Quadratic pseudosupersymmetry in two-level systems

Details Quadratic pseudosupersymmetry in two-level systems Quadratic pseudosupersymmetry in two-level systems

2005-04-08

arxiv.org/abs/quant-ph/0504065v1

J. Phys. A: Math. Gen. 38 (2005) 4715--4725

Physics

Quantum Physics

5 figures

Scientific paper

10.1088/0305-4470/38/21/015

Using the intertwining relation we construct a pseudosuperpartner for a (non-Hermitian) Dirac-like Hamiltonian describing a two-level system interacting in the rotating wave approximation with the electric component of an electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry generators close a quadratic pseudosuperalgebra. A class of time dependent electric fields for which the equation of motion for a two level system placed in this field can be solved exactly is obtained. New interesting phenomenon is observed. There exists such a time-dependent detuning of the field frequency from the resonance value that the probability to populate the excited level ceases to oscillate and becomes a monotonically growing function of time tending to 3/4. It is shown that near this fixed excitation regime the probability exhibits two kinds of oscillations. The oscillations with a small amplitude and a frequency close to the Rabi frequency (fast oscillations) take place at the background of the ones with a big amplitude and a small frequency (slow oscillations). During the period of slow oscillations the minimal value of the probability to populate the excited level may exceed 1/2 suggesting for an ensemble of such two-level atoms the possibility to acquire the inverse population and exhibit lasing properties.

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