Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems
We analyze periodically modulated quantum systems with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)<...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/3/1/11 |
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| author | Isabel Sainz Andrés García Andrei B. Klimov |
| author_facet | Isabel Sainz Andrés García Andrei B. Klimov |
| author_sort | Isabel Sainz |
| collection | DOAJ |
| description | We analyze periodically modulated quantum systems with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems. In the case of a single periodically perturbed system, we propose an explicit iterative procedure for the determination of the effective interaction constants corresponding to every resonance both for weak and strong modulation. For coupled quantum systems we determine the efficient resonant transitions appearing as a result of time modulation and intrinsic non-linearities. |
| first_indexed | 2024-03-09T06:20:05Z |
| format | Article |
| id | doaj.art-bb74c234eeec425583fa44ea1eed21e8 |
| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-09T06:20:05Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj.art-bb74c234eeec425583fa44ea1eed21e82023-12-03T11:49:01ZengMDPI AGQuantum Reports2624-960X2021-02-013117319510.3390/quantum3010011Effective and Efficient Resonant Transitions in Periodically Modulated Quantum SystemsIsabel Sainz0Andrés García1Andrei B. Klimov2Departamento de Física, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, MexicoDepartamento de Matemáticas, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, MexicoDepartamento de Física, Universidad de Guadalajara, Revolución 1500, Guadalajara 44420, MexicoWe analyze periodically modulated quantum systems with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems. In the case of a single periodically perturbed system, we propose an explicit iterative procedure for the determination of the effective interaction constants corresponding to every resonance both for weak and strong modulation. For coupled quantum systems we determine the efficient resonant transitions appearing as a result of time modulation and intrinsic non-linearities.https://www.mdpi.com/2624-960X/3/1/11time dependent hamiltoniansperiodic modulationresonant interactions |
| spellingShingle | Isabel Sainz Andrés García Andrei B. Klimov Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems Quantum Reports time dependent hamiltonians periodic modulation resonant interactions |
| title | Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems |
| title_full | Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems |
| title_fullStr | Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems |
| title_full_unstemmed | Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems |
| title_short | Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems |
| title_sort | effective and efficient resonant transitions in periodically modulated quantum systems |
| topic | time dependent hamiltonians periodic modulation resonant interactions |
| url | https://www.mdpi.com/2624-960X/3/1/11 |
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