1
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Four-mode squeezed states: two-field quantum systems and the symplectic group \(\mathrm {Sp}(4,{\mathbb {R}})\)

      , ,
      The European Physical Journal C
      Springer Science and Business Media LLC

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We construct the four-mode squeezed states and study their physical properties. These states describe two linearly-coupled quantum scalar fields, which makes them physically relevant in various contexts such as cosmology. They are shown to generalise the usual two-mode squeezed states of single-field systems, with additional transfers of quanta between the fields. To build them in the Fock space, we use the symplectic structure of the phase space. For this reason, we first present a pedagogical analysis of the symplectic group \[\mathrm {Sp}(4,{\mathbb {R}})\] and its Lie algebra, from which we construct the four-mode squeezed states and discuss their structure. We also study the reduced single-field system obtained by tracing out one of the two fields. This procedure being easier in the phase space, it motivates the use of the Wigner function which we introduce as an alternative description of the state. It allows us to discuss environmental effects in the case of linear interactions. In particular, we find that there is always a range of interaction coupling for which decoherence occurs without substantially affecting the power spectra (hence the observables) of the system.

          Related collections

          Most cited references50

          • Record: found
          • Abstract: not found
          • Article: not found

          Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?

          W. Zurek (1981)
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            The emergence of classical properties through interaction with the environment

            E Joos, H. Zeh (1985)
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Environment-induced superselection rules

              W. Zurek (1982)
                Bookmark

                Author and article information

                Contributors
                Journal
                The European Physical Journal C
                Eur. Phys. J. C
                Springer Science and Business Media LLC
                1434-6044
                1434-6052
                January 2022
                January 05 2022
                January 2022
                : 82
                : 1
                Article
                10.1140/epjc/s10052-021-09922-y
                018fcabc-a74e-49eb-8ca1-1f530520e36c
                © 2022

                https://creativecommons.org/licenses/by/4.0

                https://creativecommons.org/licenses/by/4.0

                History

                Comments

                Comment on this article