Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators
In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline&quo...
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MDPI AG
2021-10-01
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| author | Radouan Hab-arrih Ahmed Jellal Dionisis Stefanatos Abdeldjalil Merdaci |
| author_facet | Radouan Hab-arrih Ahmed Jellal Dionisis Stefanatos Abdeldjalil Merdaci |
| author_sort | Radouan Hab-arrih |
| collection | DOAJ |
| description | In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="⟨" close="⟩"><msub><mi>N</mi><mi>j</mi></msub></mfenced></semantics></math></inline-formula>) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators. |
| first_indexed | 2024-03-10T03:13:21Z |
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| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-10T03:13:21Z |
| publishDate | 2021-10-01 |
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| spelling | doaj.art-28fc4bbf4b0a4694aa0f3e617fc9359b2023-11-23T10:20:46ZengMDPI AGQuantum Reports2624-960X2021-10-013468470210.3390/quantum3040043Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum OscillatorsRadouan Hab-arrih0Ahmed Jellal1Dionisis Stefanatos2Abdeldjalil Merdaci3Laboratory of Theoretical Physics, Faculty of Sciences, Chouaïb Doukkali University, P.O. Box 20, El Jadida 24000, MoroccoLaboratory of Theoretical Physics, Faculty of Sciences, Chouaïb Doukkali University, P.O. Box 20, El Jadida 24000, MoroccoMaterials Science Department, School of Natural Sciences, University of Patras, 26504 Patras, GreeceFaculté des Sciences, Université 20 Août 1955 Skikda, BP 26, Route El-Hadaiek 21000, AlgeriaIn this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="⟨" close="⟩"><msub><mi>N</mi><mi>j</mi></msub></mfenced></semantics></math></inline-formula>) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.https://www.mdpi.com/2624-960X/3/4/43classical instability mapstime-dependent coupled oscillatorsphoton excitationsentanglementErmakov equationMeissner equation |
| spellingShingle | Radouan Hab-arrih Ahmed Jellal Dionisis Stefanatos Abdeldjalil Merdaci Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators Quantum Reports classical instability maps time-dependent coupled oscillators photon excitations entanglement Ermakov equation Meissner equation |
| title | Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators |
| title_full | Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators |
| title_fullStr | Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators |
| title_full_unstemmed | Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators |
| title_short | Instability of Meissner Differential Equation and Its Relation with Photon Excitations and Entanglement in a System of Coupled Quantum Oscillators |
| title_sort | instability of meissner differential equation and its relation with photon excitations and entanglement in a system of coupled quantum oscillators |
| topic | classical instability maps time-dependent coupled oscillators photon excitations entanglement Ermakov equation Meissner equation |
| url | https://www.mdpi.com/2624-960X/3/4/43 |
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