Sub-Doppler cooling is a class of laser cooling techniques that reduce the temperature of atoms and molecules below the Doppler cooling limit. In experiment implementation, Doppler cooling is limited by the broad natural linewidth of the lasers used in cooling. [1] Regardless of the transition used, however, Doppler cooling processes have an intrinsic cooling limit that is characterized by the momentum recoil from the emission of a photon from the particle. This is called the recoil temperature and is usually far below the linewidth-based limit mentioned above. By laser cooling methods beyond the two-level approximations of atoms, temperature below this limit can be achieved.
Optical pumping between the sublevels that make up an atomic state introduces a new mechanism for achieving ultra-low temperatures. The essential feature of sub-Doppler cooling is the non-adiabaticity of the moving atoms to the light field. For a spatially dependent light field, the orientation of moving atoms is adjusted by optical pumping to fit the conditions of the light field. Yet the moving atoms do not instantly adjust to the light field as they move, their orientation always lags behind the orientation that would exist for stationary atoms, which determines the velocity-dependent differential absorption and hence the cooling. With this cooling process, lower temperatures can be obtained. [2]
Various methods have been used independently or combined in an experimental sequence to achieve sub-Doppler cooling. One method to produce spatially dependent optical pumping is polarization gradient cooling, where the superposition of two counter-propagating laser beams of orthogonal polarizations lead to a light field with polarization varying on the wavelength scale. A specific mechanism within polarization gradient cooling is Sisyphus cooling, where atoms climb "potential hills" created by the interaction of their internal energy states with spatially varying light fields. The light field in optical molasses in three-dimension also has polarization gradient.
Other methods of sub-Doppler cooling include evaporative cooling, free space Raman cooling, Raman side-band cooling, resolved sideband cooling, electromagnetically induced transparency (EIT) cooling, and the use of a dark magneto-optical trap. These techniques can be used depending on the minimum temperature needed and specifications of the individual setup. For example, an optical molasses time-of-flight technique was used to cool sodium (Doppler limit ) to . [3]
Motivations for sub-doppler cooling include motional ground state cooling, cooling to the motional ground state, a requirement for maintaining fidelity during many quantum computation operations.
A magneto-optical trap (MOT) is commonly used for cooling and trapping a substance by Doppler cooling. In the process of Doppler cooling, the red detuned light would be absorbed by atoms from one certain direction and re-emitted in a random direction. The electrons of the atoms would decay to an alternative ground states if the atoms have more than one hyperfine ground level. There is the case of all the atoms in the other ground states rather than the ground states of Doppler cooling, then system cannot cool the atoms further.
In order to solve this problem, the other re-pumping light would be incident on the system to repopulate the atoms to restart the Doppler cooling process. This would induce higher amounts of fluorescence being emitted from the atoms which can be absorbed by other atoms, acting as a repulsive force. Due to this problem, the Doppler limit would increase and is easy to meet. When there is a dark spot or lines on the shape of the re-pumping light, the atoms in the middle of the atomic gas would not be excited by the re-pumping light which can decrease the repulsion force from the previous cases.
This can help to cool the atoms to a lower temperature than the typical Doppler cooling limit. This is called a dark magneto-optical trap (DMOT). [4]
The Doppler cooling limit is set by balancing the heating from the momentum kicks. Applying the results from the Fokker-Planck equation to the sub-Doppler processes would lead to an arbitrarily low final temperature as the damping coefficient become arbitrarily large. A few more considerations is needed. For instance, When a photon is scattered, the momentum change of the atom is assumed to be small relative to the its overall momentum, but when the atom slows down to around the region of , the momentum change becomes significant. Thus at low velocities, spontaneous emission would leave the atom with a residual momentum around , which sets a minimum velocity scale. The velocity distribution around cannot be well described by the Fokker Planck equation, and this sets an intuitive lower limit on the temperature. [2]
Furthermore, polarization gradient cooling depends on the ability to localize atoms to a scale of , where is the wavelength of the light. Due to the uncertainty principle, this localization also imposes a minimum momentum spread , which also leads to a limit on how much the atoms can be cooled.
