### 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 = ω^{2}/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.

Original language | English |
---|---|

Article number | 063036 |

Journal | New Journal of Physics |

Volume | 13 |

DOIs | |

Publication status | Published - 1 Jun 2011 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

*13*, [063036]. https://doi.org/10.1088/1367-2630/13/6/063036

**Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically.** / Lemeshko, Mikhail; Mustafa, Mustafa; Kais, Sabre; Friedrich, Bretislav.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 13, 063036. https://doi.org/10.1088/1367-2630/13/6/063036

}

TY - JOUR

T1 - Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically

AU - Lemeshko, Mikhail

AU - Mustafa, Mustafa

AU - Kais, Sabre

AU - Friedrich, Bretislav

PY - 2011/6/1

Y1 - 2011/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79959670048&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959670048&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/13/6/063036

DO - 10.1088/1367-2630/13/6/063036

M3 - Article

AN - SCOPUS:79959670048

VL - 13

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 063036

ER -