Stark effect

In atomic physics, the Stark effect is the shifting and splitting of atomic or molecular spectral lines in a static electric field . It is the analogue of the Zeeman effect , in which spectral lines split in the presence of a magnetic field . The Stark effect is named after its discoverer Johannes Stark , who first demonstrated it in 1913 at RWTH Aachen University and was honored with the Nobel Prize for Physics in 1919 .

Independently of Stark, the effect was also discovered in 1913 by the Italian physicist Antonio Lo Surdo (1880–1949). Earlier, unsuccessful attempts to demonstrate the effect were made by Woldemar Voigt as early as 1899. Experiments with high field strengths by Heinrich Rausch von Traubenberg were particularly successful .

Mechanisms

Splitting of the spectral lines in a hydrogen atom as a function of the electric field strength.

In the quantum mechanical view, the electric field leads to another term in the Hamilton operator (see fine structure ). If the field is sufficiently weak, this term has the form ${\displaystyle {\vec {E}}}$

${\displaystyle {\hat {H}}_{1}={\vec {p}}\cdot {\vec {E}}.}$

Here is the electric dipole moment and the electric field strength . With the help of perturbation theory, the new energy eigenvalues and states can be determined. The following energy shifts can result: ${\displaystyle {\vec {p}}}$ ${\displaystyle {\vec {E}}}$

Linear Stark effect

The linear Stark effect splits k -fold degenerate energy levels in the electric field, where

${\displaystyle k=n_{1}+n_{2}}$

with parabolic quantum numbers and . ${\displaystyle n_{1}}$ ${\displaystyle n_{2}}$

If so, the atom has a permanent dipole moment and the energy of the dipole is proportional to the applied field strength: ${\displaystyle k\neq 0}$ ${\displaystyle {\vec {p}}}$ ${\displaystyle U_{dip}}$

${\displaystyle U_{dip}=-{\vec {p}}\cdot {\vec {E}}.}$

In the literature, the degeneracy of the angular momentum in the zero field is often given as a condition for the strong displacement . Since this always occurs together with the degeneracy, this is correct. Nevertheless, the degeneracy has nothing to do directly with the strong shift. ${\displaystyle l}$ ${\displaystyle k}$ ${\displaystyle l}$

Square Stark effect

The square Stark effect leads to a shift in energy levels proportional to the square of the field strength. It occurs in all atoms and can be explained in a classically clear way: the electric field induces an electric dipole moment in the atom

${\displaystyle {\vec {p}}({\vec {E}})=\alpha {\vec {E}}}$

with electrical polarizability . ${\displaystyle \alpha }$

This adds the following energy to the energy of the free atom:

${\displaystyle U_{el}=-\int _{0}^{|{\vec {E}}|}{\vec {p}}({\vec {E}})\cdot \mathrm {d} {\vec {E}}=-{\frac {1}{2}}\alpha {\vec {E}}^{2}.}$

Dynamic strong effect

The dynamic Stark effect, also known as the optical Stark effect or AC-Stark effect (after AC for alternating current , de. Alternating current ) describes the energy shift due to alternating electrical fields such as As light (hence the term light shift , Eng. LightShift ). In the case of high light intensities, however , the application of the perturbation theory is no longer permissible and the problem is usually treated using the Jaynes-Cummings model . In solids , especially in semiconductors , many-particle interactions lead to some properties of the effect that can no longer be described with this model. Instead, the semiconductor Bloch equations can be used here.

QCSE

The quantum confined stark effect (QCSE, for example "restricted / restricted stark effect ") is used in semiconductor physics. It describes the Stark effect that occurs in heterostructures (e.g. laser diodes ) due to local electrical fields which, among other things, a. can be generated by polarization charges. These charges can e.g. B. can be generated by the piezo effect due to internal stresses when combining different semiconductor materials. They create internal electric fields that change the optical properties of the material. In addition to a part of red shift of the emission wavelength of a reduction in the efficiency of radiative transitions because of the smaller overlap integral by spatial separation of the electron and hole - wave functions .

Applications

After the discovery, the structure of atoms was precisely elucidated with the help of the Stark effect. Nowadays the effect is used in cryogenic single molecule spectroscopy and in laser cooling . The latter due to the dipole forces resulting from the AC Stark shift .

literature

• Hermann hook , Hans Christoph Wolf : atomic and quantum physics. Introduction to the experimental and theoretical basics (Springer textbook). 6th edition Springer, Berlin 1996, ISBN 3-540-61237-8 .

Individual evidence

1. ↑ Othmar Marti: Atoms in an electric field . Ulm University
2. ^ TP Hezel, Charles E. Burkhardt, Marco Ciocca, Jacob J. Leventhal: Classical view of the Stark effect in hydrogen atoms . In: American Journal of Physics . tape 60 , 1992, ISSN  0002-9505 , pp. 324-335 , doi : 10.1119 / 1.16875 .
3. ^ A. Hooker, Chris H. Greene, William Clark: Classical examination of the Stark effect in hydrogen . In: Physical Review A . tape 55 , no. 6 , 1997, ISSN  0556-2791 , pp. 4609-4612 , doi : 10.1103 / PhysRevA.55.4609 .
4. ↑ Peter Brick et al .: Coulomb Memory Effects and Higher-Order Coulomb Correlations in the Excitonic Optical Stark Effect . In: physica status solidi (a) . tape 178 , no. 1 , 2000, ISSN  0031-8965 , p. 459-463 , doi : 10.1002 / 1521-396X (200003) 178: 1 <459 :: AID-PSSA459> 3.0.CO; 2-2 .
5. ^ Stephan W. Koch et al .: Theory of coherent effects in semiconductors . In: Journal of Luminescence . tape 83-84 , 1999, ISSN  0022-2313 , pp. 1-6 , doi : 10.1016 / S0022-2313 (99) 00065-4 .