The term quantum defect refers to two concepts: energy loss in lasers and energy levels in alkali elements. Both deal with

quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity ( physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizat ...

systems where matter interacts with light.

In laser science

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The ...

science, the term "quantum defect" refers to the fact that the energy of a pump photon is generally higher than that of a ''signal photon'' (photon of the output radiation). The energy difference is lost to heat, which may carry away the excess

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...

delivered by the multimode incoherent pump. The quantum defect of a

can be defined as part of the energy of the pumping photon, which is lost (not turned into photons at the lasing wavelength) in the

gain medium The active laser medium (also called gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a h ...

at the

lasing A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...

. At given frequency

\omega_

pump A pump is a device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they ...

and given frequency

\omega_

, the quantum defect

q = \hbar \omega_ - \hbar\omega_

. Such quantum defect has dimension of energy; for the efficient operation, the

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

of the

(measured in units of energy) should be small compared to the quantum defect. At a fixed pump frequency, the higher the quantum defect, the lower is the upper bound for the power efficiency.

In hydrogenic atoms

The quantum defect of an alkali atom refers to a correction to the energy levels predicted by the classic calculation of the hydrogen wavefunction. A simple model of the potential experienced by the single valence electron of an alkali atom is that the ionic core acts as a point charge with effective charge e and the wavefunctions are

hydrogenic A hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single valence electron. These atoms are isoelectronic with hydrogen. Examples of hydrogen-like atoms include, but are not limited to, hydrogen itself, all alkali metals such a ...

. However, the structure of the ionic core alters the potential at small radii. The 1/''r'' potential in the

hydrogen atom A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen cons ...

leads to an

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 n ...

binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...

given by

E_\text = -\dfrac,

where

R

is the

Rydberg constant In spectroscopy, the Rydberg constant, symbol R_\infty for heavy atoms or R_\text for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first aro ...

h

is Planck's constant,

c

is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...

and

n

is the

principal quantum number In quantum mechanics, the principal quantum number (symbolized ''n'') is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. A ...

. For alkali atoms with small orbital angular momentum, the

wavefunction A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...

of the valence electron is non-negligible in the ion core where the screened

Coulomb potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...

with an effective charge of e no longer describes the potential. The spectrum is still described well by the

Rydberg formula In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It wa ...

with an angular momentum dependent quantum defect,

\delta_l

E_\text = -\dfrac.

The largest shifts occur when the orbital angular momentum is equal to 0 (normally labeled 's') and these are shown in the table for the

alkali metals The alkali metals consist of the chemical elements lithium (Li), sodium (Na), potassium (K),The symbols Na and K for sodium and potassium are derived from their Latin names, ''natrium'' and ''kalium''; these are still the origins of the names ...

:C.J.Foot, Atomic Physics, Oxford University Press,

References

Atoms Laser science

In laser science

In hydrogenic atoms

See also

References