# Two-level systems: Exact solutions and underlying pseudo-supersymmetry

## Abstract

Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a polynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.

- Authors:

- Department of Quantum Field Theory, Tomsk State University, 36 Lenin Ave., 634050 Tomsk (Russian Federation)
- Institute of Physics, USP (Brazil). E-mail: gitman@dfn.if.usp.br

- Publication Date:

- OSTI Identifier:
- 20976755

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 5; Other Information: DOI: 10.1016/j.aop.2006.05.004; PII: S0003-4916(06)00116-3; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ELECTROMAGNETIC FIELDS; EQUATIONS; EXACT SOLUTIONS; EXCITED STATES; HAMILTONIANS; POLYNOMIALS; PROBABILITY; SPIN; SUPERSYMMETRY; TIME DEPENDENCE; TRANSFORMATIONS

### Citation Formats

```
Shamshutdinova, V.V., Samsonov, Boris F., and Gitman, D.M..
```*Two-level systems: Exact solutions and underlying pseudo-supersymmetry*. United States: N. p., 2007.
Web. doi:10.1016/j.aop.2006.05.004.

```
Shamshutdinova, V.V., Samsonov, Boris F., & Gitman, D.M..
```*Two-level systems: Exact solutions and underlying pseudo-supersymmetry*. United States. doi:10.1016/j.aop.2006.05.004.

```
Shamshutdinova, V.V., Samsonov, Boris F., and Gitman, D.M.. Tue .
"Two-level systems: Exact solutions and underlying pseudo-supersymmetry". United States.
doi:10.1016/j.aop.2006.05.004.
```

```
@article{osti_20976755,
```

title = {Two-level systems: Exact solutions and underlying pseudo-supersymmetry},

author = {Shamshutdinova, V.V. and Samsonov, Boris F. and Gitman, D.M.},

abstractNote = {Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a polynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final Hamiltonian of a chain and for solutions of the spin equation are derived. Applications are intended for a two-level atom in an electromagnetic field with a possible time-dependence of the field frequency. For a specific form of this dependence, the time oscillations of the probability to populate the excited level disappear. Under certain conditions this probability becomes a function tending monotonously to a constant value which can exceed 1/2.},

doi = {10.1016/j.aop.2006.05.004},

journal = {Annals of Physics (New York)},

number = 5,

volume = 322,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}

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