Time dependent Markovian master equation beyond the adiabatic limit
We derive a Markovian master equation that models the evolution of systems subject to driving and control fields. Our approach combines time rescaling and weak-coupling limits for the system-environment interaction with a secular approximation. The derivation makes use of the adiabatic time-evolutio...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-11-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-11-21-1534/pdf/ |
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| author | Giovanni Di Meglio Martin B. Plenio Susana F. Huelga |
| author_facet | Giovanni Di Meglio Martin B. Plenio Susana F. Huelga |
| author_sort | Giovanni Di Meglio |
| collection | DOAJ |
| description | We derive a Markovian master equation that models the evolution of systems subject to driving and control fields. Our approach combines time rescaling and weak-coupling limits for the system-environment interaction with a secular approximation. The derivation makes use of the adiabatic time-evolution operator in a manner that allows for the efficient description of strong driving, while recovering the well-known adiabatic master equation in the appropriate limit. To illustrate the effectiveness of our approach, firstly we apply it to the paradigmatic case of a two-level (qubit) system subject to a form of periodic driving that remains unsolvable using a Floquet representation and lastly we extend this scenario to the situation of two interacting qubits, the first driven while the second one directly in contact with the environment. We demonstrate the reliability and broad scope of our approach by benchmarking the solutions of the derived reduced time evolution against numerically exact simulations using tensor networks. Our results provide rigorous conditions that must be satisfied by phenomenological master equations for driven systems that do not rely on first-principles derivations. |
| format | Article |
| id | doaj-art-a7f9d09a6b584ce19e94b0ecb8c3511f |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-a7f9d09a6b584ce19e94b0ecb8c3511f2024-11-21T12:18:52ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-11-018153410.22331/q-2024-11-21-153410.22331/q-2024-11-21-1534Time dependent Markovian master equation beyond the adiabatic limitGiovanni Di MeglioMartin B. PlenioSusana F. HuelgaWe derive a Markovian master equation that models the evolution of systems subject to driving and control fields. Our approach combines time rescaling and weak-coupling limits for the system-environment interaction with a secular approximation. The derivation makes use of the adiabatic time-evolution operator in a manner that allows for the efficient description of strong driving, while recovering the well-known adiabatic master equation in the appropriate limit. To illustrate the effectiveness of our approach, firstly we apply it to the paradigmatic case of a two-level (qubit) system subject to a form of periodic driving that remains unsolvable using a Floquet representation and lastly we extend this scenario to the situation of two interacting qubits, the first driven while the second one directly in contact with the environment. We demonstrate the reliability and broad scope of our approach by benchmarking the solutions of the derived reduced time evolution against numerically exact simulations using tensor networks. Our results provide rigorous conditions that must be satisfied by phenomenological master equations for driven systems that do not rely on first-principles derivations.https://quantum-journal.org/papers/q-2024-11-21-1534/pdf/ |
| spellingShingle | Giovanni Di Meglio Martin B. Plenio Susana F. Huelga Time dependent Markovian master equation beyond the adiabatic limit Quantum |
| title | Time dependent Markovian master equation beyond the adiabatic limit |
| title_full | Time dependent Markovian master equation beyond the adiabatic limit |
| title_fullStr | Time dependent Markovian master equation beyond the adiabatic limit |
| title_full_unstemmed | Time dependent Markovian master equation beyond the adiabatic limit |
| title_short | Time dependent Markovian master equation beyond the adiabatic limit |
| title_sort | time dependent markovian master equation beyond the adiabatic limit |
| url | https://quantum-journal.org/papers/q-2024-11-21-1534/pdf/ |
| work_keys_str_mv | AT giovannidimeglio timedependentmarkovianmasterequationbeyondtheadiabaticlimit AT martinbplenio timedependentmarkovianmasterequationbeyondtheadiabaticlimit AT susanafhuelga timedependentmarkovianmasterequationbeyondtheadiabaticlimit |