Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically

Mikhail Lemeshko, Max Planck Society
Mustafa Mustafa, Birck Nanotechnology Center, Purdue University
Sabre Kais, Birck Nanotechnology Center, Purdue University
Bretislav Friedrich, Max Planck Society

Date of this Version



Mikhail Lemeshko, Mustafa Mustafa, Sabre Kais and Bretislav Friedrich. New Journal of Physics, Volume 13, June 2011


Copyright (2011) IOP Science. This article may be downloaded for personal use only. Any other use requires prior permission of the author and IOP Science. The following article appeared in New Journal of Physics and may be found at The following article has been submitted to/accepted by New Journal of Physics. Copyright (2011) Mikhail Lemeshko, Mustafa Mustafa, Sabre Kais and Bretislav Friedrich. This article is distributed under a Creative Commons Attribution 3.0 Unported License.


We made use of supersymmetric (SUSY) quantum mechanics to find the condition under which the Stark effect problem for a polar and polarizable closed-shell diatomic molecule subjected to collinear electrostatic and nonresonant radiative fields becomes exactly solvable. The condition Delta omega = omega(2)/4(m+1)(2) connects values of the dimensionless parameters omega and Delta omega that characterize the strengths of the permanent and induced dipole interactions of the molecule with the respective fields. The exact solutions are obtained for the vertical bar(J) over tilde = m, m; omega, Delta omega > family of 'stretched' states. The field-free and strong-field limits of the combined-fields problem were found to exhibit supersymmetry and shape invariance, which is indeed the reason why they are analytically solvable. By making use of the analytic form of the vertical bar(J) over tilde = m, m; omega, Delta omega > wavefunctions, we obtained simple formulae for the expectation values of the space-fixed electric dipole moment, the alignment cosine and the angular momentum squared, and derived a 'sum rule' that combines the above expectation values into a formula for the eigenenergy. The analytic expressions for the characteristics of the strongly oriented and aligned states provide direct access to the values of the interaction parameters required for creating such states in the laboratory.


Nanoscience and Nanotechnology