Fourmode squeezed states: twofield quantum systems and the symplectic group Sp (4 ,R )
Abstract
We construct the fourmode squeezed states and study their physical properties. These states describe two linearlycoupled quantum scalar fields, which makes them physically relevant in various contexts such as cosmology. They are shown to generalise the usual twomode squeezed states of singlefield 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 Sp (4 ,R ) and its Lie algebra, from which we construct the fourmode squeezed states and discuss their structure. We also study the reduced singlefield 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.
 Publication:

European Physical Journal C
 Pub Date:
 January 2022
 DOI:
 10.1140/epjc/s1005202109922y
 arXiv:
 arXiv:2104.14942
 Bibcode:
 2022EPJC...82....6C
 Keywords:

 Quantum Physics;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 38 pages without appendices (total 49 pages), matches published version in EPJC