These theories are tested in the analytical and numerical calculations in [5] with a one-dimensional polarization gradient molasses. It was shown that in the limit of large detuning, the velocity distribution depends only on a dimensionless parameter, the light shift of the ground state divided by the recoil energy. The minimum kinetic energy was found to be on the order of 40 times the recoil energy.
Laser cooling, sometimes also referred to as Doppler cooling, includes several techniques where atoms, molecules, and small mechanical systems are cooled with laser light. The directed energy of lasers is often associated with heating materials, e.g. laser cutting, so it can be counterintuitive that laser cooling often results in sample temperatures approaching absolute zero. It is a routine step in many atomic physics experiments where the laser-cooled atoms are then subsequently manipulated and measured, or in technologies, such as atom-based quantum computing architectures. Laser cooling relies on the change in momentum when an object, such as an atom, absorbs and re-emits a photon. For example, if laser light illuminates a warm cloud of atoms from all directions and the laser's frequency is tuned below an atomic resonance, the atoms will be cooled. This common type of laser cooling relies on the Doppler effect where individual atoms will preferentially absorb laser light from the direction opposite to the atom's motion. The absorbed light is re-emitted by the atom in a random direction. After repeated emission and absorption of light the net effect on the cloud of atoms is that they will expand more slowly. The slower expansion reflects a decrease in the velocity distribution of the atoms, which corresponds to a lower temperature and therefore the atoms have been cooled. For an ensemble of particles, their thermodynamic temperature is proportional to the variance in their velocity, therefore the lower the distribution of velocities, the lower temperature of the particles.
Evaporative cooling is an atomic physics technique to achieve high phase space densities which optical cooling techniques alone typically can not reach.
Resolved sideband cooling is a laser cooling technique allowing cooling of tightly bound atoms and ions beyond the Doppler cooling limit, potentially to their motional ground state. Aside from the curiosity of having a particle at zero point energy, such preparation of a particle in a definite state with high probability (initialization) is an essential part of state manipulation experiments in quantum optics and quantum computing.
In condensed matter physics and atomic physics, the recoil temperature is a fundamental lower limit of temperature attainable by some laser cooling schemes. When an atom decays from an excited electronic state at rest to a lower energy electronic state by the spontaneous emission of a photon, due to conservation of momentum, the atom gains momentum equivalent to the momentum of the photon. This kinetic energy gain corresponds to the recoil temperature of the atom. The recoil temperature is
Optical molasses is a laser cooling technique that can cool neutral atoms to as low as a few microkelvin, depending on the atomic species. An optical molasses consists of 3 pairs of counter-propagating orthogonally polarized laser beams intersecting in the region where the atoms are present. The main difference between an optical molasses (OM) and a magneto-optical trap (MOT) is the absence of magnetic field in the former. Unlike a MOT, an OM provides only cooling and no trapping.
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 at the potential extrema. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation.
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.
In atomic, molecular, and optical physics, a magneto-optical trap (MOT) is an apparatus which uses laser cooling and a spatially-varying magnetic field to create a trap which can produce samples of cold, neutral atoms. Temperatures achieved in a MOT can be as low as several microkelvin, depending on the atomic species, which is two or three times below the photon recoil limit. However, for atoms with an unresolved hyperfine structure, such as 7Li, the temperature achieved in a MOT will be higher than the Doppler cooling limit.
In condensed matter physics, an ultracold atom is an atom with a temperature near absolute zero. At such temperatures, an atom's quantum-mechanical properties become important.
In spectroscopy, the Autler–Townes effect, is a dynamical Stark effect corresponding to the case when an oscillating electric field is tuned in resonance to the transition frequency of a given spectral line, and resulting in a change of the shape of the absorption/emission spectra of that spectral line. The AC Stark effect was discovered in 1955 by American physicists Stanley Autler and Charles Townes.
In experimental physics, a magnetic trap is an apparatus which uses a magnetic field gradient to trap neutral particles with magnetic moments. Although such traps have been employed for many purposes in physics research, they are best known as the last stage in cooling atoms to achieve Bose–Einstein condensation. The magnetic trap was first proposed by David E. Pritchard.
