Atom localization deals with estimating the position of an atom using techniques of quantum optics with increasing precision. This field finds its origins in the thought experiment by

Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...

called

Heisenberg's microscope Heisenberg's microscope is a thought experiment proposed by Werner Heisenberg that has served as the nucleus of some commonly held ideas about quantum mechanics. In particular, it provides an argument for the uncertainty principle on the basis of t ...

, which is commonly used as an illustration of Heisenberg's Uncertainty relation in quantum mechanics textbooks. The techniques have matured enough to offer atom localization along all three spatial dimensions in the subwavelength domain. Atom localization techniques have been applied to other fields requiring precise control or measurement of the position of atom-like entities such as

microscopy Microscopy is the technical field of using microscopes to view objects and areas of objects that cannot be seen with the naked eye (objects that are not within the resolution range of the normal eye). There are three well-known branches of micr ...

nanolithography Nanolithography (NL) is a growing field of techniques within nanotechnology dealing with the engineering (patterning e.g. etching, depositing, writing, printing etc) of nanometer-scale structures on various materials. The modern term reflects on ...

, optical trapping of atoms,

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 congregat ...

s, and

atom optics Atom optics (or atomic optics) is the area of physics which deals with beams of cold, slowly moving neutral atoms, as a special case of a particle beam. Like an optical beam, the atomic beam may exhibit diffraction and interference, and can be focu ...

. Atom localization is based on employing atomic coherence to determine the position of the atom to a precision smaller than the wavelength of the light being used. This seemingly surpasses the Rayleigh limit of resolution and opens up possibilities of super-resolution for a variety of fields.

Subwavelength atom localization: surpassing the Rayleigh limit

Given that in the discussion of the

, Rayleigh limit of resolution and Heisenberg's Uncertainty are intricately related creates an impression that surpassing Rayleigh limit would lead to violation of Heisenberg's Uncertainty limit. It can be mathematically shown that the spatial resolution can be enhanced to any amount without violating Heisenberg's Uncertainty relation. The price to be paid is the momentum kick received by the particle whose position is being measured. This is depicted in the figure on the right. UncertaintyHyperbolaPNG

One dimensional atom localization

Localization of an atom in a transverse direction from its direction of motion can be easily achieved using techniques such as quantum interference effects,

coherent population trapping In atomic physics, a dark state refers to a state of an atom or molecule that cannot absorb (or emit) photons. All atoms and molecules are described by quantum states; different states can have different energies and a system can make a transition ...

, via modification of atomic spectra such as through Autler-Towns Spectroscopy,

resonance fluorescence Resonance fluorescence is the process in which a two-level atom system interacts with the quantum electromagnetic field if the field is driven at a frequency near to the natural frequency of the atom. General theory Typically the photon contai ...

Ramsey interferometry Ramsey interferometry, also known as the separated oscillating fields method, is a form of particle interferometry that uses the phenomenon of magnetic resonance to measure transition frequencies of particles. It was developed in 1949 by Norman Rams ...

, and via the monitoring of probe susceptibility through electromagnetically-induced transparency, when the atom is interacting with at least one spatially-dependent

standing wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect ...

field.

Applications

The study of atom localization has offered practical applications to the area of

at the

Heisenberg limit In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of Inequality (mathematics), mathematical inequalities asserting a fundamental limit to the accuracy with which the values fo ...

along with its fundamental importance to the areas of

, and laser cooling and trapping of neutral atoms. Extending the atom localization schemes to two dimensions,

s with tighter than usual confinement at each lattice point can be obtained. Such strongly confined lattice structures could be useful to study several predictions of the Bloch theory of solids, and Mott transitions in much cleaner systems as compared to conventional solids. Such tighter trapping potentials could have further applications to the area of

quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...

specifically for the development of deterministic sources of single atoms and single-atom quantum register. Techniques of atom localization are also important to the subwavelength microscopy and imaging and determination of the center-of-mass wavefunction of atom-like entities.{{cite journal , last1=Rudy , first1=P. , last2=Ejnisman , first2=R. , last3=Bigelow , first3=N.P. , title=Fluorescence investigation of parametrically excited motional wave packets in optical lattices , journal=Phys. Rev. Lett. , date=1997 , volume=78 , issue=26 , pages=4906–4909, doi=10.1103/PhysRevLett.78.4906

Footnotes

Atomic physics