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 (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...

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'' originated as an acronym for light amplification by stimulated emission of radi ...

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, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...

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

can be defined as the 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 a 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 ...

during lasing. At given frequency

\omega_

pump A pump is a device that moves fluids (liquids or gases), or sometimes Slurry, slurries, by mechanical action, typically converted from electrical energy into hydraulic or pneumatic energy. Mechanical pumps serve in a wide range of application ...

and given frequency

\omega_

of lasing, the quantum defect

q = \hbar \omega_ - \hbar\omega_

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

temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...

of the

(measured in units of energy) should be small compared to the quantum defect. The quantum defect may also be defined as follows: at a given frequency

\omega_

and given frequency

\omega_

of lasing, the quantum defect

q = 1 - \omega_/\omega_

; according to this definition, quantum defect is dimensionless. 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. 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 hydrogen atom contains a single positively charged proton in the nucleus, and a single negatively charged electron bound to the nucleus by the Coulomb for ...

leads to an

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

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 ...

h

is the

Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

c

is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

and

n

is the

principal quantum number In quantum mechanics, the principal quantum number (''n'') of an electron in an atom indicates which electron shell or energy level it is in. Its values are natural numbers (1, 2, 3, ...). Hydrogen and Helium, at their lowest energies, have just ...

. For alkali atoms with small

orbital angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed sy ...

, the

wavefunction In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...

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

Coulomb potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physic ...

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 was ...

with an angular momentum dependent quantum defect,

\delta_l

E_\text = -\dfrac.

The largest shifts occur when the orbital angular momentum is zero (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