The manipulation of atoms using optical fields is a vital and fundamental area of research within the field of atomic physics. This research revolves around leveraging the distinct characteristics of laser light and coherent optical fields to achieve precise control over various aspects of atomic systems. These aspects encompass regulating atomic motion, positioning atoms, manipulating internal states, and facilitating intricate interactions with neighboring atoms and photons. The utilization of optical fields provides a powerful toolset for exploring and understanding the quantum behavior of atoms and opens up promising avenues for applications in atomic, molecular, and optical physics.
Photofragment ion imaging or, more generally, Product Imaging is an experimental technique for making measurements of the velocity of product molecules or particles following a chemical reaction or the photodissociation of a parent molecule. The method uses a two-dimensional detector, usually a microchannel plate, to record the arrival positions of state-selected ions created by resonantly enhanced multi-photon ionization (REMPI). The first experiment using photofragment ion imaging was performed by David W Chandler and Paul L Houston in 1987 on the phototodissociation dynamics of methyl iodide (iodomethane, CH3I).
The Kapitza–Dirac effect is a quantum mechanical effect consisting of the diffraction of matter by a standing wave of light, in complete analogy to the diffraction of light by a periodic grating, but with the role of matter and light reversed. The effect was first predicted as the diffraction of electrons from a standing wave of light by Paul Dirac and Pyotr Kapitsa in 1933. The effect relies on the wave–particle duality of matter as stated by the de Broglie hypothesis in 1924. The matter-wave diffraction by a standing wave of light was first observed using a beam of neutral atoms. Later, the Kapitza-Dirac effect as originally proposed was observed in 2001.
In ultra-low-temperature physics, Sisyphus cooling, the Sisyphus effect, or polarization gradient cooling involves the use of specially selected laser 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 until it has lost its kinetic energy. It is a type of laser cooling of atoms used to reach temperatures below the Doppler cooling limit. This cooling method was first proposed by Claude Cohen-Tannoudji in 1989, motivated by earlier experiments which observed sodium atoms cooled below the Doppler limit in an optical molasses. Cohen-Tannoudji received part of the Nobel Prize in Physics in 1997 for his work. The technique is named after Sisyphus, a figure in the Greek mythology 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.
In atomic physics, a Zeeman slower is a scientific instrument 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 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 a substantial number of atoms are 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. The Zeeman slower is attached close to where the hot atoms exit the oven and are used to slow them to less than 10 m/s (slowing) with a very small velocity spread (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, Doppler cooling being 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 sideband cooling. Both techniques make use of Raman scattering of laser light by the atoms.
Cavity optomechanics is a branch of physics which focuses on the interaction between light and mechanical objects on low-energy scales. It is a cross field of optics, quantum optics, solid-state physics and materials science. The motivation for research on cavity optomechanics comes from fundamental effects of quantum theory and gravity, as well as technological applications.
Gray molasses is a method of sub-Doppler laser cooling of atoms. It employs principles from Sisyphus cooling in conjunction with a so-called "dark" state whose transition to the excited state is not addressed by the resonant lasers. Ultracold atomic physics experiments on atomic species with poorly-resolved hyperfine structure, like isotopes of lithium and potassium, often utilize gray molasses instead of Sisyphus cooling as a secondary cooling stage after the ubiquitous magneto-optical trap (MOT) to achieve temperatures below the Doppler limit. Unlike a MOT, which combines a molasses force with a confining force, a gray molasses can only slow but not trap atoms; hence, its efficacy as a cooling mechanism lasts only milliseconds before further cooling and trapping stages must be employed.
Polarization gradient cooling is a technique in laser cooling of atoms. It was proposed to explain the experimental observation of cooling below the doppler limit. Shortly after the theory was introduced experiments were performed that verified the theoretical predictions. While Doppler cooling allows atoms to be cooled to hundreds of microkelvin, PG cooling allows atoms to be cooled to a few microkelvin or less.