Singlet state

In quantum mechanics, a singlet state usually refers to a system in which all electrons are paired.

The term 'singlet' originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number

In contrast, a doublet state contains one unpaired electron and shows splitting of spectral lines into a doublet, and a triplet state has two unpaired electrons and shows threefold splitting of spectral lines.

Singlets and the related spin concepts of doublets and triplets occur frequently in atomic physics and nuclear physics, where one often needs to determine the total spin of a collection of particles.

Since the only observed fundamental particle with zero spin is the extremely inaccessible Higgs boson, singlets in everyday physics are necessarily composed of sets of particles whose individual spins are non-zero, e.g. ⁠1/2⁠ or 1.

in this singlet-style terminology has a simple relationship to the spin quantum number:

In particular, the concept of isospin was developed early in the history of particle physics to address the remarkable similarities of protons and neutrons.

Within atomic nuclei, protons and neutrons behave in many ways as if they were a single type of particle, the nucleon, with two states.

The isospin doublet notably shares the same SU(2) mathematical structure as the

While for angular momentum states the singlet-style terminology is seldom used beyond triplets (spin=1), it has proven historically useful for describing much larger particle groups and subgroups that share certain features and are distinguished from each other by quantum numbers beyond spin.

The simplest possible angular momentum singlet is a set (bound or unbound) of two spin-1/2 (fermion) particles that are oriented so that their spin directions ("up" and "down") oppose each other; that is, they are antiparallel.

The simplest possible bound particle pair capable of exhibiting the singlet state is positronium, which consists of an electron and positron (antielectron) bound by their opposite electric charges.

An unbound singlet consists of a pair of entities small enough to exhibit quantum behavior (e.g. particles, atoms, or small molecules), not necessarily of the same type, for which four conditions hold: Any spin value can be used for the pair, but the entanglement effect will be strongest both mathematically and experimentally if the spin magnitude is as small as possible, with the maximum possible effect occurring for entities with spin-1/2 (such as electrons and positrons).

Early thought experiments for unbound singlets usually assumed the use of two antiparallel spin-1/2 electrons.

The ability of positronium to form both singlet and triplet states is described mathematically by saying that the product of two doublet representations (meaning the electron and positron, which are both spin-1/2 doublets) can be decomposed into the sum of an adjoint representation (the triplet or spin 1 state) and a trivial representation (the singlet or spin 0 state).

This greater mathematical precision for example makes it possible to assess how singlets and doublets behave under rotation operations.

Similarly, for a system of two electrons, it is possible to measure the total spin by applying

For example, when the spin states of two electrons are correlated by their emission from a single quantum event that conserves angular momentum, the resulting electrons remain in a shared singlet state even as their separation in space increases indefinitely over time, provided only that their angular momentum states remain unperturbed.

Along with Podolsky and Rosen, Einstein proposed the EPR paradox thought experiment to help define his concerns with what he viewed as the non-locality of spatially separated entangled particles, using it in an argument that quantum mechanics was incomplete.

In 1951 David Bohm formulated a version of the "paradox" using spin singlet states.

[3] The difficulty captured by the EPR-Bohm thought experiment was that by measuring a spatial component of the angular momentum of either of two particles that have been prepared in a spatially distributed singlet state, the quantum state of the remaining particle, conditioned on the measurement result obtained, appears to be "instantaneously" altered, even if the two particles have over time become separated by light years of distance.

Decades later, John Stewart Bell, who was a strong advocate of Einstein's locality-first perspective, proved Bell's theorem and showed that it could be used to assess the existence or non-existence of singlet entanglement experimentally.

[citation needed] A weaker form of Einstein's locality principle remains intact, which is this: Classical information cannot be transmitted faster than the speed of light c, not even by using quantum entanglement events.