Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing
We consider the problem of minimization of products of mean values of the high powers of operators x and p. From this point of view, we study several two-term superpositions of the Fock states, as well as three popular families of infinite superpositions: squeezed states, even/odd coherent states, a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/9/980 |
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| author | Miguel Citeli de Freitas Vitor Dantas Meireles Viktor V. Dodonov |
| author_facet | Miguel Citeli de Freitas Vitor Dantas Meireles Viktor V. Dodonov |
| author_sort | Miguel Citeli de Freitas |
| collection | DOAJ |
| description | We consider the problem of minimization of products of mean values of the high powers of operators x and p. From this point of view, we study several two-term superpositions of the Fock states, as well as three popular families of infinite superpositions: squeezed states, even/odd coherent states, and orthogonal even coherent states (or compass states). The new element is the analysis of products of the corresponding (co)variances and the related generalized (Robertson–Schrödinger) intelligent states (RSIS). In particular, we show that both Fock and pure Gaussian homogeneous states are RSIS for the fourth powers (but not for the sixth ones). We show that lower bounds of the high-order uncertainty products can be significantly below the vacuum values. In this connection, the concept of significant and weak high-order squeezing is introduced. |
| first_indexed | 2024-03-10T16:35:43Z |
| format | Article |
| id | doaj.art-44b43a1b3ca8450cb3c53d4dfda20b8c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T16:35:43Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-44b43a1b3ca8450cb3c53d4dfda20b8c2023-11-20T12:25:33ZengMDPI AGEntropy1099-43002020-09-0122998010.3390/e22090980Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order SqueezingMiguel Citeli de Freitas0Vitor Dantas Meireles1Viktor V. Dodonov2Institute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, DF, BrazilInstitute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, DF, BrazilInstitute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, DF, BrazilWe consider the problem of minimization of products of mean values of the high powers of operators x and p. From this point of view, we study several two-term superpositions of the Fock states, as well as three popular families of infinite superpositions: squeezed states, even/odd coherent states, and orthogonal even coherent states (or compass states). The new element is the analysis of products of the corresponding (co)variances and the related generalized (Robertson–Schrödinger) intelligent states (RSIS). In particular, we show that both Fock and pure Gaussian homogeneous states are RSIS for the fourth powers (but not for the sixth ones). We show that lower bounds of the high-order uncertainty products can be significantly below the vacuum values. In this connection, the concept of significant and weak high-order squeezing is introduced.https://www.mdpi.com/1099-4300/22/9/980Fock statesGaussian stateseven/odd coherent statescompass statesgeneralized intelligent statesminimal uncertainty products |
| spellingShingle | Miguel Citeli de Freitas Vitor Dantas Meireles Viktor V. Dodonov Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing Entropy Fock states Gaussian states even/odd coherent states compass states generalized intelligent states minimal uncertainty products |
| title | Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing |
| title_full | Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing |
| title_fullStr | Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing |
| title_full_unstemmed | Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing |
| title_short | Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing |
| title_sort | minimal products of coordinate and momentum uncertainties of high orders significant and weak high order squeezing |
| topic | Fock states Gaussian states even/odd coherent states compass states generalized intelligent states minimal uncertainty products |
| url | https://www.mdpi.com/1099-4300/22/9/980 |
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