Non-Gaussianity of Four-Photon Superpositions of Fock States
We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close t...
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MDPI AG
2021-07-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/3/3/22 |
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| author | Miguel Citeli de Freitas Viktor V. Dodonov |
| author_facet | Miguel Citeli de Freitas Viktor V. Dodonov |
| author_sort | Miguel Citeli de Freitas |
| collection | DOAJ |
| description | We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function. |
| first_indexed | 2024-03-10T07:16:13Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-10T07:16:13Z |
| publishDate | 2021-07-01 |
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| series | Quantum Reports |
| spelling | doaj.art-3a6ffd1932534e95a5e26ffd8110f5d42023-11-22T15:01:49ZengMDPI AGQuantum Reports2624-960X2021-07-013335036510.3390/quantum3030022Non-Gaussianity of Four-Photon Superpositions of Fock StatesMiguel Citeli de Freitas0Viktor V. Dodonov1Institute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, BrazilInstitute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, BrazilWe study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.https://www.mdpi.com/2624-960X/3/3/22four-photon superpositionseven vacuum squeezed statesorthogonal-even coherent stateskurtosisWigner function |
| spellingShingle | Miguel Citeli de Freitas Viktor V. Dodonov Non-Gaussianity of Four-Photon Superpositions of Fock States Quantum Reports four-photon superpositions even vacuum squeezed states orthogonal-even coherent states kurtosis Wigner function |
| title | Non-Gaussianity of Four-Photon Superpositions of Fock States |
| title_full | Non-Gaussianity of Four-Photon Superpositions of Fock States |
| title_fullStr | Non-Gaussianity of Four-Photon Superpositions of Fock States |
| title_full_unstemmed | Non-Gaussianity of Four-Photon Superpositions of Fock States |
| title_short | Non-Gaussianity of Four-Photon Superpositions of Fock States |
| title_sort | non gaussianity of four photon superpositions of fock states |
| topic | four-photon superpositions even vacuum squeezed states orthogonal-even coherent states kurtosis Wigner function |
| url | https://www.mdpi.com/2624-960X/3/3/22 |
| work_keys_str_mv | AT miguelcitelidefreitas nongaussianityoffourphotonsuperpositionsoffockstates AT viktorvdodonov nongaussianityoffourphotonsuperpositionsoffockstates |