Doublet (physics)
Encyclopedia
In quantum mechanics
, a doublet is a quantum state of a system with a 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 system
s. Essentially all occurrences of doublets in nature arise from rotational symmetry
; spin 1/2 is associated with the fundamental representation
of the Lie group
SU(2), the group
that defines rotational symmetry in three-dimensional space.
, in an effect known as the anomalous Zeeman effect. Such spectral lines were observed not only in the laboratory, but also in astronomical spectroscopy
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
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)
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
. In this technology, a spectroscopic doublet occurs in a spin-1/2 atomic nucleus
, 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.
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, a doublet is a quantum state of a system with a spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
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
Two-level system
In quantum mechanics, a two-state system is a system which has two possible states. More formally, the Hilbert space of a two-state system has two degrees of freedom, so a complete basis spanning the space must consist of two independent states...
s. Essentially all occurrences of doublets in nature arise from rotational symmetry
Rotational symmetry
Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag has...
; spin 1/2 is associated with the fundamental representation
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...
of the Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
SU(2), the group
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
that defines rotational symmetry in three-dimensional space.
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 fieldMagnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
, 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
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
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
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
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 (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
for greater detail.
Doublets continue to play an important role in physics. For example, the healthcare technology of magnetic resonance imaging
Magnetic resonance imaging
Magnetic resonance imaging , nuclear magnetic resonance imaging , or magnetic resonance tomography is a medical imaging technique used in radiology to visualize detailed internal structures...
is based on nuclear magnetic resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
. In this technology, a spectroscopic doublet occurs in a spin-1/2 atomic nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
, 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
Rabi cycle
In physics, the Rabi cycle is the cyclic behaviour of a two-state quantum system in the presence of an oscillatory driving field. A two-state system has two possible states, and if they are not degenerate energy levels the system can become "excited" when it absorbs a quantum of energy.The effect...
. The strength and frequency of the emitted radio waves allows the concentration of such nuclei to be measured.
See also
- Singlet state
- Triplet stateTriplet stateA spin triplet is a set of three quantum states of a system, each with total spin S = 1 . The system could consist of a single elementary massive spin 1 particle such as a W or Z boson, or be some multiparticle state with total spin angular momentum of one.In physics, spin is the angular momentum...
- Spin multiplicity