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, q ...

, a doublet is a composite quantum state of a system with an effective spin 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 systems. 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 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 addit ...

SU(2).

History and applications

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

, in an effect known as the

anomalous Zeeman effect The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel prize ...

. 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 ...

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 in nuclear reactions) 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 partic ...

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 nuclei. Spin is one of two types of angular momentum in quantum mechanics, the other being ''orbital angular momentum''. The orbi ...

for greater detail. Doublets continue to play an important role in physics. For example, the healthcare technology of magnetic resonance imaging 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 experiments, Geiger–Marsden gold foil experiment. After th ...

, 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. 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