In atomic physics, the Stark effect is the splitting and shift of a spectral line into several components in the presence of an electric field. The amount of splitting itself is called the Stark shift. It is analogous to the Zeeman effect where a spectral line is split into several components in the presence of a magnetic field. The Stark effect is responsible for the pressure broadening (Stark broadening) of spectral lines by charged particles.

History

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The effect is named after Johannes Stark, who discovered it in 1913. It was independently discovered in the same year by the Italian physicist Antonino Lo Surdo, and is thus sometimes called the Stark-Lo Surdo effect. Earlier, unsuccessful, attempts to compute the magnitude of the effect, and to discover the perturbation, had been made by Voigt in 1899. In 1916, Epstein and Schwarzschild were able to perform computations using the Bohr model of the atom to exactly fit the magnitude of the Stark effect in hydrogen. In 1920, Hendrik Kramers was able to perform calculations within the Bohr model to estimate the relative intensities of the lines in the line pattern.

While first-order perturbation effects for the Stark effect in hydrogen are in agreement for the Bohr model and the quantum-mechanical theory of the atom, higher order effects are not. Measurements of the Stark effect under high field strengths confirmed the correctness of the quantum theory over the Bohr model.

Mechanism

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The effect arises because of the interaction between the electric dipole moment of an electron with an external electric field. If the electric field is uniform over the length scale of the atom, then the perturbing Hamiltonian is of the form

$H^1\; =\; \backslash vec\; p\; \backslash cdot\; \backslash vec\; E\; =\; e\; E\_z\; \backslash hat\; z$.

The first order energy shift of the state $\backslash left\; |\; \{\backslash psi\}\_m\; \backslash right\; \backslash rangle$ due to the perturbation is given by $\backslash Delta\; E\_m\; =\; e\; E\_z\; \backslash left\; \backslash langle\; \{\backslash psi\}\_m\; \backslash right\; |\; \backslash hat\; z\; \backslash left\; |\; \{\backslash psi\}\_m\; \backslash right\; \backslash rangle$ (see Perturbation theory). Since the unperturbed states may be degenerate, we normally need to use the eigenvectors of H¹ when calculating the energy shifts. The effect of H¹ is therefore to lift this degeneracy, which is observed experimentally as a splitting of spectral lines.

Quantum-Confined Stark Effect

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In a semiconductor heterostructure, where a small bandgap material is sandwiched between two layers of a larger bandgap material, the Stark effect can be dramatically enhanced by bound excitons. This is due to the fact that the electron and hole which form the exciton are pulled in opposite directions by the applied electric field, but they remain confined in the smaller bandgap material, so the exciton is not merely pulled apart by the field. The quantum-confined Stark effect is widely used for semiconductor-based optical modulators, particularly for optical fiber communications.

See also

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• Zeeman splitting

References

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• Voigt, Annalen der Physik, 69, 297 (1899), and 4, 197 (1901).
• Epstein, Annalen der Physik, 50, 489 (1916).
• Schwarzschild, Sitzber. Berliner Akad., (1916) p. 548.
• Kramers, Danske Vidensk. Selsk. Skrifter (8), III, 3, 287. (1920), and Zeitschrift fur Physik, 3. 169 (1920).
• (Chapter 17 provides a comprehensive treatment, as of 1935.)

Atomic physics | Foundational quantum physics | Physical phenomena

Stark-Effekt | Efekt Starka | Штарков ефекат