Controlling several atoms in a cavity
We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of infinite-dimensional system algebras. Hence we address problems arisi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2014-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/16/6/065010 |
| _version_ | 1797751424562495488 |
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| author | Michael Keyl Robert Zeier Thomas Schulte-Herbrüggen |
| author_facet | Michael Keyl Robert Zeier Thomas Schulte-Herbrüggen |
| author_sort | Michael Keyl |
| collection | DOAJ |
| description | We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of infinite-dimensional system algebras. Hence we address problems arising with infinite-dimensional Lie algebras and those of unbounded operators. For the models considered, these problems can be solved by splitting the set of control Hamiltonians into two subsets: the first obeys an Abelian symmetry and can be treated in terms of infinite-dimensional Lie algebras and strongly closed subgroups of the unitary group of the system Hilbert space. The second breaks this symmetry, and its discussion introduces new arguments. Yet, full controllability can be achieved in a strong sense: e.g., in a time dependent Jaynes–Cummings model we show that, by tuning coupling constants appropriately, every unitary of the coupled system (atoms and cavity) can be approximated with arbitrarily small error. |
| first_indexed | 2024-03-12T16:49:20Z |
| format | Article |
| id | doaj.art-29f7df075b2c4cc5bceb453ec8336841 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:49:20Z |
| publishDate | 2014-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-29f7df075b2c4cc5bceb453ec83368412023-08-08T11:25:21ZengIOP PublishingNew Journal of Physics1367-26302014-01-0116606501010.1088/1367-2630/16/6/065010Controlling several atoms in a cavityMichael Keyl0Robert Zeier1Thomas Schulte-Herbrüggen2Zentrum Mathematik, M5, Technische Universität München , Boltzmannstrasse 3, D-85748 Garching, GermanyDepartment Chemie, Technische Universität München , Lichtenbergstrasse 4, D-85747 Garching, GermanyDepartment Chemie, Technische Universität München , Lichtenbergstrasse 4, D-85747 Garching, GermanyWe treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of infinite-dimensional system algebras. Hence we address problems arising with infinite-dimensional Lie algebras and those of unbounded operators. For the models considered, these problems can be solved by splitting the set of control Hamiltonians into two subsets: the first obeys an Abelian symmetry and can be treated in terms of infinite-dimensional Lie algebras and strongly closed subgroups of the unitary group of the system Hilbert space. The second breaks this symmetry, and its discussion introduces new arguments. Yet, full controllability can be achieved in a strong sense: e.g., in a time dependent Jaynes–Cummings model we show that, by tuning coupling constants appropriately, every unitary of the coupled system (atoms and cavity) can be approximated with arbitrarily small error.https://doi.org/10.1088/1367-2630/16/6/065010quantum controlcavity QEDinfinite dimensions03.67.Ac02.30.Yy42.50.Ct |
| spellingShingle | Michael Keyl Robert Zeier Thomas Schulte-Herbrüggen Controlling several atoms in a cavity New Journal of Physics quantum control cavity QED infinite dimensions 03.67.Ac 02.30.Yy 42.50.Ct |
| title | Controlling several atoms in a cavity |
| title_full | Controlling several atoms in a cavity |
| title_fullStr | Controlling several atoms in a cavity |
| title_full_unstemmed | Controlling several atoms in a cavity |
| title_short | Controlling several atoms in a cavity |
| title_sort | controlling several atoms in a cavity |
| topic | quantum control cavity QED infinite dimensions 03.67.Ac 02.30.Yy 42.50.Ct |
| url | https://doi.org/10.1088/1367-2630/16/6/065010 |
| work_keys_str_mv | AT michaelkeyl controllingseveralatomsinacavity AT robertzeier controllingseveralatomsinacavity AT thomasschulteherbruggen controllingseveralatomsinacavity |