dorsal/arxiv
View SchemaQuadratic pseudosupersymmetry in two-level systems
| Authors | Boris F Samsonov, V V Shamshutdinova |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0504065 |
| URL | https://arxiv.org/abs/quant-ph/0504065 |
| DOI | 10.1088/0305-4470/38/21/015 |
| Journal | J. Phys. A: Math. Gen. 38 (2005) 4715--4725 |
Abstract
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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"abstract": "Using the intertwining relation we construct a pseudosuperpartner for a\n(non-Hermitian) Dirac-like Hamiltonian describing a two-level system\ninteracting in the rotating wave approximation with the electric component of\nan electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry\ngenerators close a quadratic pseudosuperalgebra. A class of time dependent\nelectric fields for which the equation of motion for a two level system placed\nin this field can be solved exactly is obtained. New interesting phenomenon is\nobserved. There exists such a time-dependent detuning of the field frequency\nfrom the resonance value that the probability to populate the excited level\nceases to oscillate and becomes a monotonically growing function of time\ntending to 3/4. It is shown that near this fixed excitation regime the\nprobability exhibits two kinds of oscillations. The oscillations with a small\namplitude and a frequency close to the Rabi frequency (fast oscillations) take\nplace at the background of the ones with a big amplitude and a small frequency\n(slow oscillations). During the period of slow oscillations the minimal value\nof the probability to populate the excited level may exceed 1/2 suggesting for\nan ensemble of such two-level atoms the possibility to acquire the inverse\npopulation and exhibit lasing properties.",
"arxiv_id": "quant-ph/0504065",
"authors": [
"Boris F Samsonov",
"V V Shamshutdinova"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/38/21/015",
"journal_ref": "J. Phys. A: Math. Gen. 38 (2005) 4715--4725",
"title": "Quadratic pseudosupersymmetry in two-level systems",
"url": "https://arxiv.org/abs/quant-ph/0504065"
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