
Using laser light to trap, manipulate, or control particles and materials.Laser trapping is a technique that uses the momentum and electric field of laser light to confine, manipulate, and cool microscopic and even macroscopic particles—from individual atoms and molecules to dust grains and living cells. It encompasses optical tweezers, which trap transparent objects in a focused beam, and magneto-optical traps, which cool and confine neutral atoms. The method is fundamental to modern physics, enabling experiments from quantum computing to dark matter detection, and it has become a versatile tool in biology and materials science.
The foundational ideas were developed in the 1970s and 1980s. Arthur Ashkin pioneered optical tweezers in the 1970s, while Steven Chu, Claude Cohen-Tannoudji, and William Phillips developed laser cooling and trapping of atoms in the 1980s, earning the 1997 Nobel Prize in Physics.
The mechanism relies on the transfer of momentum from photons to the trapped object. In optical tweezers, a tightly focused laser beam creates a gradient force that pulls a dielectric particle toward the region of highest intensity, while scattering forces push it along the beam direction; by balancing these, a stable trap forms. For atoms, laser cooling uses the Doppler effect: atoms moving toward a red-detuned laser beam absorb photons and slow down, while the trap's magnetic field creates a position-dependent force, confining the cooled atoms at a specific point.
Laser trapping is used to hold single molecules for biophysical studies, to isolate and study individual atoms for quantum computing, and to levitate microspheres as ultra-sensitive detectors of forces, including potential dark matter interactions.
Laser trapping can hold a living bacterium without killing it, allowing scientists to study its behavior in a controlled optical 'cage'.
| C^ell | variable | Angular power spectrum at multipole ell — angular power spectrum |
| z | variable | Redshift — redshift |
| H(z) | variable | Hubble parameter at redshift z — hubble parameter kilometre per second per megaparsec |
| chi(z) | variable | Comoving distance to redshift z — comoving distance metre |
| W(z) | variable | Window function (selection function) at redshift z — window function |
| P(k,z) | variable | Three-dimensional power spectrum at wavenumber k and redshift z — power spectrum cubic metre |
| k | variable | Wavenumber — wavenumber reciprocal metre |
| ell | variable | Multipole moment — multipole moment |
| c | constant | Fundamental constant relating distance and time in relativity — speed of light = 299792458 metre per second |
| ∫ dz | operator | Sum over all redshifts along the line of sight — integral operator |
















