Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols
The time evolution and the asymptotic outcome of a Landau–Zener–Stueckelberg–Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weak...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/1/013001 |
| _version_ | 1797751261851811840 |
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| author | Anna Novelli Wolfgang Belzig Abraham Nitzan |
| author_facet | Anna Novelli Wolfgang Belzig Abraham Nitzan |
| author_sort | Anna Novelli |
| collection | DOAJ |
| description | The time evolution and the asymptotic outcome of a Landau–Zener–Stueckelberg–Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly) monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabatic measurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language of measurement theory makes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the different measurement protocols. In particular, under measurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of the measured system in its initial state, but rather as an approach to equal asymptotic populations of the two diabatic states. This behavior can be traced to the way by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength. |
| first_indexed | 2024-03-12T16:45:55Z |
| format | Article |
| id | doaj.art-cd41580a768147e088b14e3fbaa131dc |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:45:55Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-cd41580a768147e088b14e3fbaa131dc2023-08-08T14:15:27ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117101300110.1088/1367-2630/17/1/013001Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocolsAnna Novelli0Wolfgang Belzig1Abraham Nitzan2Department of Physics, University of Konstanz , D-78457 Konstanz, Germany; School of Chemistry, Tel Aviv University , Tel Aviv 69978, IsraelDepartment of Physics, University of Konstanz , D-78457 Konstanz, GermanySchool of Chemistry, Tel Aviv University , Tel Aviv 69978, IsraelThe time evolution and the asymptotic outcome of a Landau–Zener–Stueckelberg–Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly) monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabatic measurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language of measurement theory makes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the different measurement protocols. In particular, under measurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of the measured system in its initial state, but rather as an approach to equal asymptotic populations of the two diabatic states. This behavior can be traced to the way by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength.https://doi.org/10.1088/1367-2630/17/1/013001quantum measurementZeno effectLandau–Zener problem |
| spellingShingle | Anna Novelli Wolfgang Belzig Abraham Nitzan Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols New Journal of Physics quantum measurement Zeno effect Landau–Zener problem |
| title | Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols |
| title_full | Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols |
| title_fullStr | Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols |
| title_full_unstemmed | Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols |
| title_short | Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols |
| title_sort | landau zener evolution under weak measurement manifestation of the zeno effect under diabatic and adiabatic measurement protocols |
| topic | quantum measurement Zeno effect Landau–Zener problem |
| url | https://doi.org/10.1088/1367-2630/17/1/013001 |
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