Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation
Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master e...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2019-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab54ac |
| _version_ | 1797750379455184896 |
|---|---|
| author | Marco Cattaneo Gian Luca Giorgi Sabrina Maniscalco Roberta Zambrini |
| author_facet | Marco Cattaneo Gian Luca Giorgi Sabrina Maniscalco Roberta Zambrini |
| author_sort | Marco Cattaneo |
| collection | DOAJ |
| description | Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born–Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach. |
| first_indexed | 2024-03-12T16:32:53Z |
| format | Article |
| id | doaj.art-d66d054a79304220801ad4340f13b19f |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:32:53Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-d66d054a79304220801ad4340f13b19f2023-08-08T15:26:04ZengIOP PublishingNew Journal of Physics1367-26302019-01-01211111304510.1088/1367-2630/ab54acLocal versus global master equation with common and separate baths: superiority of the global approach in partial secular approximationMarco Cattaneo0https://orcid.org/0000-0001-6614-5286Gian Luca Giorgi1Sabrina Maniscalco2Roberta Zambrini3Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat Illes Balears , E-07122 Palma de Mallorca, Spain; QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku , FI-20014 Turun Yliopisto, FinlandInstituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat Illes Balears , E-07122 Palma de Mallorca, SpainQTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku , FI-20014 Turun Yliopisto, Finland; QTF Centre of Excellence, Department of Applied Physics, School of Science, Aalto University , FI-00076 Aalto, FinlandInstituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat Illes Balears , E-07122 Palma de Mallorca, SpainOpen systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born–Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.https://doi.org/10.1088/1367-2630/ab54acMarkovian master equationsecular approximationcoupled qubitscommon and separate baths |
| spellingShingle | Marco Cattaneo Gian Luca Giorgi Sabrina Maniscalco Roberta Zambrini Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation New Journal of Physics Markovian master equation secular approximation coupled qubits common and separate baths |
| title | Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation |
| title_full | Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation |
| title_fullStr | Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation |
| title_full_unstemmed | Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation |
| title_short | Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation |
| title_sort | local versus global master equation with common and separate baths superiority of the global approach in partial secular approximation |
| topic | Markovian master equation secular approximation coupled qubits common and separate baths |
| url | https://doi.org/10.1088/1367-2630/ab54ac |
| work_keys_str_mv | AT marcocattaneo localversusglobalmasterequationwithcommonandseparatebathssuperiorityoftheglobalapproachinpartialsecularapproximation AT gianlucagiorgi localversusglobalmasterequationwithcommonandseparatebathssuperiorityoftheglobalapproachinpartialsecularapproximation AT sabrinamaniscalco localversusglobalmasterequationwithcommonandseparatebathssuperiorityoftheglobalapproachinpartialsecularapproximation AT robertazambrini localversusglobalmasterequationwithcommonandseparatebathssuperiorityoftheglobalapproachinpartialsecularapproximation |