photon in some other random direction, and the dot is redrawn that quantum distance in the opposite direction.
Such an apparatus would be constructed with many lasers, corresponding to many boundary lines that completely surround that cloud of dots.
As the laser frequency is increased, the boundary contracts, pushing all the dots on that graph towards zero velocity, the given definition of "cold".
Minimum temperature
The atom performs a random walkRandom walk
A random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the...
in momentum space with steps equal to the photon momentum due to spontaneous emission and photon absorption
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
. This constitutes a heating effect, which counteracts the cooling process and imposes a limit on the amount by which the atom can be cooled. Moreover, the optical transition used for cooling in reality must have a finite frequency width, which limits the velocity discrimination (i.e. the likelihood that an atom will scatter light from the "correct" beam, as described above), and therefore the temperature. This temperature is called the Doppler temperature. Lower temperatures, down to the recoil temperature, may be obtained by sub-Doppler cooling such as Raman Cooling
Raman Cooling
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...
. Beyond that, evaporative cooling is used to further cool the ultracold atom
Ultracold atom
Ultracold atoms is a term used to describe atoms that are maintained at temperatures close to 0 kelvins , typically below some tenths of microkelvins , where their quantum-mechanical properties become important...
s.
Maximum concentration
The concentration must be minimal to prevent the absorption of the photons into the gas in the form of heat. This absorption happens when two atoms collide with each other while one of them has an excited electron. There is then a possibility of the excited electron dropping back to the ground state with its extra energy liberated in additional kinetic energy to the colliding atoms — which heats the atoms. This works against the cooling process and therefore limits the maximum concentration of gas that can be cooled using this method.Atomic Structure
Only certain atoms and ions have optical transitions amenable to laser cooling, since it is extremely difficult to generate the amounts of laser power needed at wavelengths much shorter than 300 nm. Furthermore, the more hyperfine structureHyperfine 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...
an atom has, the more ways there are for it to emit a photon from the upper state and not return to its original state, putting it in a dark state
Dark state
The term dark state refers to state of an atom or molecule which can no longer absorb photons and therefore appears dark. All atoms and molecules are described by quantum states -- different states can have different energies and a system can make a transition from one energy level to another by,...
and removing it from the cooling process. It is possible to use other lasers to optically pump
Optical 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...
those atoms back into the excited state and try again, but the more complex the hyperfine structure is, the more (narrow-band, frequency locked) lasers are required. Since frequency-locked lasers are both complex and expensive, atoms which need more than one extra repump laser are rarely cooled; the common rubidium
Rubidium
Rubidium is a chemical element with the symbol Rb and atomic number 37. Rubidium is a soft, silvery-white metallic element of the alkali metal group. Its atomic mass is 85.4678. Elemental rubidium is highly reactive, with properties similar to those of other elements in group 1, such as very rapid...
Magneto-optical trap
Magneto-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...
, for example, requires one repump laser. This is also the reason why, to date, molecules have not been laser cooled: in addition to hyperfine structure, molecules also have rovibronic coupling
Rovibronic coupling
Rovibronic coupling denotes the simultaneous interactions between rotational, vibrational, and electronic degrees of freedom in a molecule. When a rovibronic transition occurs, the rotational, vibrational, and electronic states change simultaneously, unlike in rovibrational coupling...
s and so can also decay into excited rotational or vibrational states.
Configurations
Counter-propagating sets of laser beams in all three CartesianCartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
dimensions may be used to cool the three motional degrees of freedom
Degrees of freedom (physics and chemistry)
A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...
of the atom.
Common laser-cooling configurations include optical molasses, the magneto-optical trap
Magneto-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...
, and the Zeeman
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...
slower
Zeeman slower
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...
.
Atomic ions, trapped in an ion trap
Ion trap
An ion trap is a combination of electric or magnetic fields that captures ions in a region of a vacuum system or tube. Ion traps have a number of scientific uses such as mass spectrometery and trapping ions while the ion's quantum state is manipulated...
, can be cooled with a single laser beam as long as that beam has a component along all three motional degrees of freedom. This is in contrast to the six beams required to trap neutral atoms. The original laser cooling experiments were performed on ions in ion traps. (In theory, neutral atoms could be cooled with a single beam if they could be trapped in a deep trap, but in practice neutral traps are much shallower than ion traps and a single recoil event can be enough to kick a neutral atom out of the trap.)
Applications
The one use for Doppler cooling is the optical molassesOptical 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...
technique. This process itself forms a part of the magneto-optical trap
Magneto-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...
but it can be used independently.
Doppler cooling is also used in spectroscopy and metrology, where cooling allows narrower spectroscopic features. For example, all of the best atomic clock technologies involve Doppler cooling at some point.