Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically

M. Lemeshko, M. Mustafa, S. Kais, B. Friedrich, New Journal of Physics 13 (2011).


Journal Article | Published
Author
Lemeshko, MikhailIST Austria ; Mustafa, Mustafa K; Kais, Sabre; Friedrich, Břetislav
Abstract
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 Δω = ω2/4(m+1)2 connects values of the dimensionless parameters ω and Δω 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 \J̃ = m, m; ω, Δω) 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 \J̃ = m,m; ω, Δω) 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.
Publishing Year
Date Published
2011-06-20
Journal Title
New Journal of Physics
Acknowledgement
SK thanks the ARO for financial support
Volume
13
IST-REx-ID

Cite this

Lemeshko M, Mustafa M, Kais S, Friedrich B. Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically. New Journal of Physics. 2011;13. doi:10.1088/1367-2630/13/6/063036
Lemeshko, M., Mustafa, M., Kais, S., & Friedrich, B. (2011). Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically. New Journal of Physics, 13. https://doi.org/10.1088/1367-2630/13/6/063036
Lemeshko, Mikhail, Mustafa Mustafa, Sabre Kais, and Břetislav Friedrich. “Supersymmetry Identifies Molecular Stark States Whose Eigenproperties Can Be Obtained Analytically.” New Journal of Physics 13 (2011). https://doi.org/10.1088/1367-2630/13/6/063036.
M. Lemeshko, M. Mustafa, S. Kais, and B. Friedrich, “Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically,” New Journal of Physics, vol. 13, 2011.
Lemeshko M, Mustafa M, Kais S, Friedrich B. 2011. Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically. New Journal of Physics. 13.
Lemeshko, Mikhail, et al. “Supersymmetry Identifies Molecular Stark States Whose Eigenproperties Can Be Obtained Analytically.” New Journal of Physics, vol. 13, IOP Publishing Ltd., 2011, doi:10.1088/1367-2630/13/6/063036.
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