quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

, a doublet is a composite quantum state of a system with an effective

spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...

of 1/2, such that there are two allowed values of the spin component, −1/2 and +1/2. Quantum systems with two possible states are sometimes called

two-level system In quantum mechanics, a two-state system (also known as a two-level system) is a quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states. The Hilbert space describing such a syst ...

s. Essentially all occurrences of doublets in nature arise from

rotational symmetry Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which i ...

; spin 1/2 is associated with the

fundamental representation In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group or Lie algebra whose highest weight is a fundamental weight. For example, the defini ...

of the

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

SU(2) In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special ...

History and applications

The term "doublet" dates back to the 19th century, when it was observed that certain

spectral lines A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to ident ...

of an ionized, excited gas would split into two under the influence of a strong

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...

, in an effect known as the anomalous Zeeman effect. Such spectral lines were observed not only in the laboratory, but also in astronomical

spectroscopy Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...

observations, allowing astronomers to deduce the existence of, and measure the strength of magnetic fields around the sun, stars and galaxies. Conversely, it was the observation of doublets in spectroscopy that allowed physicists to deduce that the

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...

had a spin, and that furthermore, the magnitude of the spin had to be 1/2. See the history section of the article on

spin (physics) Spin is a conserved quantity carried by elementary particles, and thus by composite particles (hadrons) and atomic nucleus, atomic nuclei. Spin is one of two types of angular momentum in quantum mechanics, the other being ''orbital angular moment ...

for greater detail. Doublets continue to play an important role in physics. For example, the

healthcare Health care or healthcare is the improvement of health via the prevention, diagnosis, treatment, amelioration or cure of disease, illness, injury, and other physical and mental impairments in people. Health care is delivered by health profe ...

technology of

magnetic resonance imaging Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...

is based on

nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...

. In this technology, a spectroscopic doublet occurs in a spin-1/2

atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron i ...

, whose doublet splitting is in the radio-frequency range. By applying both a magnetic field and carefully tuning a radio-frequency transmitter, the nuclear spins will flip and re-emit radiation, in an effect known as the

Rabi cycle In physics, the Rabi cycle (or Rabi flop) is the cyclic behaviour of a two-level quantum system in the presence of an oscillatory driving field. A great variety of physical processes belonging to the areas of quantum computing, condensed matter, ...

. The strength and frequency of the emitted radio waves allows the concentration of such nuclei to be measured. Another potential application is the use of doublets as the emitting layer in light emitting diodes (LEDs). These materials have the advantage of having 100% theoretical quantum efficiency based on spin statistics whereas singlet systems and triplet systems have significantly lower efficiencies or rely on noble metals such as Pt and Ir to emit light.

References

* {{DEFAULTSORT:Doublet State Spectroscopy Rotational symmetry Quantum states

History and applications

See also

References