Finite-time Stückelberg interferometry with nanomechanical modes
Stückelberg interferometry describes the interference of two strongly coupled modes during a double passage through an avoided energy level crossing. In this work, we investigate finite-time effects in Stückelberg interferometry and discuss the exact analytical solution of the double passage Stückel...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2017-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/aa5a3f |
| _version_ | 1797750822225838080 |
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| author | Maximilian J Seitner Hugo Ribeiro Johannes Kölbl Thomas Faust Eva M Weig |
| author_facet | Maximilian J Seitner Hugo Ribeiro Johannes Kölbl Thomas Faust Eva M Weig |
| author_sort | Maximilian J Seitner |
| collection | DOAJ |
| description | Stückelberg interferometry describes the interference of two strongly coupled modes during a double passage through an avoided energy level crossing. In this work, we investigate finite-time effects in Stückelberg interferometry and discuss the exact analytical solution of the double passage Stückelberg problem by expanding the finite-time solution of the Landau–Zener problem. Approximating the return probability amplitudes of the double passage in distinct limits reveals uncharted parameter regimes of Stückelberg interferometry where finite-time effects affect the coherent exchange of energy. We find the long-time limit of the exact solution to formally coincide with the well-established adiabatic impulse model which is, to the best of our knowledge, the only regime of Stückelberg interferometry reported so far. Experimentally, we study all predicted regimes using a purely classical, strongly coupled nanomechanical two-mode system of high quality factor. The classical two-mode system consists of the in-plane and out-of-plane fundamental flexural mode of a high stress silicon nitride string resonator, coupled via electric gradient fields. We exploit our experimental and theoretical findings by studying the onset of Stückelberg interference in dependence of the characteristic system control parameters and obtain characteristic excitation oscillations between the two modes even without the explicit need of traversing the avoided crossing. The presented findings are not limited to classical mechanical two-mode systems but can be applied to every strongly coupled (quantum) two-level system, for example a spin-1/2 system or superconducting qubit. |
| first_indexed | 2024-03-12T16:38:27Z |
| format | Article |
| id | doaj.art-52faf44baf644132aec6ab937337f889 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:38:27Z |
| publishDate | 2017-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-52faf44baf644132aec6ab937337f8892023-08-08T14:37:45ZengIOP PublishingNew Journal of Physics1367-26302017-01-0119303301110.1088/1367-2630/aa5a3fFinite-time Stückelberg interferometry with nanomechanical modesMaximilian J Seitner0Hugo Ribeiro1Johannes Kölbl2Thomas Faust3Eva M Weig4Department of Physics, University of Konstanz , D-78457 Konstanz, Germany; Center for NanoScience (CeNS) and Fakultät für Physik, Ludwig-Maximilians-Universität , Geschwister-Scholl-Platz 1, München D-80539, GermanyDepartment of Physics, McGill University , Montreal, Quebec, H3A 2T8, CanadaDepartment of Physics, University of Konstanz , D-78457 Konstanz, GermanyCenter for NanoScience (CeNS) and Fakultät für Physik, Ludwig-Maximilians-Universität , Geschwister-Scholl-Platz 1, München D-80539, GermanyDepartment of Physics, University of Konstanz , D-78457 Konstanz, Germany; Center for NanoScience (CeNS) and Fakultät für Physik, Ludwig-Maximilians-Universität , Geschwister-Scholl-Platz 1, München D-80539, GermanyStückelberg interferometry describes the interference of two strongly coupled modes during a double passage through an avoided energy level crossing. In this work, we investigate finite-time effects in Stückelberg interferometry and discuss the exact analytical solution of the double passage Stückelberg problem by expanding the finite-time solution of the Landau–Zener problem. Approximating the return probability amplitudes of the double passage in distinct limits reveals uncharted parameter regimes of Stückelberg interferometry where finite-time effects affect the coherent exchange of energy. We find the long-time limit of the exact solution to formally coincide with the well-established adiabatic impulse model which is, to the best of our knowledge, the only regime of Stückelberg interferometry reported so far. Experimentally, we study all predicted regimes using a purely classical, strongly coupled nanomechanical two-mode system of high quality factor. The classical two-mode system consists of the in-plane and out-of-plane fundamental flexural mode of a high stress silicon nitride string resonator, coupled via electric gradient fields. We exploit our experimental and theoretical findings by studying the onset of Stückelberg interference in dependence of the characteristic system control parameters and obtain characteristic excitation oscillations between the two modes even without the explicit need of traversing the avoided crossing. The presented findings are not limited to classical mechanical two-mode systems but can be applied to every strongly coupled (quantum) two-level system, for example a spin-1/2 system or superconducting qubit.https://doi.org/10.1088/1367-2630/aa5a3fStückelberg interferometrynanoelectromechanical systemsstrong couplingfinite times |
| spellingShingle | Maximilian J Seitner Hugo Ribeiro Johannes Kölbl Thomas Faust Eva M Weig Finite-time Stückelberg interferometry with nanomechanical modes New Journal of Physics Stückelberg interferometry nanoelectromechanical systems strong coupling finite times |
| title | Finite-time Stückelberg interferometry with nanomechanical modes |
| title_full | Finite-time Stückelberg interferometry with nanomechanical modes |
| title_fullStr | Finite-time Stückelberg interferometry with nanomechanical modes |
| title_full_unstemmed | Finite-time Stückelberg interferometry with nanomechanical modes |
| title_short | Finite-time Stückelberg interferometry with nanomechanical modes |
| title_sort | finite time stuckelberg interferometry with nanomechanical modes |
| topic | Stückelberg interferometry nanoelectromechanical systems strong coupling finite times |
| url | https://doi.org/10.1088/1367-2630/aa5a3f |
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